SCIENCE CHINA-MATHEMATICS, ISSN 1674-7283, 06/2019, Volume 62, Issue 6, pp. 1143 - 1166

We show that Mehler's formula can be used to handle several formulas involving the quantization of singular Hamiltonians. In particular, we diagonalize in the...

MATHEMATICS | MATHEMATICS, APPLIED | 46F12 | Mehler's formula | rough Hamiltonians | 81S30 | quantization

MATHEMATICS | MATHEMATICS, APPLIED | 46F12 | Mehler's formula | rough Hamiltonians | 81S30 | quantization

Journal Article

Applied and Computational Harmonic Analysis, ISSN 1063-5203, 2018, Volume 48, Issue 1, pp. 374 - 394

Gaussian states are at the heart of quantum mechanics and play an essential role in quantum information processing. In this paper we provide approximation...

Gaussians | Density matrices | Phase space frame | Weyl–Heisenberg frame | Wigner distribution

Gaussians | Density matrices | Phase space frame | Weyl–Heisenberg frame | Wigner distribution

Journal Article

Journal of Fourier Analysis and Applications, ISSN 1069-5869, 6/2019, Volume 25, Issue 3, pp. 819 - 841

We introduce and study a new class of translation–modulation invariant Banach spaces of ultradistributions. These spaces show stability under Fourier transform...

Gelfand–Shilov spaces | Mathematics | Translation-invariant Banach space | Abstract Harmonic Analysis | Ultradistributions | Mathematical Methods in Physics | Fourier Analysis | 46F12 | Signal,Image and Speech Processing | Secondary 46E10 | Approximations and Expansions | Translation–modulation invariant Banach spaces of ultradistributions | Modulation spaces | 81S30 | Primary 46F05 | Partial Differential Equations | 46H25 | Translation-modulation invariant Banach spaces of ultradistributions | MATHEMATICS, APPLIED | Gelfand-Shilov spaces | Mechanical engineering | Algebra | Mathematics - Functional Analysis

Gelfand–Shilov spaces | Mathematics | Translation-invariant Banach space | Abstract Harmonic Analysis | Ultradistributions | Mathematical Methods in Physics | Fourier Analysis | 46F12 | Signal,Image and Speech Processing | Secondary 46E10 | Approximations and Expansions | Translation–modulation invariant Banach spaces of ultradistributions | Modulation spaces | 81S30 | Primary 46F05 | Partial Differential Equations | 46H25 | Translation-modulation invariant Banach spaces of ultradistributions | MATHEMATICS, APPLIED | Gelfand-Shilov spaces | Mechanical engineering | Algebra | Mathematics - Functional Analysis

Journal Article

Communications in Partial Differential Equations, ISSN 0360-5302, 10/2017, Volume 42, Issue 10, pp. 1537 - 1548

We compute the Weyl symbol of the resolvent of the harmonic oscillator and study its properties.

33C15 | 47A10 | 81S30 | Weyl quantization | Harmonic oscillator | MATHEMATICS | MATHEMATICS, APPLIED | Oscillators

33C15 | 47A10 | 81S30 | Weyl quantization | Harmonic oscillator | MATHEMATICS | MATHEMATICS, APPLIED | Oscillators

Journal Article

Science China Mathematics, ISSN 1674-7283, 6/2019, Volume 62, Issue 6, pp. 1143 - 1166

We show that Mehler’s formula can be used to handle several formulas involving the quantization of singular Hamiltonians. In particular, we diagonalize in the...

46F12 | Mehler’s formula | Mathematics | rough Hamiltonians | Applications of Mathematics | 81S30 | quantization

46F12 | Mehler’s formula | Mathematics | rough Hamiltonians | Applications of Mathematics | 81S30 | quantization

Journal Article

2006, Progress in mathematics, ISBN 3764375570, Volume 250, x, 220

Book

Communications in Partial Differential Equations, ISSN 0360-5302, 05/2018, Volume 43, Issue 5, pp. 733 - 749

We prove a criterion for a "magnetic" Weyl operator to be trace-class by extending a method developed by Cordes, Kato and Arsu. Using the Calderon-Vaillancourt...

