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Communications in Mathematical Physics, ISSN 0010-3616, 6/2009, Volume 288, Issue 3, pp. 1023 - 1059
In the mean-field limit the dynamics of a quantum Bose gas is described by a Hartree equation. We present a simple method for proving the convergence of the... 
Quantum Computing, Information and Physics | Relativity and Cosmology | Mathematical and Computational Physics | Quantum Physics | Physics | Statistical Physics | Complexity | CLASSICAL-LIMIT | EQUATIONS | CAUCHY-PROBLEM | PHYSICS, MATHEMATICAL
Journal Article
Bulletin of the London Mathematical Society, ISSN 0024-6093, 08/2017, Volume 49, Issue 4, pp. 649 - 659
In this note, we prove that toric Kähler metrics on complex projective space, which are also U(n)‐invariant, are determined by their equivariant spectrum, that... 
58J50 (primary) | 81Q20 | 53D20 (secondary) | MATHEMATICS | MANIFOLDS
Journal Article
Communications in Partial Differential Equations, ISSN 0360-5302, 02/2018, Volume 43, Issue 2, pp. 286 - 291
In this note, we consider semiclassical scattering on a manifold which is Euclidean near infinity or asymptotically hyperbolic. We show that, if the cut-off... 
35P25 | 58J50 | scattering theory | 81Q20 | Quantum resonances | 47A10 | resolvent estimates | semiclassical analysis | MATHEMATICS | MATHEMATICS, APPLIED | CHAOTIC SCATTERING | Resonance scattering
Journal Article
Mathematika, ISSN 0025-5793, 2018, Volume 64, Issue 2, pp. 406 - 429
This paper is devoted to dimensional reductions via the norm‐resolvent convergence. We derive explicit bounds on the resolvent difference as well as spectral... 
35P20 | 81Q10 | 35P05 | 81Q15 (primary) | 81Q20 (secondary) | 58J50 | LAPLACIAN | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Discrete and Continuous Dynamical Systems- Series A, ISSN 1078-0947, 08/2018, Volume 38, Issue 8, pp. 3851 - 3873
Bohr-Sommerfeld type quantization conditions of semiclassical eigenvalues for the non-selfadjoint Zakharov-Shabat operator on the unit circle are derived using... 
Eigenvalues | Transition matrix | Zakharov-Shabat system | Quantization condition | Exact WKB method | SCHRODINGER OPERATOR | MATHEMATICS | MATHEMATICS, APPLIED | eigenvalues | transition matrix | quantization condition | exact WKB method | RESONANCES | SCATTERING | Mathematics - Analysis of PDEs
Journal Article
Letters in Mathematical Physics, ISSN 0377-9017, 12/2019, Volume 109, Issue 12, pp. 2723 - 2751
Recently Ohsawa (Lett Math Phys 105:1301–1320, 2015) has studied the Marsden–Weinstein–Meyer quotient of the manifold $$T^*\mathbb {R}^n\times T^*\mathbb... 
Semiclassical mechanics | Theoretical, Mathematical and Computational Physics | Complex Systems | Gaussian wave packet | 53D20 | Dual pair | Frame bundle | Physics | Geometry | 70G65 | Symplectic reduction | Group Theory and Generalizations | 81Q20 | 81Q70
Journal Article
Communications in Contemporary Mathematics, ISSN 0219-1997, 08/2018, Volume 20, Issue 5, p. 1750055
In this paper, we aim to characterize the cylindrical Wigner measures associated to regular quantum states in the Weyl C*-algebra of canonical commutation... 
quantum field theory | Semiclassical analysis | cylindrical Wigner measures | MATHEMATICS | MATHEMATICS, APPLIED | DYNAMICS | CONVERGENCE | LIMIT
Journal Article
Mathematische Annalen, ISSN 0025-5831, 4/2016, Volume 364, Issue 3, pp. 1393 - 1413
Quantum semitoric systems form a large class of quantum Hamiltonian integrable systems with circular symmetry which has received great attention in the past... 
37J35 | 53D05 | 70H06 | Mathematics, general | Mathematics | 81Q20 | 35P20 | MATHEMATICS | QUANTIZATION | TOEPLITZ-OPERATORS | SURFACES | Sects | Physicists | Analysis | Symplectic Geometry | Spectral Theory
Journal Article
Physica D: Nonlinear Phenomena, ISSN 0167-2789, 05/2016, Volume 321-322, pp. 39 - 50
A Bose–Einstein condensate (BEC) confined in a one-dimensional lattice under the effect of an external homogeneous field is described by the Gross–Pitaevskii... 
