| 1. |
- Månsson, Teresia, 1974-
(författare)
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Is there a tower of charges to be discovered?
- 2007
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Ingår i: Journal of Physics A. - : Institute of Physics Publishing (IOPP). - 1751-8113 .- 1751-8121. ; 41, s. 194014-
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Tidskriftsartikel (refereegranskat)abstract
- We investigate higher-loop integrability for a q-deformation of the -sector of SYM theory. First we construct a generalization of the long-range spin chain, which for the lowest orders describes the non-deformed dilatation operator. This generalized model is built up from Temperley–Lieb algebra generators and describes the deformed theory to at least two loops. When constructing the model we have demanded the existence of one commuting charge, which puts strong constraints on the parameters to three-loop orders. We also write the five first charges for this model at two-loops order. Our main goal is to obtain an explicit expression for an infinite number of commuting charges, all commuting with the dilatation operator. This would imply integrability. As a step towards this goal we present in this paper an expression for a generic local charge of the one-loop dilatation operator, which happens to be a generator of the Temperley–Lieb algebra.
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| 2. |
- Kieburg, Mario, et al.
(författare)
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Arbitrary rotation invariant random matrix ensembles and supersymmetry: orthogonal and unitary-symplectic case
- 2009
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Ingår i: Journal of Physics A: Mathematical and Theoretical. - : IOP Publishing. - 1751-8113 .- 1751-8121. ; 42:27
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Tidskriftsartikel (refereegranskat)abstract
- Recently, the supersymmetry method was extended from Gaussian ensembles to arbitrary unitarily invariant matrix ensembles by generalizing the Hubbard-Stratonovich transformation. Here, we complete this extension by including arbitrary orthogonally and unitary-symplectically invariant matrix ensembles. The results are equivalent to, but the approach is different from, the superbosonization formula. We express our results in a unifying way. We also give explicit expressions for all one-point functions and discuss features of the higher order correlations.
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| 3. |
- Manninen, M., et al.
(författare)
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Electron correlation in metal clusters, quantum dots and quantum rings
- 2009
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Ingår i: Journal of Physics A: Mathematical and Theoretical. - : IOP Publishing. - 1751-8113 .- 1751-8121. ; 42:21, s. 214019-214019
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Konferensbidrag (refereegranskat)abstract
- This paper presents a few case studies of finite electron systems for which strong correlations play a dominant role. In simple metal clusters, the valence electrons determine the stability and shape of the clusters. The ionic skeleton of alkali metals is soft, and cluster geometries are often solely determined by electron correlations. In quantum dots and rings, the electrons may be confined by an external electrostatic potential formed by a gated heterostructure. In the low-density limit, the electrons may form the so-called Wigner molecules, for which the many-body quantum spectra reveal the classical vibration modes. High rotational states increase the tendency for the electrons to localize. At low angular momenta, the electrons may form a quantum Hall liquid with vortices. In this case, the vortices act as quasi-particles with long-range effective interactions that localize in a vortex molecule, in much analogy with the electron localization at strong rotation.
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| 4. |
- Marlettta, Marco, et al.
(författare)
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A Laplace operator with boundary conditions singular at one point
- 2009
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Ingår i: JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL. - : IOP Publishing. - 1751-8113 .- 1751-8121. ; 42:12
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Tidskriftsartikel (refereegranskat)abstract
- We discuss a recent paper of Berry and Dennis (J. Phys. A: Math. Theor. 2008 41 135203) concerning a Laplace operator on a smooth domain with singular boundary condition. We explain a paradox in the article (J. Phys. A: Math. Theor. 2008 41 135203) and show that if a certain additional condition is imposed, the result is a spectral problem for a self-adjoint operator having only eigenvalues and no continuous spectrum. The eigenvalues accumulate at ±∞ only, and we obtain the asymptotic behaviours of the counting functions n+(λ) and n−(λ) for positive and negative eigenvalues. The physical meaning of the additional boundary condition is not yet clear.
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| 5. |
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| 6. |
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| 7. |
- Sohl, Christian, et al.
