| 1. |
- Kurasov, Pavel
(författare)
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On the Coulomb potential in one dimension
- 1996
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Ingår i: Journal of Physics A. - : IOP Publishing. - 0305-4470 .- 1361-6447. ; 29:8, s. 1767-1771
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Tidskriftsartikel (refereegranskat)abstract
- A mathematically rigorous definition of the one-dimensional Schrödinger operator -d2/dx2 - γ/x is given. It is proven that the domain of the operator is defined by the boundary conditions connecting the values of the function on the left and right half-axes. The investigated operator is compared with the Schrödinger operator containing the Coulomb potential -γ/|x
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| 2. |
- Brack, M., et al.
(författare)
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Uniform semiclassical trace formula for U(3) → SO(3) symmetry breaking
- 2005
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Ingår i: Journal of Physics A. - : Institute of Physics (IOP). - 0305-4470 .- 1361-6447. ; 38:46, s. 9941-9967
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Tidskriftsartikel (refereegranskat)abstract
- We develop a uniform semiclassical trace formula for the density of states of a three-dimensional isotropic harmonic oscillator (HO), perturbed by a term . This term breaks the U(3) symmetry of the HO, resulting in a spherical system with SO(3) symmetry. We first treat the anharmonic term for small ε in semiclassical perturbation theory by integration of the action of the perturbed periodic HO orbit families over the manifold which is covered by the parameters describing their four-fold degeneracy. Then, we obtain an analytical uniform trace formula for arbitrary ε which in the limit of strong perturbations (or high energy) asymptotically goes over into the correct trace formula of the full anharmonic system with SO(3) symmetry, and in the limit ε (or energy) →0 restores the HO trace formula with U(3) symmetry. We demonstrate that the gross-shell structure of this anharmonically perturbed system is dominated by the two-fold degenerate diameter and circular orbits, and not by the orbits with the largest classical degeneracy, which are the three-fold degenerate tori with rational ratios ωr:ωφ ≤ N:M of radial and angular frequencies. The same holds also for the limit of a purely quartic spherical potential V(r) ∝ r4.
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| 3. |
- Egorov, Igor
(författare)
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Time-domain Green dyadics for temporally dispersive, bi-isotropic media
- 1998
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Ingår i: Journal of Physics A: Mathematical and General. - : IOP Publishing. - 0305-4470 .- 1361-6447. ; 31:36, s. 78-7363
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Tidskriftsartikel (refereegranskat)abstract
- Time-domain Green dyadics for linear, homogeneous, temporally dispersive bi-isotropic media are presented. A complex time-dependent electromagnetic field is introduced. Approximation to the complex field from an electric point dipole in an unbounded bi-isotropic medium with respect to the slowly varying components (second forerunner approximation) is obtained. Numerical examples are presented. Surface integral equations for the tangential components of the electromagnetic fields are derived for two standard scattering problems.
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| 4. |
- Egorov, Igor, et al.
(författare)
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Time-domain Green dyadics for temporally dispersive, simple media
- 1998
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Ingår i: Journal of Physics A: Mathematical and General. - : IOP Publishing. - 0305-4470 .- 1361-6447. ; 31:14, s. 40-3219
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Tidskriftsartikel (refereegranskat)abstract
- Time-domain fundamental solutions and Green dyadics for temporally dispersive, simple media are introduced. Second forerunner approximations to the electromagnetic fields from an electric point dipole in unbounded dispersive materials are obtained. Numerical results for two frequently used material models are presented. Moreover, surface integral representations of the electromagnetic fields in dispersive media are obtained, and, finally, surface integral equations are derived for impenetrable and permeable scatterers.
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| 5. |
- Gnutzmann, S, et al.
(författare)
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Resolving isospectral 'drums' by counting nodal domains
- 2005
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Ingår i: Journal of Physics A: Mathematical and General. - : IOP Publishing. - 0305-4470 .- 1361-6447. ; 38:41, s. 8921-8933
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Tidskriftsartikel (refereegranskat)abstract
- Several types of systems have been put forward during the past few decades to show that there exist isospectral systems which are metrically different. One important class consists of Laplace-Beltrami operators for pairs of flat tori in R-n with n >= 4. We propose that the spectral ambiguity can be resolved by comparing the nodal sequences (the numbers of nodal domains of eigenfunctions, arranged by increasing eigenvalues). In the case of isospectral flat tori in four dimensions-where a four-parameter family of isospectral pairs is known-we provide heuristic arguments supported by numerical simulations to support the conjecture that the isospectrality is resolved by the nodal count. Thus one can count the shape of a drum (if it is designed as a flat torus in four dimensions).
