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

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

2.
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Recovering U(n)‐invariant toric Kähler metrics on CPn from the torus equivariant spectrum

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

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

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

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

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

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

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

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

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

We deal with kernel theorems for modulation spaces. We completely characterize the continuity of a linear operator on the modulation spaces $$M^p$$ M p for...

Time-frequency analysis | Mathematics | Abstract Harmonic Analysis | Mathematical Methods in Physics | 42B35 | Fourier Analysis | Signal,Image and Speech Processing | 47G30 | Approximations and Expansions | 81Q20 | Modulation spaces | 42C15 | Partial Differential Equations | Gabor frames | MATHEMATICS, APPLIED | CALCULUS | CONTINUITY PROPERTIES | BOUNDEDNESS | PSEUDODIFFERENTIAL-OPERATORS

Time-frequency analysis | Mathematics | Abstract Harmonic Analysis | Mathematical Methods in Physics | 42B35 | Fourier Analysis | Signal,Image and Speech Processing | 47G30 | Approximations and Expansions | 81Q20 | Modulation spaces | 42C15 | Partial Differential Equations | Gabor frames | MATHEMATICS, APPLIED | CALCULUS | CONTINUITY PROPERTIES | BOUNDEDNESS | PSEUDODIFFERENTIAL-OPERATORS

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

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

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

Numerische Mathematik, ISSN 0029-599X, 9/2017, Volume 137, Issue 1, pp. 119 - 157

The Herman–Kluk propagator is a well-known semi-classical approximation of the unitary evolution operator in quantum molecular dynamics. In this paper we...

Semi-classical approximation | 65P10 | Theoretical, Mathematical and Computational Physics | Symplectic methods | Mathematics | 65D30 | Mathematical Methods in Physics | 65Z05 | Herman–Kluk propagator | Numerical Analysis | Appl.Mathematics/Computational Methods of Engineering | Mathematics, general | 81Q20 | Numerical and Computational Physics, Simulation | Mesh-less discretisation | QUANTUM DYNAMICS | MATHEMATICS, APPLIED | Herman-Kluk propagator | HAGEDORN WAVEPACKETS | WAVE-PACKETS | CONSTANTS | SCHRODINGER-EQUATION | TIME | Molecular dynamics | Analysis

Semi-classical approximation | 65P10 | Theoretical, Mathematical and Computational Physics | Symplectic methods | Mathematics | 65D30 | Mathematical Methods in Physics | 65Z05 | Herman–Kluk propagator | Numerical Analysis | Appl.Mathematics/Computational Methods of Engineering | Mathematics, general | 81Q20 | Numerical and Computational Physics, Simulation | Mesh-less discretisation | QUANTUM DYNAMICS | MATHEMATICS, APPLIED | Herman-Kluk propagator | HAGEDORN WAVEPACKETS | WAVE-PACKETS | CONSTANTS | SCHRODINGER-EQUATION | TIME | Molecular dynamics | Analysis

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

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

15.
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Asymptotic expansion of the heat kernel trace of Laplacians with polynomial potentials

Letters in Mathematical Physics, ISSN 0377-9017, 11/2018, Volume 108, Issue 11, pp. 2453 - 2478

It is well known that the asymptotic expansion of the trace of the heat kernel for Laplace operators on smooth compact Riemannian manifolds can be obtained...

35J10 | Theoretical, Mathematical and Computational Physics | Complex Systems | Heat kernel | Semiclassical techniques | Physics | 34E05 | Geometry | Asymptotic expansion | 35K08 | Schrödinger operator | Operators in quantum field theory | Group Theory and Generalizations | 81Q20 | 81Q10 | 81Q80 | Harmonic oscillator | FORM | BOUNDARY-VALUE-PROBLEMS | PHYSICS, MATHEMATICAL | BOSE-EINSTEIN CONDENSATION | SEMIGROUPS | ULTRACONTRACTIVITY | Schrodinger operator | SCHRODINGER | PROPAGATOR

35J10 | Theoretical, Mathematical and Computational Physics | Complex Systems | Heat kernel | Semiclassical techniques | Physics | 34E05 | Geometry | Asymptotic expansion | 35K08 | Schrödinger operator | Operators in quantum field theory | Group Theory and Generalizations | 81Q20 | 81Q10 | 81Q80 | Harmonic oscillator | FORM | BOUNDARY-VALUE-PROBLEMS | PHYSICS, MATHEMATICAL | BOSE-EINSTEIN CONDENSATION | SEMIGROUPS | ULTRACONTRACTIVITY | Schrodinger operator | SCHRODINGER | PROPAGATOR

Journal Article

Journal of Nonlinear Science, ISSN 0938-8974, 4/2019, Volume 29, Issue 2, pp. 655 - 708

We give a detailed study of the symplectic geometry of a family of integrable systems obtained by coupling two angular momenta in a non-trivial way. These...

