Journal of the Mathematical Society of Japan, ISSN 0025-5645, 2009, Volume 61, Issue 1, pp. 65 - 106

.... Within the reduction to an h-dependent linear problem with uniform regularity estimates for the potential already established in the first part, explicit computations of the asymptotic finite...

Multiscale problems | Schrödinger-Poisson system | Asymptotic analysis | multiscale problems | MATHEMATICS | Schrodinger-Poisson system | TRANSPORT | HETEROSTRUCTURES | SEMI-CLASSICAL LIMIT | asymptotic analysis | NONLINEARITIES | MODEL | EIGENVALUE SPLITTINGS | SCHRODINGER-OPERATORS

Multiscale problems | Schrödinger-Poisson system | Asymptotic analysis | multiscale problems | MATHEMATICS | Schrodinger-Poisson system | TRANSPORT | HETEROSTRUCTURES | SEMI-CLASSICAL LIMIT | asymptotic analysis | NONLINEARITIES | MODEL | EIGENVALUE SPLITTINGS | SCHRODINGER-OPERATORS

Journal Article

09/2013, ISBN 9814508462, 172

Dimensional and order-of-magnitude estimates are practiced by almost everybody but taught almost nowhere...

Quantum Information | MATHEMATICS | Quantum Theory | Quantum Mechanics | Partial | Quantum Physics | Differential Equations | SCIENCE | Physics | Mathematical & Computational | Quantum Mechanics, WKB, Semi-Classical, Bohr-Sommerfeld Quantization, Perturbation Theory, Order of Magnitude, Dimensional Analysis, Back-of-the-Envelope, Integrable Nonlinear Partial Differential Equations, Solitons, Breathers, Nonlinear Schrödinger Equation, Korteweg-de Vries Equation, Sine-Gordon Equation, Kadomtsev-Petviashvili Equation, Lieb-Liniger Model, Calogero Model, Hellmann-Feynman Theorem, Virial Theorem, Calculus of Variations

Quantum Information | MATHEMATICS | Quantum Theory | Quantum Mechanics | Partial | Quantum Physics | Differential Equations | SCIENCE | Physics | Mathematical & Computational | Quantum Mechanics, WKB, Semi-Classical, Bohr-Sommerfeld Quantization, Perturbation Theory, Order of Magnitude, Dimensional Analysis, Back-of-the-Envelope, Integrable Nonlinear Partial Differential Equations, Solitons, Breathers, Nonlinear Schrödinger Equation, Korteweg-de Vries Equation, Sine-Gordon Equation, Kadomtsev-Petviashvili Equation, Lieb-Liniger Model, Calogero Model, Hellmann-Feynman Theorem, Virial Theorem, Calculus of Variations

eBook

Journal of Functional Analysis, ISSN 0022-1236, 2005, Volume 225, Issue 1, pp. 193 - 228

We study the spectral shift function s ( λ , h ) and the resonances of the operator P ( h ) = - Δ + V ( x ) + W ( hx ) . Here V is a periodic potential, W a...

Spectral shift function | Resonances | Semi-classical asymption | Periodic Hamiltonian | Trace formula | Semi-classical asymptotics | MATHEMATICS | TRACE ASYMPTOTICS | PHASE | spectral shift function | trace formula | periodic Hamiltonian | resonances | SCATTERING-THEORY | FORMULA | semi-classical asymptotics | EQUATION

Spectral shift function | Resonances | Semi-classical asymption | Periodic Hamiltonian | Trace formula | Semi-classical asymptotics | MATHEMATICS | TRACE ASYMPTOTICS | PHASE | spectral shift function | trace formula | periodic Hamiltonian | resonances | SCATTERING-THEORY | FORMULA | semi-classical asymptotics | EQUATION

Journal Article

84.
Full Text
Precise Asymptotics of Small Eigenvalues of Reversible Diffusions in the Metastable Regime

The Annals of Probability, ISSN 0091-1798, 1/2005, Volume 33, Issue 1, pp. 244 - 299

... ↓ 0 with optimal and uniform error estimates. Each metastable state can be viewed as an eigenstate of L with eigenvalue which converges to zero exponentially fast in 1/ε...

