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1.	Abedin, Raschid, et al. (författare) Topological Lie Bialgebras, Manin Triples and Their Classification Over g[[x]] 2024 Ingår i: Communications in Mathematical Physics. - 1432-0916 .- 0010-3616. ; 405:1 Tidskriftsartikel (refereegranskat)abstract The main result of the paper is classification of topological Lie bialgebra structures on the Lie algebra g[[x]] , where g is a finite-dimensional simple Lie algebra over an algebraically closed field F of characteristic 0. We introduce the notion of a topological Manin pair (L,g[[x]]) and present their classification by relating them to trace extensions of F[[x]] . Then we recall the classification of topological doubles of Lie bialgebra structures on g[[x]] and view it as a special case of the classification of Manin pairs. The classification of topological doubles states that up to an appropriate equivalence there are only three non-trivial doubles. It is proven that topological Lie bialgebra structures on g[[x]] are in bijection with certain Lagrangian Lie subalgebras of the corresponding doubles. We then attach algebro-geometric data to such Lagrangian subalgebras and, in this way, obtain a classification of all topological Lie bialgebra structures with non-trivial doubles. For F= C the classification becomes explicit. Furthermore, this result enables us to classify formal solutions of the classical Yang–Baxter equation.
2.	Adler, Mark, et al. (författare) Tilings of Non-convex Polygons, Skew-Young Tableaux and Determinantal Processes 2018 Ingår i: Communications in Mathematical Physics. - : Springer. - 0010-3616 .- 1432-0916. ; 364:1, s. 287-342 Tidskriftsartikel (refereegranskat)abstract This paper studies random lozenge tilings of general non-convex polygonal regions. We show that the pairwise interaction of the non-convexities leads asymptotically to new kernels and thus to new statistics for the tiling fluctuations. The precise geometrical figure here consists of a hexagon with cuts along opposite edges. For this model, we take limits when the size of the hexagon and the cuts tend to infinity, while keeping certain geometric data fixed in order to guarantee sufficient interaction between the cuts in the limit. We show in this paper that the kernel for the finite tiling model can be expressed as a multiple integral, where the number of integrations is related to the fixed geometric data above. The limiting kernel is believed to be a universal master kernel.
3.	Aigner, Mats (författare) Existence of the Ginzburg-Landau vortex number 2001 Ingår i: Communications in Mathematical Physics. - : Springer Science and Business Media LLC. - 0010-3616 .- 1432-0916. ; 216:1, s. 17-22 Tidskriftsartikel (refereegranskat)abstract The existence of the Ginzburg-Landau vortex number is established for any configuration with finite action. As a consequence, Bogomol'nyi's formula for the critical action is valid for any finite action configuration.
4.	Aksteiner, Steffen, et al. (författare) Compatibility Complex for Black Hole Spacetimes 2021 Ingår i: Communications in Mathematical Physics. - : Springer Science and Business Media LLC. - 1432-0916 .- 0010-3616. ; 384:3, s. 1585-1614 Tidskriftsartikel (refereegranskat)abstract The set of local gauge invariant quantities for linearized gravity on the Kerr spacetime presented by two of the authors (Aksteiner and Bäckdahl in Phys Rev Lett 121:051104, 2018) is shown to be complete. In particular, any gauge invariant quantity for linearized gravity on Kerr that is local and of finite order in derivatives can be expressed in terms of these gauge invariants and derivatives thereof. The proof is carried out by constructing a complete compatibility complex for the Killing operator, and demonstrating the equivalence of the gauge invariants from Aksteiner and Bäckdahl (Phys Rev Lett 121:051104, 2018) with the first compatibility operator from that complex.
5.	Alberts, Tom, et al. (författare) A Dimension Spectrum for SLE Boundary Collisions 2016 Ingår i: Communications in Mathematical Physics. - : Springer-Verlag New York. - 0010-3616 .- 1432-0916. ; 343:1, s. 273-298 Tidskriftsartikel (refereegranskat)abstract We consider chordal SLE curves for , where the intersection of the curve with the boundary is a random fractal of almost sure Hausdorff dimension . We study the random sets of points at which the curve collides with the real line at a specified "angle" and compute an almost sure dimension spectrum describing the metric size of these sets. We work with the forward SLE flow and a key tool in the analysis is Girsanov's theorem, which is used to study events on which moments concentrate. The two-point correlation estimates are proved using the direct method.
6.	Alho, Artur, et al. (författare) Multi-body Spherically Symmetric Steady States of Newtonian Self-Gravitating Elastic Matter 2019 Ingår i: Communications in Mathematical Physics. - : Springer Science and Business Media LLC. - 1432-0916 .- 0010-3616. ; 371:3, s. 975-1004 Tidskriftsartikel (refereegranskat)abstract We study the problem of static, spherically symmetric, self-gravitating elastic matter distributions in Newtonian gravity. To this purpose we first introduce a new definition of homogeneous, spherically symmetric (hyper)elastic body in Euler coordinates, i.e., in terms of matter fields defined on the current physical state of the body. We show that our definition is equivalent to the classical one existing in the literature and which is given in Lagrangian coordinates, i.e. in terms of the deformation of the body from a given reference state. After a number of well-known examples of constitutive functions of elastic bodies are re-defined in our new formulation, a detailed study of the Seth model is presented. For this type of material the existence of single and multi-body solutions is established.
7.	Ameur, Yacin (författare) Repulsion in Low Temperature β-Ensembles 2018 Ingår i: Communications in Mathematical Physics. - : Springer Science and Business Media LLC. - 0010-3616 .- 1432-0916. ; 359:3, s. 1079-1089 Tidskriftsartikel (refereegranskat)abstract We prove a result on separation of particles in a two-dimensional Coulomb plasma, which holds provided that the inverse temperature (Formula presented.) satisfies (Formula presented.). For large (Formula presented.), separation is obtained at the same scale as the conjectural Abrikosov lattice optimal separation.