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| 6. |
- Grönqvist, Johan, et al.
(författare)
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The k-point random matrix kernels obtained from one-point supermatrix models
- 2004
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Ingår i: Journal of Physics A: Mathematical and General. - : IOP Publishing. - 0305-4470 .- 1361-6447. ; 37:6, s. 2331-2344
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Tidskriftsartikel (refereegranskat)abstract
- The k-point correlation functions of the Gaussian random matrix ensembles are certain determinants of functions which depend on only two arguments. They are referred to as kernels, since they are the building blocks of all correlations. We show that the kernels are obtained, for arbitrary level number, directly from supermatrix models for one-point functions. More precisely, the generating functions of the one-point functions are equivalent to the kernels. This is surprising, because it implies that already the one-point generating function holds essential information about the k-point correlations. This also establishes a link to the averaged ratios of spectral determinants, i.e. of characteristic polynomials.
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| 7. |
- Guhr, Thomas, et al.
(författare)
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A supersymmetry approach to billiards with randomly distributed scatterers: II. Correlations
- 2004
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Ingår i: Journal of Physics A: Mathematical and General. - : IOP Publishing. - 0305-4470 .- 1361-6447. ; 37:6, s. 2175-2190
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Tidskriftsartikel (refereegranskat)abstract
- In a previous contribution (Stockmann H J 2002 J. Phys. A: Math. Gen. 35 5165), the density of states was calculated for a billiard with randomly distributed delta-like scatterers, doubly averaged over the positions of the impurities and the billiard shape. This result is now extended to the k-point correlation function. Using supersymmetric methods, we show that the correlations in the bulk are always identical to those of the Gaussian unitary ensemble (GUE) of random matrices. In passing from the band centre to the tail states, the density of states is depleted considerably and the two-point correlation function shows a gradual change from the GUE behaviour to that found for completely uncorrelated eigenvalues. This can be viewed as similar to a mobility edge.
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| 8. |
- Guhr, Thomas
(författare)
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Arbitrary unitarily invariant random matrix ensembles and supersymmetry
- 2006
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Ingår i: Journal of Physics A: Mathematical and General. - : IOP Publishing. - 0305-4470 .- 1361-6447. ; 39:42, s. 13191-13223
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Tidskriftsartikel (refereegranskat)abstract
- We generalize the supersymmetry method in random matrix theory to ensembles which are unitarily invariant, but otherwise arbitrary. Our exact approach extends a previous contribution in which we constructed a supersymmetric representation for the class of norm-dependent random matrix ensembles. Here, we derive a supersymmetric formulation under very general circumstances. A reduced probability density and a projector are identified that map the probability density from ordinary to superspace. Furthermore, it is demonstrated that setting up the theory in Fourier superspace has considerable advantages. General and exact expressions for the correlation functions are given. We also show how the use of hyperbolic symmetry can be circumvented in the present context in which the nonlinear sigma model is not used. We construct exact supersymmetric integral representations of the correlation functions for arbitrary positions of the imaginary increments in the Green's functions.
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| 9. |
- Guhr, Thomas
(författare)
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Norm-dependent random matrix ensembles in external field and supersymmetry
- 2006
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Ingår i: Journal of Physics A: Mathematical and General. - : IOP Publishing. - 0305-4470 .- 1361-6447. ; 39:40, s. 12327-12342
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Tidskriftsartikel (refereegranskat)abstract
- The class of norm-dependent random matrix ensembles is studied in the presence of an external field. The probability density of the ensemble depends on the trace of the squared random matrices, but is otherwise arbitrary. An exact mapping to superspace is performed. A transformation formula is derived which gives the probability density in superspace as a single integral over the probability density in ordinary space. This is done for orthogonal, unitary and symplectic symmetries. In the case of unitary symmetry, some explicit results for the correlation functions are derived.
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| 10. |
- Gustafsson, Mats
(författare)
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The Bremmer series for a multi-dimensional acoustic scattering problem
- 2000
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Ingår i: Journal of Physics A: Mathematical and General. - : IOP Publishing. - 0305-4470 .- 1361-6447. ; 33:9, s. 1921-1932
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Tidskriftsartikel (refereegranskat)abstract
- The Bremmer series is used to reduce a complex scattering problem to a sequence of simpler single-scattering problems. In the Bremmer series, the wave equation is first decomposed into a coupled system of one-way wave equations. The system is then decoupled into a sequence of one-way wave equations with a fixed-point iteration. In this paper, a left-symbol representation of the decomposition operator and the vertical-propagation operator are used. Time-domain convergence of the Bremmer series is shown for a set of dispersive medium models. The non-dispersive case is treated with an approximation procedure.
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