(författare)
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Physical limitations on broadband scattering by heterogeneous obstacles
- 2007
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Ingår i: Journal of Physics A: Mathematical and Theoretical. - : IOP Publishing. - 1751-8113 .- 1751-8121. ; 40:36, s. 11165-11182
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, new physical limitations on the extinction cross section and broadband scattering are investigated. A measure of broadband scattering in terms of the integrated extinction is derived for a large class of scatterers based on the holomorphic properties of the forward scattering dyadic. Closed-form expressions of the integrated extinction are given for the homogeneous ellipsoids, and theoretical bounds are discussed for arbitrary heterogeneous scatterers. Finally, the theoretical results are illustrated by numerical computations for a series of generic scatterers
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| 8. |
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| 9. |
- Sernelius, Bo E.
(författare)
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The energy spectrum of electromagnetic normal modes in dissipative media: Modes between two metal half spaces
- 2008
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Ingår i: Journal of Physics A. - : Institutionen för fysik, kemi och biologi. - 0305-4470 .- 1361-6447. ; 41:16, s. 164016-
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Tidskriftsartikel (refereegranskat)abstract
- The energy spectrum of electromagnetic normal modes plays a central role in the theory of the van der Waals and Casimir interaction. Here we study the modes in connection with the van der Waals interaction between two metal half spaces. Neglecting dissipation leads to distinct normal modes with real-valued frequencies. Including dissipation seems to have the effect that these distinct modes move away from the real axis into the complex frequency plane. The summation of the zero-point energies of these modes render a complex-valued result. Using the contour integration, resulting from the use of the generalized argument principle, gives a real-valued and different result. We resolve this contradiction and show that the spectrum of true normal modes forms a continuum with real frequencies.
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| 10. |
- Román-Velázquez, Carlos Enrique, et al.
(författare)
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Numerical study of the effect of structure and geometry on van der Waals forces
- 2008
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Ingår i: Journal of Physics A. - : Institutionen för fysik, kemi och biologi. - 0305-4470 .- 1361-6447. ; 41:16, s. 164008-
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Tidskriftsartikel (refereegranskat)abstract
- We use multipolar expansions to find the force on a gold-coated sphere above a gold substrate; we study both an empty gold shell and a gold-coated polystyrene sphere. We find four characteristic separation ranges. In the first region, which for the empty gold shell occurs for distances, d, smaller than the thickness of the coating, the result agrees with that on a solid gold sphere and varies as d-2; for larger separations there is a region where the force behaves as if the coating is strictly two-dimensional and varies as d-5/2; in the third region the dependence is more unspecific; in the fourth region, when d is larger than the radius, the force varies as d -4. For homogeneous objects of more general shapes, we introduce a numerical method based on the solution of an integral equation for the electric field over a system of objects with arbitrary shapes. We study the effect of shape and orientation on the van der Waals interaction between an object and a substrate and between two objects.
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| 11. |
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| 12. |
- Blaszak, Maciej, et al.
(författare)
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Stackel systems generating coupled KdV hierarchies and their finite-gap and rational solutions
- 2008
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Ingår i: JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL. - : IOP Publishing. - 1751-8113 .- 1751-8121. ; 41:48
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Tidskriftsartikel (refereegranskat)abstract
- We show how to generate coupled KdV hierarchies from Stackel separable systems of Benenti type. We further show that the solutions of these Stackel systems generate a large class of finite-gap and rational solutions for cKdV hierarchies. Most of these solutions are new.
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| 13. |
- Bordag, Michael, et al.
(författare)
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Casimir force for a sphere in front of a plane beyond proximity force approximation
- 2008
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Ingår i: Journal of Physics A. - Bristol : Institute of Physics Publishing (IOPP). - 1751-8113 .- 1751-8121. ; 41:16, s. 164002-
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Tidskriftsartikel (refereegranskat)abstract
- For the configuration of a sphere in front of a plane, we calculate the first two terms of the asymptotic expansion for small separation of the Casimir force. We consider both Dirichlet and Neumann boundary conditions.
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| 14. |
- Bordag, Michael, et al.
(författare)
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The vacuum energy for two cylinders with one increasing in size
- 2009
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Ingår i: Journal of Physics A. - Bristol : Institute of Physics (IOP). - 1751-8113 .- 1751-8121. ; 42:41, s. 415203-
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Tidskriftsartikel (refereegranskat)abstract
- We consider the vacuum energy for the configuration of two cylinders and obtain its asymptotic expansion if the radius of one of these cylinders becomes large while the radius of the other one and their separation are kept fixed. We calculate explicitly the next-to-leading order correction to the vacuum energy for the radius of the other cylinder becoming large or small.