A priori knowledge | Local minimum | Spectral theory | Uncertainty principle | Eigenvalues | Eigenfunctions | Markov chains | Laplace transformation | Metastability | Ground-state splitting | Witten's Laplace | Exponential distribution | Perron-Frobenius eigenvalues | Potential theory | Large deviations | Relaxation time | Exit problem | Capacity | Diffusion process | Reversibility | Eigenvalue problem | Semiclassical limit | large deviations | STOCHASTIC DYNAMICS | exit problem | metastability | MULTIPLE WELLS | semiclassical limit | capacity | SEMI-CLASSICAL LIMIT | ground-state splitting | relaxation time | TIMES | BEHAVIOR | MARKOV SEMIGROUPS | STATISTICS & PROBABILITY | potential theory | exponential distribution | OPERATOR | reversibility | SYSTEMS | diffusion process | SPECTRA | eigenvalue problem | PROBABILITIES | Mathematics - Probability | 60F10 | 60J60 | 58J50 | 35P20 | 31C15 | 58J37 | 31C05 | Perron–Frobenius eigenvalues | 35P15 | Witten’s Laplace | 60F05

A priori knowledge | Local minimum | Spectral theory | Uncertainty principle | Eigenvalues | Eigenfunctions | Markov chains | Laplace transformation | Metastability | Ground-state splitting | Witten's Laplace | Exponential distribution | Perron-Frobenius eigenvalues | Potential theory | Large deviations | Relaxation time | Exit problem | Capacity | Diffusion process | Reversibility | Eigenvalue problem | Semiclassical limit | large deviations | STOCHASTIC DYNAMICS | exit problem | metastability | MULTIPLE WELLS | semiclassical limit | capacity | SEMI-CLASSICAL LIMIT | ground-state splitting | relaxation time | TIMES | BEHAVIOR | MARKOV SEMIGROUPS | STATISTICS & PROBABILITY | potential theory | exponential distribution | OPERATOR | reversibility | SYSTEMS | diffusion process | SPECTRA | eigenvalue problem | PROBABILITIES | Mathematics - Probability | 60F10 | 60J60 | 58J50 | 35P20 | 31C15 | 58J37 | 31C05 | Perron–Frobenius eigenvalues | 35P15 | Witten’s Laplace | 60F05

Journal Article

85.
Full Text
Semi-classical limit of Schrödinger–Poisson equations in space dimension

Journal of Differential Equations, ISSN 0022-0396, 02/2007, Volume 233, Issue 1, pp. 241 - 275

Journal Article

AIP Conference Proceedings, ISSN 0094-243X, 2006, Volume 853, Issue 1, pp. 390 - 395

.... The corresponding form factors for excitations to the continuum are used in a semiclassical coupled channel scheme to get estimates for the break-up cross section in a heavy ion reaction...

Break-upreaction | Cluster model | Semi classical coupled channels | BREAKUP REACTIONS | EXCITATION | ENERGY SPECTRA | CLUSTER MODEL | HEAVY ION REACTIONS | NUCLEAR PHYSICS AND RADIATION PHYSICS | CROSS SECTIONS | SEMICLASSICAL APPROXIMATION | DIPOLES | FORM FACTORS | QUADRUPOLES | SUM RULES | COUPLED CHANNEL THEORY | LITHIUM 7 | COULOMB FIELD | MINUS-PLUS RATIO

Break-upreaction | Cluster model | Semi classical coupled channels | BREAKUP REACTIONS | EXCITATION | ENERGY SPECTRA | CLUSTER MODEL | HEAVY ION REACTIONS | NUCLEAR PHYSICS AND RADIATION PHYSICS | CROSS SECTIONS | SEMICLASSICAL APPROXIMATION | DIPOLES | FORM FACTORS | QUADRUPOLES | SUM RULES | COUPLED CHANNEL THEORY | LITHIUM 7 | COULOMB FIELD | MINUS-PLUS RATIO

Conference Proceeding

Journal of Statistical Physics, ISSN 0022-4715, 5/2006, Volume 123, Issue 4, pp. 811 - 829

.... Via sharp spectral estimates, this fluctuation indicates the presence of a critical point and allows to reconstruct partially the local shape of the potential...