81V99 | 45P05 | Pseudodifferential operators | magnetic fields | 81S10 | 47B10 | Schatten-von Neumann classes | 81Q10 | 81S30 | integral operators | 35S05 | quantization | Schatten–von Neumann classes | MATHEMATICS | MATHEMATICS, APPLIED | DEFORMATION QUANTIZATION | OPERATORS | Interpolation | Criteria

81V99 | 45P05 | Pseudodifferential operators | magnetic fields | 81S10 | 47B10 | Schatten-von Neumann classes | 81Q10 | 81S30 | integral operators | 35S05 | quantization | Schatten–von Neumann classes | MATHEMATICS | MATHEMATICS, APPLIED | DEFORMATION QUANTIZATION | OPERATORS | Interpolation | Criteria

Journal Article

Frontiers of Mathematics in China, ISSN 1673-3452, 2/2019, Volume 14, Issue 1, pp. 77 - 93

A non-local abstract Cauchy problem with a singular integral is studied, which is a closed system of two evolution equations for a real-valued function and a...

47D03 | well-posedness | Partial integro-differential equation (PIDE) | 35S10 | Mathematics, general | Mathematics | singular integral | Wigner equation | 81S30 | MATHEMATICS | VELOCITY | BOUNDARY-CONDITIONS | PARITY-DECOMPOSITION | STATIONARY WIGNER EQUATION

47D03 | well-posedness | Partial integro-differential equation (PIDE) | 35S10 | Mathematics, general | Mathematics | singular integral | Wigner equation | 81S30 | MATHEMATICS | VELOCITY | BOUNDARY-CONDITIONS | PARITY-DECOMPOSITION | STATIONARY WIGNER EQUATION

Journal Article

Annales Henri Poincaré, ISSN 1424-0637, 9/2019, Volume 20, Issue 9, pp. 3163 - 3195

Compatibility conditions of quantum channels featuring symmetry through covariance are studied. Compatibility here means the possibility of obtaining two or...

Theoretical, Mathematical and Computational Physics | Quantum Physics | Physics | Elementary Particles, Quantum Field Theory | 43A35 | Primary 20C35 | 81R15 | Mathematical Methods in Physics | 81S30 | Dynamical Systems and Ergodic Theory | Classical and Quantum Gravitation, Relativity Theory | 43A07 | Secondary 20C25 | PHYSICS, MULTIDISCIPLINARY | JOINT MEASURABILITY | PHYSICS, MATHEMATICAL | PHYSICS, PARTICLES & FIELDS

Theoretical, Mathematical and Computational Physics | Quantum Physics | Physics | Elementary Particles, Quantum Field Theory | 43A35 | Primary 20C35 | 81R15 | Mathematical Methods in Physics | 81S30 | Dynamical Systems and Ergodic Theory | Classical and Quantum Gravitation, Relativity Theory | 43A07 | Secondary 20C25 | PHYSICS, MULTIDISCIPLINARY | JOINT MEASURABILITY | PHYSICS, MATHEMATICAL | PHYSICS, PARTICLES & FIELDS

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

Journal of Scientific Computing, ISSN 0885-7474, 4/2019, Volume 79, Issue 1, pp. 345 - 368

Unbounded potentials are always utilized to strictly confine quantum dynamics and generate bound or stationary states due to the existence of quantum...

Moyal expansion | Computational Mathematics and Numerical Analysis | Spectral method | Uncertainty principle | Pöschl–Teller potential | 82C10 | Theoretical, Mathematical and Computational Physics | Mathematics | Unbounded potential | 81Q05 | Algorithms | 65M70 | Mathematical and Computational Engineering | Double-well | Quantum dynamics | 45K05 | Wigner equation | 81S30 | Anharmonic oscillator | MATHEMATICS, APPLIED | QUANTUM | DYNAMICS | SYSTEMS | Poschl-Teller potential | Analysis | Quantum theory | Methods

Moyal expansion | Computational Mathematics and Numerical Analysis | Spectral method | Uncertainty principle | Pöschl–Teller potential | 82C10 | Theoretical, Mathematical and Computational Physics | Mathematics | Unbounded potential | 81Q05 | Algorithms | 65M70 | Mathematical and Computational Engineering | Double-well | Quantum dynamics | 45K05 | Wigner equation | 81S30 | Anharmonic oscillator | MATHEMATICS, APPLIED | QUANTUM | DYNAMICS | SYSTEMS | Poschl-Teller potential | Analysis | Quantum theory | Methods