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| 15. |
- Cregg, P. J., et al.
(författare)
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Partition functions of classical Heisenberg spin chains with arbitrary and different exchange
- 2008
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Ingår i: Journal of Physics A: Mathematical and Theoretical. - : IOP Publishing. - 1751-8113 .- 1751-8121. ; 41:43, s. 435202-
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Tidskriftsartikel (refereegranskat)abstract
- The classical Heisenberg model has been effective in modelling exchange interactions in molecular magnets. In this model, the partition function is important as it allows the calculation of the magnetization and susceptibility. For an ensemble of N-spin sites, this typically involves integrals in 2N dimensions. Here, for two-, three- and four- spin nearest neighbour open linear Heisenberg chains these integrals are reduced to sums of known functions, using a result due to Gegenbauer. For the case of the three- and four- spin chains, the sums are equivalent in form to the results of Joyce. The general result for an N-spin chain is also obtained.
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| 16. |
- Garraway, B. M., et al.
(författare)
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Emergent randomness in the Jaynes-Cummings model
- 2008
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Ingår i: JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL. - : IOP Publishing. - 1751-8113 .- 1751-8121. ; 41:7, s. 075304-
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Tidskriftsartikel (refereegranskat)abstract
- We consider the well-known Jaynes-Cummings model and ask if it can display randomness. As a solvable Hamiltonian system, it does not display chaotic behaviour in the ordinary sense. Here, however, we look at the distribution of values taken up during the total time evolution. This evolution is determined by the eigenvalues distributed as the square roots of integers and leads to a seemingly erratic behaviour. That this may display a random Gaussian value distribution is suggested by an exactly provable result by Kac. In order to reach our conclusion we use the Kac model to develop tests for the emergence of a Gaussian. Even if the consequent double limits are difficult to evaluate numerically, we find definite indications that the Jaynes-Cummings case also produces a randomness in its value distributions. Numerical methods do not establish such a result beyond doubt, but our conclusions are definite enough to suggest strongly an unexpected randomness emerging in a dynamic time evolution.
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| 17. |
- Genkin, Michael, et al.
(författare)
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Description of resonance decay by Lindblad operators
- 2008
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Ingår i: Journal of Physics A: Mathematical and Theoretical. - : IOP Publishing. - 1751-8113 .- 1751-8121. ; 41:42, s. 425303-
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Tidskriftsartikel (refereegranskat)abstract
- Using an analytical model potential which contains resonant and bound states, we show that the decay of the resonances can be simulated by Lindblad operators. For that purpose, the unitary time evolution of an initial Gaussian wave packet in the model potential is compared with the non-unitary time evolution, obtained by solving the Lindblad equation, of the same wave packet in a potential which coincides with the model potential in the region of interest but does not contain resonances. In the latter case, dissipative effects are accounted for by Lindblad operators which lead to phenomenological friction and diffusion constants in the equations of motion. We suggest how those constants can be determined in a non-heuristic way, being directly connected to the width of the resonance in the model potential which we calculate using the complex rotation method.
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| 18. |
- Genkin, Michael, 1981-, et al.
(författare)
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Environmental effects on the phase space dynamics and decoherence time scale of a charged particle in a Penning trap
- 2009
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Ingår i: Journal of Physics A: Mathematical and Theoretical. - : IOP Publishing. - 1751-8113 .- 1751-8121. ; 42:38, s. 385302-
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Tidskriftsartikel (refereegranskat)abstract
- We study the time evolution of a charged particle in a Penning trap in the framework of open quantum systems. The interaction with the environment istaken into account by imposing Lindblad operators which are linear in the canonical variables. For the special case of a proton in an asymmetricPenning trap we compare the dynamics with earlier results obtained from the unitary time-dependent Schrödinger equation. A possibility to estimatethe spatial decoherence time of the system is discussed, and approximate decoherence time scales are given for different ions.
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| 19. |
- Genkin, Michael, 1981-, et al.