8.	Ameur, Yacin, et al. (författare) Szegő Type Asymptotics for the Reproducing Kernel in Spaces of Full-Plane Weighted Polynomials 2023 Ingår i: Communications in Mathematical Physics. - : Springer Science and Business Media LLC. - 0010-3616 .- 1432-0916. ; 398:3, s. 1291-1348 Tidskriftsartikel (refereegranskat)abstract Consider the subspace Wn of L2(C, dA) consisting of all weighted polynomials W(z)=P(z)·e-12nQ(z), where P(z) is a holomorphic polynomial of degree at most n- 1 , Q(z) = Q(z, z¯) is a fixed, real-valued function called the “external potential”, and dA=12πidz¯∧dz is normalized Lebesgue measure in the complex plane C. We study large n asymptotics for the reproducing kernel Kn(z, w) of Wn; this depends crucially on the position of the points z and w relative to the droplet S, i.e., the support of Frostman’s equilibrium measure in external potential Q. We mainly focus on the case when both z and w are in or near the component U of C^ \ S containing ∞, leaving aside such cases which are at this point well-understood. For the Ginibre kernel, corresponding to Q= \| z\| 2, we find an asymptotic formula after examination of classical work due to G. Szegő. Properly interpreted, the formula turns out to generalize to a large class of potentials Q(z); this is what we call “Szegő type asymptotics”. Our derivation in the general case uses the theory of approximate full-plane orthogonal polynomials instigated by Hedenmalm and Wennman, but with nontrivial additions, notably a technique involving “tail-kernel approximation” and summing by parts. In the off-diagonal case z≠ w when both z and w are on the boundary ∂U, we obtain that up to unimportant factors (cocycles) the correlations obey the asymptotic Kn(z,w)∼2πnΔQ(z)14ΔQ(w)14S(z,w)where S(z, w) is the Szegő kernel, i.e., the reproducing kernel for the Hardy space H02(U) of analytic functions on U vanishing at infinity, equipped with the norm of L2(∂U, \| dz\|). Among other things, this gives a rigorous description of the slow decay of correlations at the boundary, which was predicted by Forrester and Jancovici in 1996, in the context of elliptic Ginibre ensembles.
9.	Andersson, John, et al. (författare) Uniform Regularity Close to Cross Singularities in an Unstable Free Boundary Problem 2010 Ingår i: Communications in Mathematical Physics. - : Springer Science and Business Media LLC. - 0010-3616 .- 1432-0916. ; 296:1, s. 251-270 Tidskriftsartikel (refereegranskat)abstract We introduce a new method for the analysis of singularities in the unstable problem Delta u = chi{u> 0}, which arises in solid combustion as well as in the composite membrane problem. Our study is confined to points of "supercharacteristic" growth of the solution, i.e. points at which the solution grows faster than the characteristic/invariant scaling of the equation would suggest. At such points the classical theory is doomed to fail, due to incompatibility of the invariant scaling of the equation and the scaling of the solution. In the case of two dimensions our result shows that in a neighborhood of the set at which the second derivatives of u are unbounded, the level set {u = 0} consists of two C-1-curves meeting at right angles. It is important that our result is not confined to the minimal solution of the equation but holds for all solutions.
10.	Andersson, L., et al. (författare) Nonlinear Radiation Gauge for Near Kerr Spacetimes 2022 Ingår i: Communications in Mathematical Physics. - : Springer Science and Business Media LLC. - 0010-3616 .- 1432-0916. ; 396, s. 45-90 Tidskriftsartikel (refereegranskat)abstract In this paper, we introduce and explore the properties of a new gauge choice for the vacuum Einstein equation inspired by the ingoing and outgoing radiation gauges (IRG, ORG) for the linearized vacuum Einstein equation introduced by Chrzanowski in his work on metric reconstruction (Chrzanowski in Phys Rev D 11:2042-2062, 1975) on the Kerr background. It has been shown by Price et al. (Class Quantum Gravity 24:2367-2388, 2007) that the IRG/ORG are consistent gauges for the linearized vacuum Einstein equation on Petrov type II backgrounds. In (Andersson et al. Stability for linearized gravity on the Kerr spacetime, 2019), the ORG was used in proving linearized stability for the Kerr spacetime, and the new non-linear radiation gauge introduced here is a direct generalization of that gauge condition, and is intended to be used to study the stability of Kerr black holes under the evolution generated by the vacuum Einstein equation.
11.	Andreasson, Håkan, 1966, et al. (författare) Existence of axially symmetric static solutions of the Einstein-Vlasov system 2011 Ingår i: Commun. Math. Phys.. - : Springer Science and Business Media LLC. - 0010-3616 .- 1432-0916. ; 308, s. 23-47 Tidskriftsartikel (refereegranskat)abstract We prove the existence of static, asymptotically flat non-vacuum spacetimes with axial symmetry where the matter is modeled as a collisionless gas. The axially symmetric solutions of the resulting Einstein-Vlasov system are obtained via the implicit function theorem by perturbing off a suitable spherically symmetric steady state of the Vlasov-Poisson system.
12.	Andreasson, Håkan, 1966 (författare) On Static Shells and the Buchdahl Inequality for the Spherically Symmetric Einstein-Vlasov System 2007 Ingår i: Communications in Mathematical Physics. - : Springer Science and Business Media LLC. - 1432-0916 .- 0010-3616. ; 274, s. 409-425 Tidskriftsartikel (refereegranskat)abstract In a previous work [1] matter models such that the energy density ρ 0, and the radial- and tangential pressures p 0 and q, satisfy p + q Ωρ, Ω 1, were considered in the context of Buchdahl's inequality. It was proved that static shell solutions of the spherically symmetric Einstein equations obey a Buchdahl type inequality whenever the support of the shell, [R 0, R 1], R 0 > 0, satisfies R 1/R 0 < 1/4. Moreover, given a sequence of solutions such that R 1/R 0 → 1, then the limit supremum of 2M/R 1 was shown to be bounded by ((2Ω + 1)2 - 1)/(2Ω + 1)2. In this paper we show that the hypothesis that R 1/R 0 → 1, can be realized for Vlasov matter, by constructing a sequence of static shells of the spherically symmetric Einstein-Vlasov system with this property. We also prove that for this sequence not only the limit supremum of 2M/R 1 is bounded, but that the limit is ((2Ω + 1)2 - 1)/(2Ω + 1)2 = 8/9, since Ω = 1 for Vlasov matter. Thus, static shells of Vlasov matter can have 2M/R 1 arbitrary close to 8/9, which is interesting in view of [3], where numerical evidence is presented that 8/9 is an upper bound of 2M/R 1 of any static solution of the spherically symmetric Einstein-Vlasov system.
