| 1. |
- Kurasov, Pavel, et al.
(författare)
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AHARONOV-BOHM RING TOUCHING A QUANTUM WIRE : HOW TO MODEL IT AND TO SOLVE THE INVERSE PROBLEM
- 2011
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Ingår i: Reports on mathematical physics. - 0034-4877 .- 1879-0674. ; 68:3, s. 271-287
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Tidskriftsartikel (refereegranskat)abstract
- An explicitly solvable model of the gated Aharonov-Bohm ring touching a quantum wire is constructed and investigated. The inverse spectral and scattering problems are discussed. It is shown that the Titchmarsh-Weyl matrix function associated with the boundary vertices determines a unique electric potential on the graph even though the graph contains a loop. This system gives another family of isospectral quantum graphs.
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| 2. |
- Albeverio, S., et al.
(författare)
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Many body problems with "spin"-related contact interactions
- 2001
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Ingår i: Reports on mathematical physics. - 0034-4877 .- 1879-0674. ; 47:2, s. 157-166
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Tidskriftsartikel (refereegranskat)abstract
- We study quantum mechanical systems with "spin"-related contact interactions in one dimension. The boundary conditions describing the contact interactions are dependent on the spin states of the particles. In particular we investigate the integrability of N-body systems with δ-interactions and point spin couplings. Bethe ansatz solutions, bound states and scattering matrices are explicitly given. The cases of generalized separated boundary condition and some Hamiltonian operators corresponding to special spin related boundary conditions are also discussed.
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| 3. |
- Albeverio, Sergio, et al.
(författare)
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On *-representations of a deformation of a Wick analogue of the CAR algebra
- 2005
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Ingår i: Reports on Mathematical Physics. - 0034-4877. ; 56:2, s. 175-196-196
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Tidskriftsartikel (refereegranskat)abstract
- The classification of irreducible *-representations of deformations of canonical anti-commutation relations is given. A description of the corresponding enveloping C*-algebra is presented in terms of continuous matrix-functions satisfying certain boundary conditions.
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| 4. |
- Andersson, Ole, et al.
(författare)
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Clifford tori and unbiased vectors
- 2017
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Ingår i: Reports on mathematical physics. - : Elsevier. - 0034-4877 .- 1879-0674. ; 79:1, s. 33-51
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Tidskriftsartikel (refereegranskat)abstract
- The existence problem for mutually unbiased bases is an unsolved problem in quantum information theory. A related question is whether every pair of bases admits vectors that are unbiased to both. Mathematically this translates to the question whether two Lagrangian Clifford tori intersect, and a body of results exists concerning it. These results are however rather weak from the point of view of the first problem. We make a detailed study of how the intersections behave in the simplest nontrivial case, that of complex projective 2-space (the qutrit), for which the set of pairs of Clifford tori can be usefully parametrized by the unistochastic subset of Birkhoff's polytope. Pairs that do not intersect transversally are located. Some calculations in higher dimensions are included to see which results are special to the qutrit.
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| 5. |
- Baladi, V., et al.
(författare)
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Decay of random correlation functions for unimodal maps
- 2000
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Ingår i: Reports on mathematical physics. - 0034-4877 .- 1879-0674. ; 46:2-Jan, s. 15-26
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Tidskriftsartikel (refereegranskat)abstract
- Since the pioneering results of Jakobson and subsequent work by Benedicks-Carleson and others, it is known that quadratic maps f(a) (x) = a - x(2) admit a unique absolutely continuous invariant measure for a positive measure set of parameters a. For topologically mixing f(a), Young and Keller-Nowicki independently proved exponential decay of correlation functions for this a.c.i.m. and smooth observables. We consider random compositions of small perturbations f + omega (t), with f = f(a) or another unimodal map satisfying certain nonuniform hyperbolicity axioms, and omega (t) chosen independently and identically in [-epsilon, epsilon]. Baladi-Viana showed exponential mixing of the associated Markov chain, i.e., averaging over all random itineraries. We obtain stretched exponential bounds for the random correlation functions of Lipschitz observables for the sample measure mu (omega), of almost every itinerary.
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| 6. |
- Blaszak, Maciej, et al.