(författare)
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On the Penning trap coherent states
- 2009
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Ingår i: Journal of Physics A: Mathematical and Theoretical. - : IOP Publishing. - 1751-8113 .- 1751-8121. ; 42:27, s. 275305-
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Tidskriftsartikel (refereegranskat)abstract
- Recently, a class of coherent states of a particle in a Penning trap was derived byFernandez and Velazquez (J. Phys. A: Math. Theor. 42 (2009) 085304).By means of the Wigner function and density matrix associated with these states,we show that they are fully consistent with Morikawa's definition of the decoherence degree and hence they provide apossibility to directly access the decoherence process in a Penning trap.
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| 20. |
- Klimov, Andrei B., et al.
(författare)
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Geometrical approach to mutually unbiased bases
- 2007
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Ingår i: Journal of Physics a-Mathematical and Theoretical. - : IOP Publishing. - 1751-8113 .- 1751-8121. ; 40:14, s. 3987-3998
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Tidskriftsartikel (refereegranskat)abstract
- We propose a unifying phase-space approach to the construction of mutually unbiased bases for a two-qubit system. It is based on an explicit classification of the geometrical structures compatible with the notion of unbiasedness. These consist of bundles of discrete curves intersecting only at the origin and satisfying certain additional properties. We also consider the feasible transformations between different kinds of curves and show that they correspond to local rotations around the Bloch-sphere principal axes. We suggest how to generalize the method to systems in dimensions that are powers of a prime.
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| 21. |
- Lenells, Jonatan, 1981-
(författare)
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Poisson structure of a modified Hunter-Saxton equation
- 2008
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Ingår i: Journal of Physics A. - : IOP Publishing. - 1751-8113 .- 1751-8121. ; 41:28
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Tidskriftsartikel (refereegranskat)abstract
- Both the well-known Korteweg-de Vries equation and the Hunter-Saxton equation with a linear wux-term, -utxx = -2ωu x + 2uxuxx + uuxxx, ω > 0, are bi-Hamiltonian in the sense that each equation is Hamiltonian with respect to two compatible, but distinct, Poisson brackets. We present a nonlinear change of variables which maps between the two bi-Poisson structures, giving a correspondence between the infinite hierarchies of conservation laws and commuting flows associated with the equations. In particular, under this change of variables this (modified) Hunter-Saxton equation can be viewed as a member of the KdV hierarchy.
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| 22. |
- Marsh, David
(författare)
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The Grassmannian sigma model in SU(2) Yang-Mills theory
- 2007
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Ingår i: Journal of Physics A: Mathematical and Theoretical. - : IOP Publishing. - 1751-8113 .- 1751-8121. ; 40:32, s. 9919-9928
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Tidskriftsartikel (refereegranskat)abstract
- Spin–charge separation in pure SU(2) Yang–Mills theory was recently found to involve the dynamics of an O(3) nonlinear sigma model and, seemingly, a Grassmannian nonlinear sigma model. In this paper we explicitly construct the Grassmannian sigma model of the form appearing in the spin–charge separated SU(2) theory through a quaternionic decomposition of the manifold, thus verifying its relevance in this context. The coupling between this model and the O(3) nonlinear sigma model is further commented upon.
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| 23. |
- Niemi, Antti J., et al.
(författare)
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On spacetime rotation invariance, spin-charge separation and SU (2) Yang–Mills theory
- 2009
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Ingår i: Journal of Physics A. - : IOP PUBLISHING. - 0305-4470 .- 1361-6447. ; 42:32, s. 322001-
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Tidskriftsartikel (refereegranskat)abstract
- Previously, it has been shown that in a spin-charge separated SU(2) Yang– Mills theory, (Euclidean) spacetime rotation invariance can be broken by an infinitesimal 1-cocycle that appears in the S O(4) boosts. Here we study in detail the structure of this 1-cocycle. In particular, we show that its non- triviality relates to the presence of a (Dirac) magnetic monopole bundle. We also compute the finite version of the cocycle.
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| 24. |
- Praxmeyer, Ludmila, et al.