Journal Article

Mediterranean Journal of Mathematics, ISSN 1660-5446, 10/2019, Volume 16, Issue 5, pp. 1 - 35

In this paper, we are interested in the Laguerre hypergroup $$\mathbb {K} = [0,\infty )\times {\mathbb {R}}$$ K=[0,∞)×R which is the fundamental manifold of...

generalized multipliers | 45P05 | 33E30 | Schatten–von Neumann class | Mathematics | generalized Landau–Pollak–Slepian operator | generalized two-wavelet multipliers | 43A32 | 42C40 | Mathematics, general | Laguerre hypergroup | 81S30 | 94A12 | 42C25 | MATHEMATICS | MATHEMATICS, APPLIED | Schatten-von Neumann class | UNCERTAINTY | generalized Landau-Pollak-Slepian operator

generalized multipliers | 45P05 | 33E30 | Schatten–von Neumann class | Mathematics | generalized Landau–Pollak–Slepian operator | generalized two-wavelet multipliers | 43A32 | 42C40 | Mathematics, general | Laguerre hypergroup | 81S30 | 94A12 | 42C25 | MATHEMATICS | MATHEMATICS, APPLIED | Schatten-von Neumann class | UNCERTAINTY | generalized Landau-Pollak-Slepian operator

Journal Article

Journal of Pseudo-Differential Operators and Applications, ISSN 1662-9981, 9/2018, Volume 9, Issue 3, pp. 469 - 486

We formulate the hypervirial and virial theorems in terms of symbols. We use the Weyl correspondence to relate symbols to operators and express the standard...

Hypervirial theorem | Mathematics | Operator Theory | Algebra | Secondary 81S30 | Functional Analysis | Weyl symbols | Analysis | Generalized phase-space distributions | Applications of Mathematics | Primary 47G30 | Partial Differential Equations | Wigner distribution | Virial theorem | MATHEMATICS | MATHEMATICS, APPLIED | OPERATORS | VIRIAL | SPACE DISTRIBUTION-FUNCTIONS

Hypervirial theorem | Mathematics | Operator Theory | Algebra | Secondary 81S30 | Functional Analysis | Weyl symbols | Analysis | Generalized phase-space distributions | Applications of Mathematics | Primary 47G30 | Partial Differential Equations | Wigner distribution | Virial theorem | MATHEMATICS | MATHEMATICS, APPLIED | OPERATORS | VIRIAL | SPACE DISTRIBUTION-FUNCTIONS

Journal Article

Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), ISSN 1815-0659, 08/2016, Volume 12

We apply the Born-Jordan and Weyl quantization formulas for polynomials in canonical coordinates to the constants of motion of some examples of the...

Born-Jordan quantization | Superintegrable systems | Weyl quantization | Extended systems | superintegrable systems | extended systems | QUANTUM-MECHANICS | PHYSICS, MATHEMATICAL

Born-Jordan quantization | Superintegrable systems | Weyl quantization | Extended systems | superintegrable systems | extended systems | QUANTUM-MECHANICS | PHYSICS, MATHEMATICAL

Journal Article

Complex Analysis and Operator Theory, ISSN 1661-8254, 4/2019, Volume 13, Issue 3, pp. 1059 - 1092

Timelimited functions and bandlimited functions play a fundamental role in signal and image processing. But by the uncertainty principles, a signal cannot be...

45P05 | Uncertainty principle | Localization operator | Mathematics | Operator Theory | 42C40 | Analysis | Multiplier | Nash inequality | Mathematics, general | Carlson inequality | 81S30 | 94A12 | 42C25 | MATHEMATICS | MATHEMATICS, APPLIED | UNCERTAINTY | Mathematics - Classical Analysis and ODEs

45P05 | Uncertainty principle | Localization operator | Mathematics | Operator Theory | 42C40 | Analysis | Multiplier | Nash inequality | Mathematics, general | Carlson inequality | 81S30 | 94A12 | 42C25 | MATHEMATICS | MATHEMATICS, APPLIED | UNCERTAINTY | Mathematics - Classical Analysis and ODEs

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 01/2014, Volume 55, Issue 1, p. 12109

The concept of an injective affine embedding of the quantum states into a set of classical states, i.e., into the set of the probability measures on some...