13.	Andreasson, Håkan, 1966 (författare) On the Buchdahl inequality for spherically symmetric static shells 2007 Ingår i: Commun. Math. Phys.. - : Springer Science and Business Media LLC. ; 274, s. 399-408 Tidskriftsartikel (refereegranskat)
14.	Andreasson, Håkan, 1966, et al. (författare) Rotating, Stationary, Axially Symmetric Spacetimes with Collisionless Matter 2014 Ingår i: Communications in Mathematical Physics. - : Springer Science and Business Media LLC. - 0010-3616 .- 1432-0916. ; 329:2, s. 787-808 Tidskriftsartikel (refereegranskat)abstract The existence of stationary solutions to the Einstein–Vlasov system which are axially symmetric and have non-zero total angular momentum is shown. This pro- vides mathematical models for rotating, general relativistic and asymptotically flat non- vacuum spacetimes. If angular momentum is allowed to be non-zero, the system of equations to solve contains one semilinear elliptic equation which is singular on the axis of rotation. This can be handled very efficiently by recasting the equation as one for an axisymmetric unknown on R 5.
15.	Andreasson, Håkan, 1966 (författare) Sharp Bounds on the Critical Stability Radius for Relativistic Charged Spheres 2009 Ingår i: COMMUNICATIONS IN MATHEMATICAL PHYSICS. - : Springer Science and Business Media LLC. - 0010-3616 .- 1432-0916. ; 288:2, s. 715-730 Tidskriftsartikel (refereegranskat)abstract In a recent paper by Giuliani and Rothman [17], the problem of finding a lower bound on the radius R of a charged sphere with mass M and charge Q < M is addressed. Such a bound is referred to as the critical stability radius. Equivalently, it can be formulated as the problem of finding an upper bound on M for given radius and charge. This problem has resulted in a number of papers in recent years but neither a transparent nor a general inequality similar to the case without charge, i.e., M ≤ 4R/9, has been found. In this paper we derive the surprisingly transparent inequality √M≤/√R3+√/R9+/Q23R. The inequality is shown to hold for any solution which satisfies p + 2pT ≤ ρ, where p ≥ 0 and pT are the radial- and tangential pressures respectively and ρ ≥ 0 is the energy density. In addition we show that the inequality is sharp, in particular we show that sharpness is attained by infinitely thin shell solutions.
16.	Arkeryd, Leif, 1940 (författare) A quantum Boltzmann equation for Haldane statistics and hard forces; the space-homogeneous initial value problem 2010 Ingår i: Communications in mathematical physics. - : Springer Science and Business Media LLC. - 0010-3616 .- 1432-0916. ; 298:2, s. 573-583 Tidskriftsartikel (refereegranskat)abstract The paper considers equations of Boltzmann type for Haldane exclusion statistics. Existence and some basic properties of the solutions are studied for the space homogeneous initial value problem with hard forces and angular cut-off. The approach uses strong L-1 compactness. Some of the technical estimates are based on L-infinity decay properties, and the control of the filling factor on range estimates for the solutions.
17.	Arkeryd, Leif, 1940, et al. (författare) Bose condensates in interaction with excitations : a kinetic model 2012 Ingår i: Communications in mathematical physics. - : Springer Science and Business Media LLC. - 0010-3616 .- 1432-0916. ; 310:3, s. 765-788 Tidskriftsartikel (refereegranskat)abstract This paper deals with mathematical questions for Bose gases below T_c.The model is of two-component type, a kinetic equation for the excitations and a Gross Pitaevskii equation for the condensate. Existence results and moment estimates are proved in the space-homogeneous isotropic case.
18.	Arnlind, Joakim, et al. (författare) Noncommutative Riemann Surfaces by Embeddings in R-3 2009 Ingår i: Communications in Mathematical Physics. - : Springer Science and Business Media LLC. - 0010-3616 .- 1432-0916. ; 288:2, s. 403-429 Tidskriftsartikel (refereegranskat)abstract We introduce C-Algebras of compact Riemann surfaces ∑ as non-commutative analogues of the Poisson algebra of smooth functions on ∑. Representations of these algebrasgive rise to sequences of matrix-algebras for which matrix-commutators converge to Poisson-brackets as N → ∞. For a particular class of surfaces, interpolating between spheres and tori, we completely characterize (even for the intermediate singular surface) all finite dimensional representations of the corresponding C-algebras.
19.	Aspenberg, Magnus, et al. (författare) Mating Non-Renormalizable Quadratic Polynomials 2009 Ingår i: Communications in Mathematical Physics. - : Springer Science and Business Media LLC. - 0010-3616 .- 1432-0916. ; 287:1, s. 1-40 Tidskriftsartikel (refereegranskat)abstract In this paper we prove the existence and uniqueness of matings of the basilica with any quadratic polynomial which lies outside of the 1/2-limb of M, is non-renormalizable, and does not have any non-repelling periodic orbits.