(författare)
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Characteristics of a pure-state ambiguity function
- 2009
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Ingår i: JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL. - : IOP Publishing. - 1751-8113 .- 1751-8121. ; 42:49, s. 495301-
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Tidskriftsartikel (refereegranskat)abstract
- We present the necessary and sufficient condition for a square integrable function on R-2N to be an ambiguity function corresponding to a square integrable function on R-N. This condition has the form of an integral equation. We also list some easier to check necessary conditions that must be fulfilled by a function that is an ambiguity function of a pure state. We show how to construct a wavefunction corresponding to a given ambiguity function and we present examples of how our formal results can be used in practice.
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| 25. |
- Rakityansky, S. A., et al.
(författare)
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Generalized effective-range expansion
- 2009
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Ingår i: Journal of Physics A. - : IOP Publishing. - 1751-8113 .- 1751-8121. ; 42:22, s. 225302-
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Tidskriftsartikel (refereegranskat)abstract
- A systematic and accurate procedure has been developed for calculating the coefficients phi((in/out))(ln) of the series expansion f(l)((in/out))(k) = Sigma(infinity)(n=0)(k-k(0))(n) phi((in/out))(ln) of the Jost functions in the vicinity of an arbitrary point k(0) in the complex momentum plane. This makes it possible to obtain an analytic expression for the S-matrix s(l)(k) = f(l)((out))(k)/f(l)((in))(k) around k(0) and locate its possible poles. In the particular case of l = 0 and k(0) = 0, any number of the parameters of the standard effective-range expansion k cot delta(0) = -1/a + r(0)k(2)/2 - ... are easily obtained using the corresponding coefficients phi((in/out))(ln). Numerical examples demonstrate the stability and accuracy of the proposed method.
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| 26. |
- Rakityansky, S. A., et al.
(författare)
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Pade approximation of the S-matrix as a way of locating quantum resonances and bound states
- 2007
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Ingår i: J PHYS A-MATH THEOR. - : IOP Publishing. - 1751-8113. ; 40:49, s. 14857-14869
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Tidskriftsartikel (refereegranskat)abstract
- It is shown that the spectral points (bound states and resonances) generated by a central potential of a single-channel problem, can be found using rational parametrization of the S-matrix. To achieve this, one only needs values of the S-matrix along the real positive energy axis. No calculations of the S-matrix at complex energies or a complex rotation are necessary. The proposed method is therefore universal in that it is applicable to any potential (local, non-local, discontinuous, etc) provided that there is a way of obtaining the S-matrix (or scattering phase shifts) at real collision energies. Besides this, combined with any method that extracts the phase shifts from the scattering data, the proposed rational parametrization technique would be able to do the spectral analysis using the experimental data.
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| 27. |
- Sainz, Isabel, et al.
(författare)
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Quantum phase transitions in an effective Hamiltonian : fast and slow systems
- 2008
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Ingår i: JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL. - : IOP Publishing. - 1751-8113 .- 1751-8121. ; 41:35, s. 355301-
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Tidskriftsartikel (refereegranskat)abstract
- An effective Hamiltonian describing interaction between generic fast and slow systems is obtained in the strong interaction limit. The result is applied for studying the effect of quantum phase transition as a bifurcation of the ground state of the slow subsystem. Examples such as atom-field and atom-atom interactions are analyzed in detail.
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| 28. |
- Slizovskiy, Sergey
(författare)
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Interpretation of Yang-Mills instantons in terms of locally conformal geometry
- 2008
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Ingår i: Journal Of Physics A: Mathematical And Theoretical. - : IOP Publishing. - 1751-8113 .- 1751-8121. ; 41:6, s. 065402-
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Tidskriftsartikel (refereegranskat)abstract
- BPST instanton and multi-instanton solutions to Yang-Mills equations are studied in the spin-charge separation formalism and in the related conformal gravity formalism. In the former instantons give non-trivial solutions to a gauged Grassmannian model, in the latter the instanton solution describes a locally conformally flat doubly wrapped cigar manifold or a more complicated manifold for multi-instanton solutions.
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| 29. |
- Ibragimov, Nail H., et al.
