JOURNAL OF MODERN DYNAMICS, ISSN 1930-5311, 10/2007, Volume 1, Issue 4, pp. 689 - 718

We study the Gross-Pitaevskii equation with a delta function potential, q delta 0, where vertical bar q vertical bar is small and analyze the solutions for...

MATHEMATICS | MATHEMATICS, APPLIED | STATES | soliton | effective Hamiltonian | Gross-Pitaevskii equation | SCHRODINGER-EQUATION | nonlinear Schrodinger equation | semiclassical | DYNAMICS | Dirac mass potential

MATHEMATICS | MATHEMATICS, APPLIED | STATES | soliton | effective Hamiltonian | Gross-Pitaevskii equation | SCHRODINGER-EQUATION | nonlinear Schrodinger equation | semiclassical | DYNAMICS | Dirac mass potential

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 5/2011, Volume 304, Issue 1, pp. 1 - 48

... to Open Quantum Maps Stéphane Nonnenmacher 1 , Johannes Sjöstrand 2 , Maciej Zworski 3 1 Institut de Physique Théorique, CEA/DSM/PhT, Unité de Recherche Associée au...

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | TRANSFORMATION | DENSITY | BOUNDS | SEMICLASSICAL QUANTIZATION | TRACE FORMULA | CHAOTIC SCATTERING | PHYSICS, MATHEMATICAL | RESONANCES | SECTION | Chaotic Dynamics | Mathematics | Nonlinear Sciences | Mathematical Physics | Analysis of PDEs

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | TRANSFORMATION | DENSITY | BOUNDS | SEMICLASSICAL QUANTIZATION | TRACE FORMULA | CHAOTIC SCATTERING | PHYSICS, MATHEMATICAL | RESONANCES | SECTION | Chaotic Dynamics | Mathematics | Nonlinear Sciences | Mathematical Physics | Analysis of PDEs

Journal Article

43.
Full Text
Pointwise bounds on quasimodes of semiclassical schrödinger operators in dimension two

Mathematical Research Letters, ISSN 1073-2780, 03/2013, Volume 20, Issue 2, pp. 401 - 408

We prove sharp pointwise bounds on quasimodes of semiclassical Schrodinger operators with arbitrary smooth real potentials in dimension two. This end-point...

MATHEMATICS

MATHEMATICS

Journal Article

Applied Mathematics Research Express, ISSN 1687-1200, 2009, Volume 2009, Issue 1, pp. 1 - 13

We prove resolvent estimates for semiclassical operators such as − h 2 Δ + V(x) in scattering situations. Provided the set of trapped classical trajectories...

Dynamical Systems | Mathematics | Mathematical Physics | Analysis of PDEs | Physics

Dynamical Systems | Mathematics | Mathematical Physics | Analysis of PDEs | Physics

Journal Article

Annales de l'Institut Fourier, ISSN 0373-0956, 2007, Volume 57, Issue 7, pp. 2095 - 2141

We describe a simple linear algebra idea which has been used in different branches of mathematics such as bifurcation theory, partial differential equations...

Eigenvalues | Trace formulae | Feshbach reduction | Grushin problem | Schur complement | Resonances | MATHEMATICS | OPERATORS | RESONANCES

Eigenvalues | Trace formulae | Feshbach reduction | Grushin problem | Schur complement | Resonances | MATHEMATICS | OPERATORS | RESONANCES

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 01/2019, Volume 147, Issue 1, pp. 145 - 152

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 02/2004, Volume 245, Issue 1, pp. 149 - 176

We give a new upper bound on the Selberg zeta function for a convex co-compact Schottky group acting on the hyperbolic space ℍ n +1: in strips parallel to the...

Mathematics | HAUSDORFF DIMENSION | DENSITY | NUMBER | BOUNDS | SETS | DYNAMICS | ASYMPTOTICS | MANIFOLDS | SPECTRUM | PHYSICS, MATHEMATICAL | QUANTUM RESONANCES | Spectral Theory | Differential Geometry | Mathematical Physics | Physics

Mathematics | HAUSDORFF DIMENSION | DENSITY | NUMBER | BOUNDS | SETS | DYNAMICS | ASYMPTOTICS | MANIFOLDS | SPECTRUM | PHYSICS, MATHEMATICAL | QUANTUM RESONANCES | Spectral Theory | Differential Geometry | Mathematical Physics | Physics

Journal Article

Annales Henri Poincaré, ISSN 1424-0637, 08/2007, Volume 8, Issue 5, pp. 885 - 916

.../s00023-006-0324-2 Annales Henri Poincar´ e Semiclassical L p Estimates Herbert Koch, Daniel Tataru, and Maciej Zworski Abstract. The purpose of this paper is to use...

Mathematical Methods in Physics | Relativity and Cosmology | Mathematical and Computational Physics | Quantum Physics | Dynamical Systems and Ergodic Theory | Physics | Elementary Particles, Quantum Field Theory

Mathematical Methods in Physics | Relativity and Cosmology | Mathematical and Computational Physics | Quantum Physics | Dynamical Systems and Ergodic Theory | Physics | Elementary Particles, Quantum Field Theory

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 11/2005, Volume 260, Issue 1, pp. 45 - 58

... for the Semiclassical Non-linear Schr ¨ odinger Equation Nicolas Burq 1,2 , Maciej Zworski 3 1 Universit´ e Paris Sud, Math´ ematiques, Bˆ at. 425, 91405 Orsay Cedex, France. E...