20.	Assaad, Wafaa, et al. (författare) The Distribution of Superconductivity Near a Magnetic Barrier 2019 Ingår i: Communications in Mathematical Physics. - : Springer Science and Business Media LLC. - 0010-3616 .- 1432-0916. ; 366:1, s. 269-332 Tidskriftsartikel (refereegranskat)abstract We consider the Ginzburg–Landau functional, defined on a two-dimensional simply connected domain with smooth boundary, in the situation when the applied magnetic field is piecewise constant with a jump discontinuity along a smooth curve. In the regime of large Ginzburg–Landau parameter and strong magnetic field, we study the concentration of the minimizing configurations along this discontinuity by computing the energy of the minimizers and their weak limit in the sense of distributions.
21.	Atai, F., et al. (författare) Super-Macdonald Polynomials: Orthogonality and Hilbert Space Interpretation 2021 Ingår i: Communications in Mathematical Physics. - : Springer Science and Business Media LLC. - 0010-3616 .- 1432-0916. ; 388:1, s. 435-468 Tidskriftsartikel (refereegranskat)abstract The super-Macdonald polynomials, introduced by Sergeev andVeselov (Commun Math Phys 288: 653-675, 2009), generalise the Macdonald polynomials to (arbitrary numbers of) two kinds of variables, and they are eigenfunctions of the deformed Macdonald-Ruijsenaars operators introduced by the same authors in Sergeev and Veselov (CommunMath Phys 245: 249-278, 2004). We introduce a Hermitian form on the algebra spanned by the super-Macdonald polynomials, prove their orthogonality, compute their (quadratic) norms explicitly, and establish a corresponding Hilbert space interpretation of the super-Macdonald polynomials and deformed MacdonaldRuijsenaars operators. This allows for a quantum mechanical interpretation of the models defined by the deformedMacdonald-Ruijsenaars operators. Motivated by recent results in the nonrelativistic (q -> 1) case, we propose that these models describe the particles and anti-particles of an underlying relativistic quantum field theory, thus providing a natural generalisation of the trigonometric Ruijsenaars model.
22.	Avelin, Benny, 1984-, et al. (författare) Geometric Characterization of the Eyring-Kramers Formula 2023 Ingår i: Communications in Mathematical Physics. - : Springer. - 0010-3616 .- 1432-0916. ; 404, s. 401-437 Tidskriftsartikel (refereegranskat)abstract In this paper we consider the mean transition time of an over-damped Brownian particle between local minima of a smooth potential. When the minima and saddles are non-degenerate this is in the low noise regime exactly characterized by the so called Eyring-Kramers law and gives the mean transition time as a quantity depending on the curvature of the minima and the saddle. In this paper we find an extension of the Eyring-Kramers law giving an upper bound on the mean transition time when both the minima/saddles are degenerate (flat) while at the same time covering multiple saddles at the same height. Our main contribution is a new sharp characterization of the capacity of two local minima as a ratio of two geometric quantities, i.e., the minimal cut and the geodesic distance.
23.	Bao, Z., et al. (författare) Local Law of Addition of Random Matrices on Optimal Scale 2017 Ingår i: Communications in Mathematical Physics. - : Springer-Verlag New York. - 0010-3616 .- 1432-0916. ; 349:3, s. 947-990 Tidskriftsartikel (refereegranskat)abstract The eigenvalue distribution of the sum of two large Hermitian matrices, when one of them is conjugated by a Haar distributed unitary matrix, is asymptotically given by the free convolution of their spectral distributions. We prove that this convergence also holds locally in the bulk of the spectrum, down to the optimal scales larger than the eigenvalue spacing. The corresponding eigenvectors are fully delocalized. Similar results hold for the sum of two real symmetric matrices, when one is conjugated by Haar orthogonal matrix.
24.	Beisert, Niklas, et al. (författare) The Algebraic Curve of Classical Superstrings on AdS_5xS^5 2006 Ingår i: Communications in Mathematical Physics. - : Springer Science and Business Media LLC. - 0010-3616 .- 1432-0916. ; 263, s. 659-710 Tidskriftsartikel (refereegranskat)abstract We investigate the monodromy of the Lax connection for classical IIB superstrings on AdS_5xS^5. For any solution of the equations of motion we derive a spectral curve of degree 4+4. The curve consists purely of conserved quantities, all gauge degrees of freedom have been eliminated in this form. The most relevant quantities of the solution, such as its energy, can be expressed through certain holomorphic integrals on the curve. This allows for a classification of finite gap solutions analogous to the general solution of strings in flat space. The role of fermions in the context of the algebraic curve is clarified. Finally, we derive a set of integral equations which reformulates the algebraic curve as a Riemann-Hilbert problem. They agree with the planar, one-loop N=4 supersymmetric gauge theory proving the complete agreement of spectra in this approximation.
25.	Berman, Robert, 1976 (författare) Determinantal Point Processes and Fermions on Complex Manifolds: Large Deviations and Bosonization 2014 Ingår i: Communications in Mathematical Physics. - : Springer Science and Business Media LLC. - 0010-3616 .- 1432-0916. ; 327:1, s. 1-47 Tidskriftsartikel (refereegranskat)abstract We study determinantal random point processes on a compact complex manifold X associated to a Hermitian metric on a line bundle over X and a probability measure on X. Physically, this setup describes a gas of free fermions on X subject to a U(1)-gauge field and when X is the Riemann sphere it specializes to various random matrix ensembles. Our general setup will also include the setting of weighted orthogonal polynomials in , as well as in . It is shown that, in the many particle limit, the empirical random measures on X converge exponentially towards the deterministic pluripotential equilibrium measure, defined in terms of the Monge-AmpSre operator of complex pluripotential theory. More precisely, a large deviation principle (LDP) is established with a good rate functional which coincides with the (normalized) pluricomplex energy of a measure recently introduced in Berman et al. (Publ Math de l'IHA parts per thousand S 117, 179-245, 2013). We also express the LDP in terms of the Ray-Singer analytic torsion. This can be seen as an effective bosonization formula, generalizing the previously known formula in the Riemann surface case to higher dimensions and the paper is concluded with a heuristic quantum field theory interpretation of the resulting effective boson-fermion correspondence.