Physical Chemistry | Theoretical, Mathematical and Computational Physics | Semi-classical analysis | equilibriums in classical mechanics | Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Schrödinger operators | Physics | Equilibriums in classical mechanics | Schrodinger operators | semi-classical analysis | PHYSICS, MATHEMATICAL | CRITICAL-LEVEL | SEMICLASSICAL TRACE FORMULA

Physical Chemistry | Theoretical, Mathematical and Computational Physics | Semi-classical analysis | equilibriums in classical mechanics | Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Schrödinger operators | Physics | Equilibriums in classical mechanics | Schrodinger operators | semi-classical analysis | PHYSICS, MATHEMATICAL | CRITICAL-LEVEL | SEMICLASSICAL TRACE FORMULA

Journal Article

88.
Full Text
Semiclassical Resonances of Schrödinger operators as zeroes of regularized determinants

International Mathematics Research Notices, ISSN 1073-7928, 2008, Volume 2008

We prove that the resonances of long range perturbations of the (semiclassical) Laplacian are the zeroes of natural perturbation determinants. We more...

Mathematics | Spectral Theory

Mathematics | Spectral Theory

Journal Article

89.
Full Text
Convergence of Nonlinear Schrödinger-Poisson Systems to the Compressible Euler Equations

Communications in Partial Differential Equations, ISSN 0360-5302, 01/2003, Volume 28, Issue 5-6, pp. 1005 - 1022

.... The proof of these results is based on estimates of a modulated energy functional and on the Wigner measure method.

Semi-classical limit | Bipolar defocusing nonlinear Schrödinger-Poisson systems | Quasineutral limit | Wigner measure | 2000 Mathematics Subject Classification:35Q40 | Compressible Euler equations | quasineutral limit | EXISTENCE | MATHEMATICS, APPLIED | semi-classical limit | WIGNER TRANSFORMS | DRIFT-DIFFUSION MODEL | CLASSICAL LIMIT | PLASMAS | HOMOGENIZATION | QUASI-NEUTRAL LIMIT | MATHEMATICS | compressible Euler equations | bipolar defocusing nonlinear Schrodinger-Poisson systems | OSCILLATIONS | SEMICLASSICAL LIMIT | HIERARCHY

Semi-classical limit | Bipolar defocusing nonlinear Schrödinger-Poisson systems | Quasineutral limit | Wigner measure | 2000 Mathematics Subject Classification:35Q40 | Compressible Euler equations | quasineutral limit | EXISTENCE | MATHEMATICS, APPLIED | semi-classical limit | WIGNER TRANSFORMS | DRIFT-DIFFUSION MODEL | CLASSICAL LIMIT | PLASMAS | HOMOGENIZATION | QUASI-NEUTRAL LIMIT | MATHEMATICS | compressible Euler equations | bipolar defocusing nonlinear Schrodinger-Poisson systems | OSCILLATIONS | SEMICLASSICAL LIMIT | HIERARCHY

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 2004, Volume 217, Issue 1, pp. 79 - 102

We study the semi-classical trace formula at a critical energy level for a h-pseudo-differential operator on R n whose principal symbol has a totally...

Degenerate oscillatory integrals | Semi-classical analysis | Trace formula | MATHEMATICS | semi-classical analysis | degenerate oscillatory integrals | trace formula | CRITICAL-LEVEL | SCHRODINGER-OPERATORS | Mathematics - Functional Analysis

Degenerate oscillatory integrals | Semi-classical analysis | Trace formula | MATHEMATICS | semi-classical analysis | degenerate oscillatory integrals | trace formula | CRITICAL-LEVEL | SCHRODINGER-OPERATORS | Mathematics - Functional Analysis

Journal Article

JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER, ISSN 0022-4073, 09/2019, Volume 234, pp. 47 - 54

The water vapor line broadening and shifting coefficients for about 91 strongest water vapor lines in the 19,560-19,920 cm(-1) spectral region induced by...