SPACE | PHYSICS, MATHEMATICAL | Embedding | Statistical analysis | Representations | Quantum physics | Quantum mechanics | Quantum theory | Physics - Quantum Physics | PROBABILITY | MATHEMATICAL SPACE | QUANTUM STATES | QUANTUM MECHANICS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

SPACE | PHYSICS, MATHEMATICAL | Embedding | Statistical analysis | Representations | Quantum physics | Quantum mechanics | Quantum theory | Physics - Quantum Physics | PROBABILITY | MATHEMATICAL SPACE | QUANTUM STATES | QUANTUM MECHANICS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 6/2016, Volume 106, Issue 6, pp. 799 - 809

We consider Hamiltonian deformations of Gabor systems, where the window evolves according to the action of a Schrödinger propagator and the phase-space nodes...

Theoretical, Mathematical and Computational Physics | 35Q41 | Statistical Physics, Dynamical Systems and Complexity | Weyl quantization | Physics | Schrödinger equation | 35Q70 | Geometry | Gabor frame | phase space | 42C40 | 81S10 | time–frequency analysis | Group Theory and Generalizations | 81S30 | Hamiltonian flow | Wigner distribution

Theoretical, Mathematical and Computational Physics | 35Q41 | Statistical Physics, Dynamical Systems and Complexity | Weyl quantization | Physics | Schrödinger equation | 35Q70 | Geometry | Gabor frame | phase space | 42C40 | 81S10 | time–frequency analysis | Group Theory and Generalizations | 81S30 | Hamiltonian flow | Wigner distribution

Journal Article

Mediterranean Journal of Mathematics, ISSN 1660-5446, 4/2017, Volume 14, Issue 2, pp. 1 - 17

The aim of this paper is to study the uncertainty principles for the Dunkl wavelet transform, that set a limit to the possible concentration of a function in...

Localization operators | 45P05 | Dunkl wavelet transform | 42C40 | Mathematics, general | Mathematics | time–frequency concentration | uncertainty principles | 81S30 | 94A12 | 42C25 | MATHEMATICS | MATHEMATICS, APPLIED | TRANSFORM | time-frequency concentration

Localization operators | 45P05 | Dunkl wavelet transform | 42C40 | Mathematics, general | Mathematics | time–frequency concentration | uncertainty principles | 81S30 | 94A12 | 42C25 | MATHEMATICS | MATHEMATICS, APPLIED | TRANSFORM | time-frequency concentration

Journal Article

Integral Equations and Operator Theory, ISSN 0378-620X, 5/2015, Volume 82, Issue 1, pp. 95 - 117

Time–frequency localization operators are a quantization procedure that maps symbols on $${\mathbb{R}^{2d}}$$ R 2 d to operators and depends on two window...

Berezin quantization | Analysis | 42C30 | 47B10 | Mathematics | 81S30 | modulation space | 94A12 | short-time Fourier transform | Time–frequency localization | MATHEMATICS | ALGEBRAS | Time-frequency localization | TOEPLITZ-OPERATORS | CALCULUS | MODULATION SPACES | GABOR MULTIPLIERS | WEYL CORRESPONDENCE

Berezin quantization | Analysis | 42C30 | 47B10 | Mathematics | 81S30 | modulation space | 94A12 | short-time Fourier transform | Time–frequency localization | MATHEMATICS | ALGEBRAS | Time-frequency localization | TOEPLITZ-OPERATORS | CALCULUS | MODULATION SPACES | GABOR MULTIPLIERS | WEYL CORRESPONDENCE

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 2011, Volume 260, Issue 7, pp. 1944 - 1968

We investigate continuity properties of the operators obtained by the magnetic Weyl calculus on nilpotent Lie groups, using modulation spaces associated with...

Lie group | Modulation spaces | Weyl calculus | Magnetic field | SCHRODINGER OPERATOR | MATHEMATICS | INTEGRABLE GROUP-REPRESENTATIONS | ATOMIC DECOMPOSITIONS | FIELD | PSEUDODIFFERENTIAL-OPERATORS | FORMULA | Magnetic fields

Lie group | Modulation spaces | Weyl calculus | Magnetic field | SCHRODINGER OPERATOR | MATHEMATICS | INTEGRABLE GROUP-REPRESENTATIONS | ATOMIC DECOMPOSITIONS | FIELD | PSEUDODIFFERENTIAL-OPERATORS | FORMULA | Magnetic fields

Journal Article

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