26.	Berman, Robert, 1976 (författare) Large Deviations for Gibbs Measures with Singular Hamiltonians and Emergence of Kahler-Einstein Metrics 2017 Ingår i: Communications in Mathematical Physics. - : Springer Science and Business Media LLC. - 0010-3616 .- 1432-0916. ; 354:3, s. 1133-1172 Tidskriftsartikel (refereegranskat)abstract In the present paper and the companion paper (Berman, Kahler-Einstein metrics, canonical random point processes and birational geometry. arXiv:1307.3634, 2015) a probabilistic (statistical-mechanical) approach to the construction of canonical metrics on complex algebraic varieties X is introduced by sampling "temperature deformed" determinantal point processes. The main new ingredient is a large deviation principle for Gibbs measures with singular Hamiltonians, which is proved in the present paper. As an application we show that the unique Kahler-Einstein metric with negative Ricci curvature on a canonically polarized algebraic manifold X emerges in the many particle limit of the canonical point processes on X. In the companion paper (Berman in 2015) the extension to algebraic varieties X with positive Kodaira dimension is given and a conjectural picture relating negative temperature states to the existence problem for Kahler-Einstein metrics with positive Ricci curvature is developed.
27.	Bjerklöv, Kristian (författare) Dynamics of the quasi-periodic Schrodinger cocycle at the lowest energy in the spectrum 2007 Ingår i: Communications in Mathematical Physics. - : Springer Science and Business Media LLC. - 0010-3616 .- 1432-0916. ; 272:2, s. 397-442 Tidskriftsartikel (refereegranskat)abstract In this paper we consider the quasi-periodic Schrodinger cocycle over T-d (d >= 1) and, in particular, its projectivization. In the regime of large coupling constants and Diophantine frequencies, we give an affirmative answer to a question posed by M. Herman [21, p.482] concerning the geometric structure of certain Strange Nonchaotic Attractors which appear in the projective dynamical system. We also show that for some phase, the lowest energy in the spectrum of the associated Schrodinger operator is an eigenvalue with an exponentially decaying eigenfunction. This generalizes [39] to the multi-frequency case (d > 1).
28.	Bjerklöv, Kristian, Docent (författare) Positive Lyapunov Exponent for Some Schrödinger Cocycles Over Strongly Expanding Circle Endomorphisms 2020 Ingår i: Communications in Mathematical Physics. - : Springer Science and Business Media Deutschland GmbH. - 0010-3616 .- 1432-0916. ; 379:1, s. 353-360 Tidskriftsartikel (refereegranskat)abstract We show that for a large class of potential functions and big coupling constant λ the Schrödinger cocycle over the expanding map x↦bx(mod1) on T has a Lyapunov exponent > (log λ) / 4 for all energies, provided that the integer b≥ λ3.
29.	Bjerklöv, Kristian (författare) SNA's in the Quasi-Periodic Quadratic Family 2009 Ingår i: Communications in Mathematical Physics. - : Springer Science and Business Media LLC. - 0010-3616 .- 1432-0916. ; 286:1, s. 137-161 Tidskriftsartikel (refereegranskat)abstract We rigorously show that there can exist Strange Nonchaotic Attractors (SNA) in the quasi-periodically forced quadratic ( or logistic) map (theta, x) -> (theta + omega, c(theta)x(1 - x)) for certain choices of c : T bar right arrow [3/2, 4] and Diophantine omega.
30.	Björnberg, Jakob, 1983, et al. (författare) Dimerization in Quantum Spin Chains with O(n) Symmetry 2021 Ingår i: Communications in Mathematical Physics. - : Springer Science and Business Media LLC. - 1432-0916 .- 0010-3616. ; 387:2, s. 1151-1189 Tidskriftsartikel (refereegranskat)abstract We consider quantum spins with S >= 1, and two-body interactions with O (2S + 1) symmetry. We discuss the ground state phase diagram of the one-dimensional system. We give a rigorous proof of dimerization for an open region of the phase diagram, for S sufficiently large. We also prove the existence of a gap for excitations.
31.	Björnberg, Jakob E. (författare) Infrared Bound and Mean-Field Behaviour in the Quantum Ising Model 2013 Ingår i: Communications in Mathematical Physics. - : Springer Science and Business Media LLC. - 0010-3616 .- 1432-0916. ; 323:1, s. 329-366 Tidskriftsartikel (refereegranskat)abstract We prove an infrared bound for the transverse field Ising model. This bound is stronger than the previously known infrared bound for the model, and allows us to investigate mean-field behaviour. As an application we show that the critical exponent gamma for the susceptibility attains its mean-field value gamma = 1 in dimension at least 4 (positive temperature), respectively 3 (ground state), with logarithmic corrections in the boundary cases.
32.	Björnberg, Jakob, 1983, et al. (författare) Quantum Spins and Random Loops on the Complete Graph 2020 Ingår i: Communications in Mathematical Physics. - : Springer Science and Business Media LLC. - 0010-3616 .- 1432-0916. ; 375:3, s. 1629-63 Tidskriftsartikel (refereegranskat)abstract We present a systematic analysis of quantum Heisenberg-, xy- and interchange models on the complete graph. These models exhibit phase transitions accompanied by spontaneous symmetry breaking, which we study by calculating the generating function of expectations of powers of the averaged spin density. Various critical exponents are determined. Certain objects of the associated loop models are shown to have properties of Poisson-Dirichlet distributions.
33.	Björnberg, Jakob, 1983 (författare) Vanishing Critical Magnetization in the Quantum Ising Model 2015 Ingår i: Communications in Mathematical Physics. - : Springer Science and Business Media LLC. - 0010-3616 .- 1432-0916. ; 337:2, s. 879-907 Tidskriftsartikel (refereegranskat)abstract Adapting the recent argument of Aizenman, Duminil-Copin and Sidoravicius for the classical Ising model, it is shown here that the magnetization in the transverse-field Ising model vanishes at the critical point. The proof applies to the ground state in dimension d a parts per thousand yen 2 and to positive-temperature states in dimension d a parts per thousand yen 3, and relies on graphical representations as well as an infrared bound.