Bloch oscillations | Bose–Einstein condensates | Gross–Pitaevskii equations | Bose-Einstein condensates | Gross-Pitaevskii equations | ATOM INTERFEROMETRY | MATHEMATICS, APPLIED | PHYSICS, MULTIDISCIPLINARY | LIGHT | CONSTANT | PHYSICS, MATHEMATICAL | Perturbation methods | Mathematical analysis | Lattices | Nonlinearity | Oscillating | Schroedinger equation | Wavefunctions
Journal Article
Journal of Fourier Analysis and Applications, ISSN 1069-5869, 2/2019, Volume 25, Issue 1, pp. 131 - 144
Journal Article
Letters in Mathematical Physics, ISSN 0377-9017, 12/2016, Volume 106, Issue 12, pp. 1695 - 1728
We define classes of quantum states associated with isotropic submanifolds of cotangent bundles. The classes are stable under the action of semiclassical... 
Geometry | Theoretical, Mathematical and Computational Physics | Complex Systems | 58J40 | Fourier integral operators on manifolds | Group Theory and Generalizations | 81Q20 | Hermite distributions | Physics | semiclassical analysis | PHYSICS, MATHEMATICAL | Atoms | Analysis
Journal Article
Annales Henri Poincaré, ISSN 1424-0637, 3/2006, Volume 7, Issue 2, pp. 303 - 333
We consider a charged particle following the boundary of a two dimensional domain because a homogeneous magnetic field is applied. We develop the basic... 
Mathematical Methods in Physics | Relativity and Cosmology | Mathematical and Computational Physics | Quantum Physics | Dynamical Systems and Ergodic Theory | Physics | Elementary Particles, Quantum Field Theory | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | PHYSICS, PARTICLES & FIELDS
Journal Article
Journal Article
Letters in Mathematical Physics, ISSN 0377-9017, 12/2016, Volume 106, Issue 12, pp. 1817 - 1835
We study small, $${{\mathcal{PT}}}$$ PT -symmetric perturbations of self-adjoint double-well Schrödinger operators in dimension $${n\ge 1}$$ n ≥ 1 . We prove... 
double well | eigenvalues | PT-symmetry | Theoretical, Mathematical and Computational Physics | Complex Systems | 35P20 | 35Q40 | Physics | Geometry | 81Q12 | Schrödinger operator | Group Theory and Generalizations | 81Q20
Journal Article
Letters in Mathematical Physics, ISSN 0377-9017, 11/2018, Volume 108, Issue 11, pp. 2453 - 2478
Journal Article
Journal of Nonlinear Science, ISSN 0938-8974, 4/2019, Volume 29, Issue 2, pp. 655 - 708
Journal Article
Duke Mathematical Journal, ISSN 0012-7094, 04/2007, Volume 137, Issue 3, pp. 381 - 459
We consider bounds on the number of semiclassical resonances in neighbourhoods of the size of the semiclassical parameter, h, around energy levels at which the... 
MATHEMATICS | ZETA-FUNCTION | NUMBER | SET | DIMENSION | POLES | TRACE FORMULA | POTENTIALS | CHAOTIC SCATTERING | QUANTUM RESONANCES | OPERATORS | 81Q20 | 35P20 | 35B34 | 35S05
Journal Article
Letters in Mathematical Physics, ISSN 0377-9017, 3/2018, Volume 108, Issue 3, pp. 499 - 571
Journal Article
Journal of Spectral Theory, ISSN 1664-039X, 2019, Volume 9, Issue 1, pp. 315 - 348
We give the semiclassical asymptotic of barrier-top resonances for Schrodinger operators on R-n, n >= 1, whose potential is C-infinity everywhere and analytic... 
35J10 | 35S10 | 37C25 | 81Q20 | 35P20 | 35B34 | MATHEMATICS, APPLIED | SCATTERING-AMPLITUDE | SYMBOLIC POTENTIALS | MATHEMATICS | NORMAL-FORM | ASYMPTOTICS | RESIDUE | OPERATORS | SEMICLASSICAL LIMIT
Journal Article
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