(författare)
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Linearization of fourth order ordinary differential equations by point transformations
- 2008
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Ingår i: Journal of Physics A. - : IOP Publishers. - 1751-8113 .- 1751-8121. ; 23:41, s. 206-235
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Tidskriftsartikel (refereegranskat)abstract
- A general methodology for linearization of fourth order ordinary differential equations is developed using point transformations. The solution of the problem on linearization of fourth-order equations by means of point transformations is presented here. We show that all fourth-order equations that are linearizable by point transformations are contained in the class of equations which is linear in the third-order derivative. We provide the linearization test and describe the procedure for obtaining the linearizing transformations as well as the linearized equation. For ordinary differential equations of order greater than 4 we obtain necessary conditions, which separate all linearizable equations into two classes.
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| 30. |
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| 31. |
- Ozanová, Katerina, 1977
(författare)
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Approximation by point potentials in a magnetic field
- 2006
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Ingår i: Journal of Physics A: Mathematical and General. - : IOP Publishing. - 0305-4470 .- 1361-6447 .- 1751-8113 .- 1751-8121. ; 39:12, s. 3071-3083
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Tidskriftsartikel (refereegranskat)abstract
- We discuss magnetic Schrödinger operators perturbed by measures from the generalized Kato class. Using an explicit Krein-like formula for their resolvent, we prove that these operators can be approximated in the strong resolvent sense by magnetic Schrödinger operators with point potentials. Since the spectral problem of the latter operators is solvable, one in fact gets an alternative way to calculate discrete spectra; we illustrate it by numerical calculations in the case when the potential is supported by a circle.
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| 32. |
- Zhdanov, Vladimir, 1952
(författare)
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Interplay of bistable kinetics of gene expression during cellular growth
- 2009
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Ingår i: Journal of Physics A: Mathematical and Theoretical. - 1751-8121 .- 1751-8113. ; 42:6, s. 065102-
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Tidskriftsartikel (refereegranskat)abstract
- In cells, the bistable kinetics of gene expression can be observed on the level of (i) one gene with positive feedback between protein and mRNA production, (ii) two genes with negative mutual feedback between protein and mRNA production, or (iii) in more complex cases. We analyse the interplay of two genes of type (ii) governed by a gene of type (i) during cellular growth. In particular, using kinetic Monte Carlo simulations, we show that in the case where gene 1, operating in the bistable regime, regulates mutually inhibiting genes 2 and 3, also operating in the bistable regime, the latter genes may eventually be trapped either to the state with high transcriptional activity of gene 2 and low activity of gene 3 or to the state with high transcriptional activity of gene 3 and low activity of gene 2. The probability to get to one of these states depends on the values of the model parameters. If genes 2 and 3 are kinetically equivalent, the probability is equal to 0.5. Thus, our model illustrates how different intracellular states can be chosen at random with predetermined probabilities. This type of kinetics of gene expression may be behind complex processes occurring in cells, e.g., behind the choice of the fate by stem cells.
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| 33. |
- Cregg, P J, et al.
(författare)
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Comment on 'Analytical results for a Bessel function times Legendre polynomials class integrals'
- 2007
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Ingår i: Journal of physics. A, Mathematical and theoretical. - 1751-8113. ; 40:46, s. 14029-14031
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Tidskriftsartikel (refereegranskat)abstract
- A result is obtained, stemming from Gegenbauer, where the products of certainBessel functions and exponentials are expressed in terms of an infinite seriesof spherical Bessel functions and products of associated Legendre functions.Closed form solutions for integrals involving Bessel functions times associatedLegendre functions times exponentials, recently elucidated by Neves et al(J. Phys. A: Math. Gen. 39 L293), are then shown to result directly from theorthogonality properties of the associated Legendre functions. This result offersgreater flexibility in the treatment of classical Heisenberg chains and may doso in other problems such as occur in electromagnetic diffraction theory.
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| 34. |
- Søndergaard, Niels
(författare)
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Moving frames applied to shell elasticity
- 2007
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Ingår i: Journal of Physics A: Mathematical and Theoretical. - 1751-8113. ; 40, s. 5067-5081
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Tidskriftsartikel (refereegranskat)
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| 35. |
- Tanner, Gregor, et al.
(författare)
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Wave chaos in acoustics and elasticity
- 2007
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Ingår i: Journal of Physics A: Mathematical and Theoretical. - 1751-8113. ; 40, s. 443-509
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Tidskriftsartikel (refereegranskat)
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