34.	Bobylev, Alexander, 1947-, et al. (författare) From Particle Systems to the Landau Equations : A Consistency Result 2013 Ingår i: Communications in Mathematical Physics. - : Springer. - 0010-3616 .- 1432-0916. ; 319:3, s. 693-702 Tidskriftsartikel (refereegranskat)abstract We consider a system of N classical particles, interacting via a smooth, short-range potential, in a weak-coupling regime. This means that N tends to infinity when the interaction is suitably rescaled. The j-particle marginals, which obey to the usual BBGKY hierarchy, are decomposed into two contributions: one small but strongly oscillating, the other hopefully smooth. Eliminating the first, we arrive to establish the dynamical problem in term of a new hierarchy (for the smooth part) involving a memory term. We show that the first order correction to the free flow converges, as N →∞, to the corresponding term associated to the Landau equation. We also show the related propagation of chaos.
35.	Bobylev, Alexander, 1947-, et al. (författare) On the Self-Similar Asymptotics for Generalized Nonlinear Kinetic Maxwell Models 2009 Ingår i: Communications in Mathematical Physics. - : Springer. - 0010-3616 .- 1432-0916. ; 291:3, s. 599-644 Tidskriftsartikel (refereegranskat)abstract Maxwell models for nonlinear kinetic equations have many applications in physics, dynamics of granular gases, economics, etc. In the present manuscript we consider such models from a very general point of view, including those with arbitrary polynomial non-linearities and in any dimension space. It is shown that the whole class of generalized Maxwell models satisfies properties one of which can be interpreted as an operator generalization of usual Lipschitz conditions. This property allows to describe in detail a behavior of solutions to the corresponding initial value problem. In particular, we prove in the most general case an existence of self similar solutions and study the convergence, in the sense of probability measures, of dynamically scaled solutions to the Cauchy problem to those self-similar solutions, as time goes to infinity. A new application of multi-linear models to economics and social dynamics is discussed
36.	Bonechi, Francesco, et al. (författare) Poisson Sigma Model on the Sphere 2009 Ingår i: Communications in Mathematical Physics. - : Springer Science and Business Media LLC. - 0010-3616 .- 1432-0916. ; 285:3, s. 1033-1063 Tidskriftsartikel (refereegranskat)abstract We evaluate the path integral of the Poisson sigma model on the sphere and study the correlators of quantum observables. We argue that for the path integral to be well-defined the corresponding Poisson structure should be unimodular. The construction of the finite dimensional BV theory is presented and we argue that it is responsible for the leading semiclassical contribution. For a (twisted) generalized Kahler manifold we discuss the gauge fixed action for the Poisson sigma model. Using the localization we prove that for the holomorphic Poisson structure the semiclassical result for the correlators is indeed the full quantum result.
37.	Borcea, Julius, et al. (författare) Root asymptotics of spectral polynomials for the Lame operator 2008 Ingår i: Communications in Mathematical Physics. - : Springer Science and Business Media LLC. - 0010-3616 .- 1432-0916. ; 282:2, s. 323-337 Tidskriftsartikel (refereegranskat)abstract The study of polynomial solutions to the classical Lamé equation in its algebraic form, or equivalently, of double-periodic solutions of its Weierstrass form has a long history. Such solutions appear at integer values of the spectral parameter and their respective eigenvalues serve as the ends of bands in the boundary value problem for the corresponding Schrödinger equation with finite gap potential given by the Weierstrass }-function on the real line. In this paper we establish several natural (and equivalent) formulas in terms of hypergeometric and elliptic type integrals for the density of the appropriately scaled asymptotic distribution of these eigenvalues when the integer-valued spectral parameter tends to infinity. We also show that this density satisfies a Heun differential equation with four singularities.
38.	Borghini, Stefano, et al. (författare) On the Mass of Static Metrics with Positive Cosmological Constant : II 2020 Ingår i: Communications in Mathematical Physics. - : Springer Nature. - 0010-3616 .- 1432-0916. ; 377:3, s. 2079-2158 Tidskriftsartikel (refereegranskat)abstract This is the second of two works, in which we discuss the definition of an appropriate notion of mass for static metrics, in the case where the cosmological constant is positive and the model solutions are compact. In the first part, we have established a positive mass statement, characterising the de Sitter solution as the only static vacuum metric with zero mass. In this second part, we prove optimal area bounds for horizons of black hole type and of cosmological type, corresponding to Riemannian Penrose inequalities and to cosmological area bounds a la Boucher-Gibbons-Horowitz, respectively. Building on the related rigidity statements, we also deduce a uniqueness result for the Schwarzschild-de Sitter spacetime.
39.	Bourgain, Jean, et al. (författare) On the distribution of free path lengths for the periodic Lorentz gas 1998 Ingår i: Comm. Math. Phys.. - : Springer Science and Business Media LLC. - 0010-3616 .- 1432-0916. ; 190:3, s. 491-508 Tidskriftsartikel (refereegranskat)
40.	Boutet de Monvel, A., et al. (författare) The Focusing NLS Equation with Step-Like Oscillating Background : Scenarios of Long-Time Asymptotics 2021 Ingår i: Communications in Mathematical Physics. - : Springer Nature. - 0010-3616 .- 1432-0916. ; 383:2, s. 893-952 Tidskriftsartikel (refereegranskat)abstract We consider the Cauchy problem for the focusing nonlinear Schrödinger equation with initial data approaching two different plane waves Ajeiϕje-2iBjx, j= 1 , 2 as x→ ± ∞. Using Riemann–Hilbert techniques and Deift–Zhou steepest descent arguments, we study the long-time asymptotics of the solution. We detect that each of the cases B1< B2, B1> B2, and B1= B2 deserves a separate analysis. Focusing mainly on the first case, the so-called shock case, we show that there is a wide range of possible asymptotic scenarios. We also propose a method for rigorously establishing the existence of certain higher-genus asymptotic sectors.