Quantum Computing, Information and Physics | Relativity and Cosmology | Mathematical and Computational Physics | Nonlinear Dynamics, Complex Systems, Chaos, Neural Networks | Quantum Physics | Physics | Statistical Physics | PHYSICS, MATHEMATICAL

Quantum Computing, Information and Physics | Relativity and Cosmology | Mathematical and Computational Physics | Nonlinear Dynamics, Complex Systems, Chaos, Neural Networks | Quantum Physics | Physics | Statistical Physics | PHYSICS, MATHEMATICAL

Journal Article

Proceedings of the American Mathematical Society, ISSN 0002-9939, 01/2019, Volume 147, Issue 1, pp. 145 - 152

We consider Vasy's operator with analytic coefficients. That operator arises in the study of scattering on asymptotically hyperbolic manifolds and in general...

MATHEMATICS | MATHEMATICS, APPLIED

MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 06/2000, Volume 212, Issue 1, pp. 205 - 217

We consider long range semiclassical perturbations of the Laplacian on asymptotically Euclidean manifolds. We obtain precise resolvent estimates under...

PHYSICS, MATHEMATICAL | PERTURBATIONS | SCHRODINGER-OPERATORS | Mathematics - Analysis of PDEs

PHYSICS, MATHEMATICAL | PERTURBATIONS | SCHRODINGER-OPERATORS | Mathematics - Analysis of PDEs

Journal Article

Journal of mathematical physics, ISSN 0022-2488, 09/2016, Volume 57, Issue 9, p. 1

We present a Fermi golden rule giving rates of decay of states obtained by perturbing embedded eigenvalues of a quantum graph. To illustrate the procedure in a...

Boundary value problems | Experiments | Quantum theory | Eigen values

Boundary value problems | Experiments | Quantum theory | Eigen values

Journal Article

Springer Proceedings in Mathematics and Statistics, ISSN 2194-1009, 2018, Volume 269, pp. 635 - 654

Conference Proceeding

Chemical Physics Letters, ISSN 0009-2614, 03/2002, Volume 355, Issue 1-2, pp. 201 - 205

This Letter summarizes numerical results from [J. Comp. Phys. (to appear)] which show that in quantum systems with chaotic classical dynamics, the number of...

Journal Article

Nonlinearity, ISSN 0951-7715, 09/2015, Volume 28, Issue 10, pp. 3511 - 3533

Pollicott-Ruelle resonances for chaotic flows are the characteristic frequencies of correlations. They are typically defined as eigenvalues of the generator of...

Anosov flow | decay of correlations | Pollicott-Ruelle resonances | MATHEMATICS, APPLIED | ANOSOV | MAPS | SPACES | SETS | SPECTRUM | PHYSICS, MATHEMATICAL | Viscosity | Operators | Correlation | Stability | Probability theory | Eigenvalues | Nonlinearity | Stochasticity

Anosov flow | decay of correlations | Pollicott-Ruelle resonances | MATHEMATICS, APPLIED | ANOSOV | MAPS | SPACES | SETS | SPECTRUM | PHYSICS, MATHEMATICAL | Viscosity | Operators | Correlation | Stability | Probability theory | Eigenvalues | Nonlinearity | Stochasticity

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 1996, Volume 175, Issue 3, pp. 673 - 682

We give a simple proof of ergodicity of eigenfunctions of the Laplacian with Dirichlet boundary conditions on compact Riemannian manifolds with piecewise...

PHYSICS, MATHEMATICAL | 58G15 | 58G25 | 58F11

PHYSICS, MATHEMATICAL | 58G15 | 58G25 | 58F11

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 8/2007, Volume 81, Issue 2, pp. 107 - 117

... Limit DAVID BINDEL 1 and MACIEJ ZWORSKI 2 1 Department of Mathematics, Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA. 2...

Geometry | nonlinear eigenvalue problems | 65L15 | Mathematical and Computational Physics | 81U20 | 34L15 | Group Theory and Generalizations | Quantum resonances | 65F18 | finite elements methods | Physics | Statistical Physics | Nonlinear eigenvalue problems | Finite elements methods | ONE-DIMENSION | quantum resonances | POLES | PHYSICS, MATHEMATICAL | RESONANCES | SCATTERING MATRIX | REAL LINE | Finite element method

Geometry | nonlinear eigenvalue problems | 65L15 | Mathematical and Computational Physics | 81U20 | 34L15 | Group Theory and Generalizations | Quantum resonances | 65F18 | finite elements methods | Physics | Statistical Physics | Nonlinear eigenvalue problems | Finite elements methods | ONE-DIMENSION | quantum resonances | POLES | PHYSICS, MATHEMATICAL | RESONANCES | SCATTERING MATRIX | REAL LINE | Finite element method

Journal Article

04/2020

Gajic--Warnick have recently proposed a definition of scattering resonances based on Gevrey-2 regularity at infinity and introduced a new class of potentials...

Journal Article

03/2020

We consider Keldysh-type operators, $ P = x_1 D_{x_1}^2 + a (x) D_{x_1} + Q (x, D_{x'} ) $, $ x = ( x_1, x') $ with analytic coefficients, and with $ Q ( x,...

Mathematics - Analysis of PDEs

Mathematics - Analysis of PDEs

Journal Article

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