Line width and shift coefficients | PRESSURE | Fourier transform spectroscopy | Inter-molecular interactions | Multi-spectrum fitting | H2O | SPECTROSCOPY | High luminance LED light source | Semi-classical impact theory | OPTICS | COLLISIONS

Line width and shift coefficients | PRESSURE | Fourier transform spectroscopy | Inter-molecular interactions | Multi-spectrum fitting | H2O | SPECTROSCOPY | High luminance LED light source | Semi-classical impact theory | OPTICS | COLLISIONS

Journal Article

Kyushu journal of mathematics, ISSN 1340-6116, 2009, Volume 63, Issue 1, pp. 17 - 49

.... From here estimates for large eigenvalues, depending on the parameter, and an asymptotic result for the lowest eigenvalue will follow...

Sturm-Liouville problem | semi-classical limit | clustering | Clustering | Semi-classical limit | MATHEMATICS | OSCILLATOR

Sturm-Liouville problem | semi-classical limit | clustering | Clustering | Semi-classical limit | MATHEMATICS | OSCILLATOR

Journal Article

JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER, ISSN 0022-4073, 07/2019, Volume 232, pp. 165 - 179

... %. Theoretical estimates of CH3I self-broadening coefficients for large ranges of rotational quantum numbers (0 <= J <= 70, 0 <= K <= 20...

Methyl iodide | INTENSITIES | Line list | Measurements | nu band | Semi-empirical calculations | DETAILED ANALYSIS | MOLECULES | POSITIONS | SPECTROSCOPY | N-2-BROADENING COEFFICIENTS | Line intensities | J- and K-dependencies | Self-broadening coefficients | OPTICS | SPECTRA | Semi-classical calculations | EDITION | METHYL-IODIDE | CHLORIDE

Methyl iodide | INTENSITIES | Line list | Measurements | nu band | Semi-empirical calculations | DETAILED ANALYSIS | MOLECULES | POSITIONS | SPECTROSCOPY | N-2-BROADENING COEFFICIENTS | Line intensities | J- and K-dependencies | Self-broadening coefficients | OPTICS | SPECTRA | Semi-classical calculations | EDITION | METHYL-IODIDE | CHLORIDE

Journal Article

Journal of Quantitative Spectroscopy and Radiative Transfer, ISSN 0022-4073, 11/2018, Volume 219, pp. 213 - 223

• N2-broadening and shifting coefficients for 288 H2O transitions of the ν1 + 4ν2 + 2ν3, 3ν1 + 2ν2 + ν3, 4ν1 + ν3, 4ν1 + 2ν2, 5ν1 bands.• Comparison of...

Fourier transform spectroscopy | High luminance led light source | Inter-molecular interactions | Multi-spectrum fitting | Line width and shift coefficients, semi-classical impact theory

Fourier transform spectroscopy | High luminance led light source | Inter-molecular interactions | Multi-spectrum fitting | Line width and shift coefficients, semi-classical impact theory

Journal Article

Journal of Quantitative Spectroscopy and Radiative Transfer, ISSN 0022-4073, 09/2019, Volume 234, pp. 47 - 54

•N2-broadening and shifting coefficients for 91 H2O transitions of the 5ν1+ν3, 6ν1 bands.•Comparison of experimental and theoretical H216O–N2 line parameters...

High luminance LED light source | Fourier transform spectroscopy | Inter-molecular interactions | Multi-spectrum fitting | Line width and shift coefficients, Semi-classical impact theory

High luminance LED light source | Fourier transform spectroscopy | Inter-molecular interactions | Multi-spectrum fitting | Line width and shift coefficients, Semi-classical impact theory

Journal Article

03/2009

We consider the Jaynes-Cummings model of a single quantum spin $s$ coupled to a harmonic oscillator in a parameter regime where the underlying classical...

Journal Article

Annals of PDE, ISSN 2524-5317, 6/2019, Volume 5, Issue 1, pp. 1 - 174

...–Kramers formula, in the small temperature regime $$h \rightarrow 0$$ h→0 . We provide in particular sharp asymptotic estimates on the exit distribution which demonstrate the importance of the prefactors in the Eyring–Kramers formula...