41.	Breuer, Jonathan, et al. (författare) Universality of Mesoscopic Fluctuations for Orthogonal Polynomial Ensembles 2016 Ingår i: Communications in Mathematical Physics. - : Springer. - 0010-3616 .- 1432-0916. ; 342:2, s. 491-531 Tidskriftsartikel (refereegranskat)abstract We prove that the fluctuations of mesoscopic linear statistics for orthogonal polynomial ensembles are universal in the sense that two measures with asymptotic recurrence coefficients have the same asymptotic mesoscopic fluctuations (under an additional assumption on the local regularity of one of the measures). The convergence rate of the recurrence coefficients determines the range of scales on which the limiting fluctuations are identical. Our main tool is an analysis of the Green's function for the associated Jacobi matrices. As a particular consequence we obtain a central limit theorem for the modified Jacobi Unitary Ensembles on all mesoscopic scales.
42.	Brubaker, Ben, et al. (författare) Vertex Operators, Solvable Lattice Models and Metaplectic Whittaker Functions 2020 Ingår i: Communications in Mathematical Physics. - : Springer Science and Business Media LLC. - 1432-0916 .- 0010-3616. ; 380:2, s. 535-579 Tidskriftsartikel (refereegranskat)abstract We show that spherical Whittaker functions on an n-fold cover of the general linear group arise naturally from the quantum Fock space representation of Uq(sl^ (n)) introduced by Kashiwara, Miwa and Stern (KMS). We arrive at this connection by reconsidering the solvable lattice models known as “metaplectic ice” whose partition functions are metaplectic Whittaker functions. First, we show that a certain Hecke action on metaplectic Whittaker coinvariants agrees (up to twisting) with a Hecke action of Ginzburg, Reshetikhin, and Vasserot arising in quantum affine Schur-Weyl duality. This allows us to expand the framework of KMS by Drinfeld twisting to introduce Gauss sums into the quantum wedge, which are necessary for connections to metaplectic forms. Our main theorem interprets the row transfer matrices of this ice model as “half” vertex operators on quantum Fock space that intertwine with the action of Uq(sl^ (n)). In the process, we introduce new symmetric functions termed metaplectic symmetric functions and explain how they are related to Whittaker functions on an n-fold metaplectic cover of GL r. These resemble LLT polynomials or ribbon symmetric functions introduced by Lascoux, Leclerc and Thibon, and in fact the metaplectic symmetric functions are (up to twisting) specializations of supersymmetric LLT polynomials defined by Lam. Indeed Lam constructed families of symmetric functions from Heisenberg algebra actions on the Fock space commuting with the Uq(sl^ (n)) -action. The Heisenberg algebra is independent of Drinfeld twisting of the quantum group. We explain that half vertex operators agree with Lam’s construction and this interpretation allows for many new identities for metaplectic symmetric and Whittaker functions, including Cauchy identities. While both metaplectic symmetric functions and LLT polynomials can be related to vertex operators on the quantum Fock space, only metaplectic symmetric functions are connected to solvable lattice models.
43.	Bykov, Dmitri (författare) The Geometry of Antiferromagnetic Spin Chains 2013 Ingår i: Communications in Mathematical Physics. - : Springer Science and Business Media LLC. - 0010-3616 .- 1432-0916. ; 322:3, s. 807-834 Tidskriftsartikel (refereegranskat)abstract It has been a conjecture of F.D.M.Haldane that long-wavelength excitations around antiferromagnetic vacua of certain spin chains are related to relativistic two-dimensional sigma-models. We construct a class of such spin chains and associated sigma-models, using symplectic geometry as a main tool. The target space of the sigma-model can be an arbitrary complex flag manifold, and we find universal expressions for the metric and theta-term. The derivation relies on the fact that the flag manifold is a Lagrangian submanifold in a direct product of Grassmannians associated (via geometric quantization) to the representations of spins at consecutive sites of the spin chain. The true goal is not to reach the uttermost limits, but to discover a completeness that knows no boundaries. Rabindranath Tagore.
44.	Cammarota, Valentina, et al. (författare) Boundary Effect on the Nodal Length for Arithmetic Random Waves, and Spectral Semi-correlations 2020 Ingår i: Communications in Mathematical Physics. - : Springer. - 0010-3616 .- 1432-0916. ; 376:2, s. 1261-1310 Tidskriftsartikel (refereegranskat)abstract We test M. Berry’s ansatz on nodal deficiency in presence of boundary. The square billiard is studied, where the high spectral degeneracies allow for the introduction of a Gaussian ensemble of random Laplace eigenfunctions (“boundary-adapted arithmetic random waves”). As a result of a precise asymptotic analysis, two terms in the asymptotic expansion of the expected nodal length are derived, in the high energy limit along a generic sequence of energy levels. It is found that the precise nodal deficiency or surplus of the nodal length depends on arithmetic properties of the energy levels, in an explicit way. To obtain the said results we apply the Kac–Rice method for computing the expected nodal length of a Gaussian random field. Such an application uncovers major obstacles, e.g. the occurrence of “bad” subdomains, that, one hopes, contribute insignificantly to the nodal length. Fortunately, we were able to reduce this contribution to a number theoretic question of counting the “spectral semi-correlations”, a concept joining the likes of “spectral correlations” and “spectral quasi-correlations” in having impact on the nodal length for arithmetic dynamical systems. This work rests on several breakthrough techniques of J. Bourgain, whose interest in the subject helped shaping it to high extent, and whose fundamental work on spectral correlations, joint with E. Bombieri, has had a crucial impact on the field.