37J35 | Theoretical, Mathematical and Computational Physics | Classical Mechanics | Economic Theory/Quantitative Economics/Mathematical Methods | 53D05 | 70H06 | Semitoric systems | Mathematics | 35P20 | Semiclassical analysis | Analysis | Mathematical and Computational Engineering | 81Q20 | Integrable systems | Symplectic geometry | MATHEMATICS, APPLIED | MECHANICS | PHYSICS, MATHEMATICAL | Information management

37J35 | Theoretical, Mathematical and Computational Physics | Classical Mechanics | Economic Theory/Quantitative Economics/Mathematical Methods | 53D05 | 70H06 | Semitoric systems | Mathematics | 35P20 | Semiclassical analysis | Analysis | Mathematical and Computational Engineering | 81Q20 | Integrable systems | Symplectic geometry | MATHEMATICS, APPLIED | MECHANICS | PHYSICS, MATHEMATICAL | Information management

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

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

These notes are an expanded version of a mini-course given at the Poisson 2016 conference in Geneva. Starting from classical integrable systems in the sense of...

37J35 | Theoretical, Mathematical and Computational Physics | Complex Systems | Quantization | 53D05 | 70H06 | Physics | Classical and quantum integrable systems | Moment (um) maps | Geometry | Spectral theory | Group Theory and Generalizations | 81Q20 | MONODROMY | CONVEXITY | QUANTUM | ALGEBRAIC PROBLEM | PHYSICS, MATHEMATICAL | FOCUS-FOCUS | HAMILTONIAN-SYSTEMS | Moment (um) maps | NORMAL FORMS | MANIFOLDS | SEMIGLOBAL SYMPLECTIC INVARIANTS | Mathematics | Nonlinear Sciences | Symplectic Geometry | Spectral Theory | Exactly Solvable and Integrable Systems

37J35 | Theoretical, Mathematical and Computational Physics | Complex Systems | Quantization | 53D05 | 70H06 | Physics | Classical and quantum integrable systems | Moment (um) maps | Geometry | Spectral theory | Group Theory and Generalizations | 81Q20 | MONODROMY | CONVEXITY | QUANTUM | ALGEBRAIC PROBLEM | PHYSICS, MATHEMATICAL | FOCUS-FOCUS | HAMILTONIAN-SYSTEMS | Moment (um) maps | NORMAL FORMS | MANIFOLDS | SEMIGLOBAL SYMPLECTIC INVARIANTS | Mathematics | Nonlinear Sciences | Symplectic Geometry | Spectral Theory | Exactly Solvable and Integrable Systems

Journal Article

Journal of Statistical Physics, ISSN 0022-4715, 8/2014, Volume 156, Issue 4, pp. 707 - 738

In this paper we consider a one-dimensional non-linear Schrödinger equation with a periodic potential. In the semiclassical limit we prove the existence of...

Physical Chemistry | Theoretical, Mathematical and Computational Physics | Semiclassical approximation | Nonlinear Schrödinger and Discrete Nonlinear Schrödinger equations | Bose–Einstein condensates in periodic lattices | 35Q55 | Quantum Physics | 81Q20 | Statistical Physics, Dynamical Systems and Complexity | Physics | Bose-Einstein condensates in periodic lattices | PITAEVSKII EQUATIONS | Nonlinear Schrodinger and Discrete Nonlinear Schrodinger equations | PHYSICS, MATHEMATICAL | DISCRETE SOLITONS | LOCALIZED MODES | OPTICAL LATTICES

Physical Chemistry | Theoretical, Mathematical and Computational Physics | Semiclassical approximation | Nonlinear Schrödinger and Discrete Nonlinear Schrödinger equations | Bose–Einstein condensates in periodic lattices | 35Q55 | Quantum Physics | 81Q20 | Statistical Physics, Dynamical Systems and Complexity | Physics | Bose-Einstein condensates in periodic lattices | PITAEVSKII EQUATIONS | Nonlinear Schrodinger and Discrete Nonlinear Schrodinger equations | PHYSICS, MATHEMATICAL | DISCRETE SOLITONS | LOCALIZED MODES | OPTICAL LATTICES

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

35J10 | 35S10 | 37C25 | 81Q20 | 35P20 | 35B34 | MATHEMATICS, APPLIED | SCATTERING-AMPLITUDE | SYMBOLIC POTENTIALS | MATHEMATICS | NORMAL-FORM | ASYMPTOTICS | RESIDUE | OPERATORS | SEMICLASSICAL LIMIT

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