Mathematical Methods in Physics | Witten Laplacians | Exit problem | Semi-classical analysis | Eyring-Kramers formula | Kinetic Monte Carlo models | Physics | Partial Differential Equations | Metastable stochastic process | Analysis of PDEs | Mathematics

Mathematical Methods in Physics | Witten Laplacians | Exit problem | Semi-classical analysis | Eyring-Kramers formula | Kinetic Monte Carlo models | Physics | Partial Differential Equations | Metastable stochastic process | Analysis of PDEs | Mathematics

Journal Article

Communications in Partial Differential Equations, ISSN 0360-5302, 01/2002, Volume 27, Issue 3-4, pp. 669 - 691

The semi-classical and the inviscid limit in quantum trajectory models given by a one-dimensional steady-state hydrodynamic system for quantum fluids are...

Semi-classical limit | Semiconductors | Inviscid limit | Quantum hydrodynamic equations | MATHEMATICS | MATHEMATICS, APPLIED | semi-classical limit | HYDRODYNAMIC MODEL | EQUATIONS | quantum hydrodynamic equations | EULER-POISSON SYSTEM | semiconductors | inviscid limit | QUASI-NEUTRAL LIMIT

Semi-classical limit | Semiconductors | Inviscid limit | Quantum hydrodynamic equations | MATHEMATICS | MATHEMATICS, APPLIED | semi-classical limit | HYDRODYNAMIC MODEL | EQUATIONS | quantum hydrodynamic equations | EULER-POISSON SYSTEM | semiconductors | inviscid limit | QUASI-NEUTRAL LIMIT

Journal Article

JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER, ISSN 0022-4073, 11/2018, Volume 219, pp. 213 - 223

N-2 pressure broadening and shifting coefficients are presented for about 300 strongest water vapor lines in the 16,600-17,060 cm(-1) spectral region. The...

Line width and shift coefficients | Fourier transform spectroscopy | Inter-molecular interactions | Multi-spectrum fitting | SPECTROSCOPY | Semi-classical impact theory | COEFFICIENTS | HALF-WIDTHS | High luminance led light source | PARAMETERS | OPTICS | WATER

Line width and shift coefficients | Fourier transform spectroscopy | Inter-molecular interactions | Multi-spectrum fitting | SPECTROSCOPY | Semi-classical impact theory | COEFFICIENTS | HALF-WIDTHS | High luminance led light source | PARAMETERS | OPTICS | WATER

Journal Article

General Relativity and Gravitation, ISSN 0001-7701, 11/2015, Volume 47, Issue 11, pp. 1 - 23

In this work we study the dynamics of the Schrödinger–Newton (SN) equation upon different choices of initial conditions. Setting up superpositions of...

Semi-classical gravity | Schrödinger–Newton Equation | Wave function confinement | Theoretical, Mathematical and Computational Physics | Quantum Physics | Critical mass | Differential Geometry | Gravitational inhibition | Classical and Quantum Gravitation, Relativity Theory | Physics | Astronomy, Astrophysics and Cosmology | PHYSICS, MULTIDISCIPLINARY | ASTRONOMY & ASTROPHYSICS | Schrodinger-Newton Equation | EFFECTIVE POTENTIALS | GRAVITY | STRING THEORY | PHYSICS, PARTICLES & FIELDS

Semi-classical gravity | Schrödinger–Newton Equation | Wave function confinement | Theoretical, Mathematical and Computational Physics | Quantum Physics | Critical mass | Differential Geometry | Gravitational inhibition | Classical and Quantum Gravitation, Relativity Theory | Physics | Astronomy, Astrophysics and Cosmology | PHYSICS, MULTIDISCIPLINARY | ASTRONOMY & ASTROPHYSICS | Schrodinger-Newton Equation | EFFECTIVE POTENTIALS | GRAVITY | STRING THEORY | PHYSICS, PARTICLES & FIELDS

Journal Article

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