45.	Cao, Yalong, et al. (författare) Gopakumar–Vafa Type Invariants of Holomorphic Symplectic 4-Folds 2024 Ingår i: Communications in Mathematical Physics. - : Springer Nature. - 0010-3616 .- 1432-0916. ; 405:2 Tidskriftsartikel (refereegranskat)abstract Using reduced Gromov–Witten theory, we define new invariants which capture the enumerative geometry of curves on holomorphic symplectic 4-folds. The invariants are analogous to the BPS counts of Gopakumar and Vafa for Calabi–Yau 3-folds, Klemm and Pandharipande for Calabi–Yau 4-folds, and Pandharipande and Zinger for Calabi–Yau 5-folds. We conjecture that our invariants are integers and give a sheaf-theoretic interpretation in terms of reduced 4-dimensional Donaldson–Thomas invariants of one-dimensional stable sheaves. We check our conjectures for the product of two K3 surfaces and for the cotangent bundle of P2 . Modulo the conjectural holomorphic anomaly equation, we compute our invariants also for the Hilbert scheme of two points on a K3 surface. This yields a conjectural formula for the number of isolated genus 2 curves of minimal degree on a very general hyperkähler 4-fold of K3 [2] -type. The formula may be viewed as a 4-dimensional analogue of the classical Yau–Zaslow formula concerning counts of rational curves on K3 surfaces. In the course of our computations, we also derive a new closed formula for the Fujiki constants of the Chern classes of tangent bundles of both Hilbert schemes of points on K3 surfaces and generalized Kummer varieties.
46.	Carey, Alan L., et al. (författare) Loop groups, anyons and the Calogero-Sutherland model 1999 Ingår i: Communications in Mathematical Physics. - : Springer Science and Business Media LLC. - 0010-3616 .- 1432-0916. ; 201, s. 1-34 Tidskriftsartikel (refereegranskat)
47.	Cassia, Luca, et al. (författare) Virasoro constraints revisited 2021 Ingår i: Communications in Mathematical Physics. - : Springer Nature. - 0010-3616 .- 1432-0916. ; 387:3, s. 1729-1755 Tidskriftsartikel (refereegranskat)abstract We revisit the Virasoro constraints and explore the relation to the Hirota bilinear equations. We furthermore investigate and provide the solution to non-homogeneous Virasoro constraints, namely those coming from matrix models whose domain of integration has boundaries. In particular, we provide the example of Hermitean matrices with positive eigenvalues in which case one can find a solution by induction on the rank of the matrix model.
48.	Cecotti, Sergio, et al. (författare) The Characteristic Dimension of Four-Dimensional $${\mathcal {N}}$$ = 2 SCFTs 2023 Ingår i: Communications in Mathematical Physics. - : Springer Nature. - 0010-3616 .- 1432-0916. ; 400:1, s. 519-540 Tidskriftsartikel (refereegranskat)abstract In this paper we introduce the characteristic dimension of a four dimensional N=2 superconformal field theory, which is an extraordinary simple invariant determined by the scaling dimensions of its Coulomb branch operators. We prove that only nine values of the characteristic dimension are allowed, −∞, 1 ,6/5, 4/3, 3/2, 2, 3, 4, and 6, thus giving a new organizing principle to the vast landscape of 4d N=2 SCFTs. Whenever the characteristic dimension differs from 1 or 2, only very constrained special Kähler geometries (i.e. isotrivial, diagonal and rigid) are compatible with the corresponding set of Coulomb branch dimensions and extremely special, maximally strongly coupled, BPS spectra are allowed for the theories which realize them. Our discussion applies to superconformal field theories of arbitrary rank, i.e. with Coulomb branches of any complex dimension. Along the way, we predict the existence of new N=3 theories of rank two with non-trivial one-form symmetries.
49.	Cederwall, Martin, et al. (författare) Canonical supermultiplets and their Koszul duals 2024 Ingår i: Communications in Mathematical Physics. - : Springer. - 0010-3616 .- 1432-0916. ; 405:5 Tidskriftsartikel (refereegranskat)abstract The pure spinor superfield formalism reveals that, in any dimension and with any amount of supersymmetry, one particular supermultiplet is distinguished from all others. This “canonical supermultiplet” is equipped with an additional structure that is not apparent in any component-field formalism: a (homotopy) commutative algebra structure on the space of fields. The structure is physically relevant in several ways; it is responsible for the interactions in ten-dimensional super Yang–Mills theory, as well as crucial to any first-quantised interpretation. We study the L∞ algebra structure that is Koszul dual to this commutative algebra, both in general and in numerous examples, and prove that it is equivalent to the subalgebra of the Koszul dual to functions on the space of generalised pure spinors in internal degree greater than or equal to three. In many examples, the latter is the positive part of a Borcherds–Kac–Moody superalgebra. Using this result, we can interpret the canonical multiplet as the homotopy fiber of the map from generalised pure spinor space to its derived replacement. This generalises and extends work of Movshev–Schwarz and Gálvez–Gorbounov–Shaikh–Tonks in the same spirit. We also comment on some issues with physical interpretations of the canonical multiplet, which are illustrated by an example related to the complex Cayley plane, and on possible extensions of our construction, which appear relevant in an example with symmetry type G2 × A1 .
50.	Cederwall, Martin, 1961, et al. (författare) L∞ Algebras for Extended Geometry from Borcherds Superalgebras 2019 Ingår i: Communications in Mathematical Physics. - : Springer Science and Business Media LLC. - 1432-0916 .- 0010-3616. ; 369:2, s. 721-760 Tidskriftsartikel (refereegranskat)abstract We examine the structure of gauge transformations in extended geometry, the framework unifying double geometry, exceptional geometry, etc. This is done by giving the variations of the ghosts in a Batalin–Vilkovisky framework, or equivalently, an L∞ algebra. The L∞ brackets are given as derived brackets constructed using an underlying Borcherds superalgebra B(gr+1) , which is a double extension of the structure algebra gr. The construction includes a set of “ancillary” ghosts. All brackets involving the infinite sequence of ghosts are given explicitly. All even brackets above the 2-brackets vanish, and the coefficients appearing in the brackets are given by Bernoulli numbers. The results are valid in the absence of ancillary transformations at ghost number 1. We present evidence that in order to go further, the underlying algebra should be the corresponding tensor hierarchy algebra.

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