(författare)
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Deforming Lie algebras to Frobenius integrable nonautonomous Hamiltonian systems
- 2021
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Ingår i: Reports on mathematical physics. - : Elsevier. - 0034-4877 .- 1879-0674. ; 87:2, s. 249-263
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Tidskriftsartikel (refereegranskat)abstract
- Motivated by the theory of Painlevé equations and associated hierarchies, we study nonautonomous Hamiltonian systems that are Frobenius integrable. We establish sufficient conditions under which a given finite-dimensional Lie algebra of Hamiltonian vector fields can be deformed into a time-dependent Lie algebra of Frobenius integrable vector fields spanning the same distribution as the original algebra. The results are applied to quasi-Stäckel systems from [14].
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| 7. |
- Blaszak, Maciej, et al.
(författare)
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Stäckel representations of stationary Kdv systems
- 2023
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Ingår i: Reports on mathematical physics. - : PERGAMON-ELSEVIER SCIENCE LTD. - 0034-4877 .- 1879-0674. ; 92:3, s. 323-346
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Tidskriftsartikel (refereegranskat)abstract
- In this article we study Stackel representations of stationary KdV systems. Using Lax formalism we prove that these systems have two different representations as separable Stackel systems of Benenti type, related with different foliations of the stationary manifold. We do it by constructing an explicit transformation between the jet coordinates of stationary KdV systems and separation variables of the corresponding Benenti systems for arbitrary number of degrees of freedom. Moreover, on the stationary manifold, we present the explicit form of Miura map between both representations of stationary KdV systems, which also yields their bi-Hamiltonian formulation.
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| 8. |
- Bock, Wolfgang, et al.
(författare)
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Analysis of stochastic quantization for the fractional Edwards measure
- 2018
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Ingår i: Reports on mathematical physics. - : Elsevier. - 0034-4877 .- 1879-0674. ; 82:2, s. 187-202
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Tidskriftsartikel (refereegranskat)abstract
- In [10] the existence of a diffusion process whose invariant measure is the fractional polymer or Edwards measure for fractional Brownian motion in dimension d ∈ ℕ with Hurst parameter H ∈ (0, 1) fulfilling dH < 1 is shown. This Markov process is constructed via Dirichlet form techniques in infinite-dimensional (Gaussian) analysis. This article uses these results as starting point. In particular, we provide a Fukushima decomposition for the stochastic quantization of the fractional Edwards measure and prove that the constructed process solves a stochastic differential equation in infinite dimension for quasi-all starting points in a probabilistically weak sense. Moreover, the solution process is driven by an Ornstein–Uhlenbeck process taking values in an infinite-dimensional distribution space and is unique, in the sense that the underlying Dirichlet form is Markov unique. The equilibrium measure, which is by construction the fractional Edwards measure, is specified to be an extremal Gibbs state and therefore the constructed stochastic dynamics is time ergodic. The studied stochastic differential equation provides in the language of polymer physics the dynamics of the bonds, i.e. stochastically spoken the noise of the process. An integration leads then to polymer paths.
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| 9. |
- Bock, Wolfgang, et al.
(författare)
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Dynamical properties of Gaussian chains and loops with long-range interactions
- 2021
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Ingår i: Reports on mathematical physics. - : Elsevier. - 0034-4877 .- 1879-0674. ; 88:2, s. 233-246
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Tidskriftsartikel (refereegranskat)abstract
- Various authors have invoked discretized fractional Brownian motion (fBm) as a model for chain polymers with long-range interaction of monomers along the chain. We show that for these, in contrast to the Brownian case, linear forces are acting between all pairs of constituents, attractive for small Hurst index H and mostly repulsive when H is larger than 1/2. In the second part of this paper, we extend this study to periodic fBm and related models with a view to ring polymers with long range interactions.
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| 10. |
- Bock, Wolfgang, et al.
(författare)
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Fractional periodic processes : properties and an application of polymer form factors
- 2020
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Ingår i: Reports on mathematical physics. - : Elsevier. - 0034-4877 .- 1879-0674. ; 85:2, s. 267-280
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we introduce and study three classes of fractional periodic processes. An application to ring polymers is investigated. We obtain closed analytic expressions for the form factors, the Debye functions and their asymptotic decay. The relation between the end-to-halftime and radius of gyration is computed for these classes of periodic processes.
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