2012, Graduate studies in mathematics, ISBN 9780821883204, Volume 138, xii, 431

Book

Bulletin of Mathematical Sciences, ISSN 1664-3607, 4/2017, Volume 7, Issue 1, pp. 1 - 85

We provide an introduction to mathematical theory of scattering resonances and survey some recent results.

Mathematics, general | Mathematics | EXPANDING MAPS | MATHEMATICS | ANALYTIC CONTINUATION | LOWER BOUNDS | ASYMPTOTIC-DISTRIBUTION | COUNTING FUNCTION | WAVE-EQUATION | DYNAMICAL ZETA-FUNCTIONS | FREDHOLM DETERMINANTS | SEMICLASSICAL LIMIT | SCHRODINGER-OPERATORS

Mathematics, general | Mathematics | EXPANDING MAPS | MATHEMATICS | ANALYTIC CONTINUATION | LOWER BOUNDS | ASYMPTOTIC-DISTRIBUTION | COUNTING FUNCTION | WAVE-EQUATION | DYNAMICAL ZETA-FUNCTIONS | FREDHOLM DETERMINANTS | SEMICLASSICAL LIMIT | SCHRODINGER-OPERATORS

Journal Article

COMMUNICATIONS IN MATHEMATICAL PHYSICS, ISSN 0010-3616, 05/2019, Volume 367, Issue 3, pp. 941 - 989

We consider a quantum graph as a model of graphene in constant magnetic field and describe the density of states in terms of relativistic Landau levels...

SPECTRA | PHYSICS, MATHEMATICAL | Magnetic fields | Graphene | Analysis | Graphite

SPECTRA | PHYSICS, MATHEMATICAL | Magnetic fields | Graphene | Analysis | Graphite

Journal Article

Journal of Spectral Theory, ISSN 1664-039X, 2016, Volume 6, Issue 4, pp. 1087 - 1114

We revisit Vasy's method ([27] and [28]) for showing meromorphy of the resolvent for (even) asymptotically hyperbolic manifolds. It provides an effective...

Asymptotically hyperbolic manifolds | Scattering resonances | SPECTRAL THEORY | MATHEMATICS, APPLIED | NON-EUCLIDEAN SPACES | RIEMANN SURFACE | EISENSTEIN SERIES | BLACK-HOLES | MATHEMATICS | MICROLOCAL ANALYSIS | scattering resonances | RESOLVENT | LAPLACIAN OPERATOR | CONSTANT NEGATIVE CURVATURE | KERR-DE SITTER

Asymptotically hyperbolic manifolds | Scattering resonances | SPECTRAL THEORY | MATHEMATICS, APPLIED | NON-EUCLIDEAN SPACES | RIEMANN SURFACE | EISENSTEIN SERIES | BLACK-HOLES | MATHEMATICS | MICROLOCAL ANALYSIS | scattering resonances | RESOLVENT | LAPLACIAN OPERATOR | CONSTANT NEGATIVE CURVATURE | KERR-DE SITTER

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 4/2018, Volume 359, Issue 2, pp. 699 - 731

We consider scattering by star-shaped obstacles in hyperbolic space and show that resonances satisfy a universal bound $${ {\rm Im} \lambda \leq - \frac12 }$$...

Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | DECAY | SINGULARITIES | RESOLVENT | BOUNDARY-VALUE-PROBLEMS | WAVE-EQUATION | MANIFOLDS | PHYSICS, MATHEMATICAL | SCATTERING | KERR-DE SITTER

Quantum Physics | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | DECAY | SINGULARITIES | RESOLVENT | BOUNDARY-VALUE-PROBLEMS | WAVE-EQUATION | MANIFOLDS | PHYSICS, MATHEMATICAL | SCATTERING | KERR-DE SITTER

Journal Article

Inventiones mathematicae, ISSN 0020-9910, 5/2015, Volume 200, Issue 2, pp. 345 - 438

We prove that for evolution problems with normally hyperbolic trapping in phase space, correlations decay exponentially in time. Normally hyperbolic trapping...

Mathematics, general | Mathematics | DENSITY | MATHEMATICS | RESOLVENT | SPACES | BOUNDS | RESONANCE EXPANSIONS | Functions (mathematics) | Correlation | Trapping | Mathematical analysis | Decay | Evolution | Polynomials | Contact

Mathematics, general | Mathematics | DENSITY | MATHEMATICS | RESOLVENT | SPACES | BOUNDS | RESONANCE EXPANSIONS | Functions (mathematics) | Correlation | Trapping | Mathematical analysis | Decay | Evolution | Polynomials | Contact

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 09/2016, Volume 57, Issue 9, p. 92101

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...

SPECTRUM | PHYSICS, MATHEMATICAL | RESONANCES | QUASIMODES | Eigenvalues | Graphs | Boundary value problems | Cusps | Curvature

SPECTRUM | PHYSICS, MATHEMATICAL | RESONANCES | QUASIMODES | Eigenvalues | Graphs | Boundary value problems | Cusps | Curvature

Journal Article

International Mathematics Research Notices, ISSN 1073-7928, 02/2020, Volume 2020, Issue 3, pp. 781 - 812

Abstract We show directly that the fractal uncertainty principle of Bourgain–Dyatlov [3] implies that there exists σ > 0 for which the Selberg zeta function...

MATHEMATICS

MATHEMATICS

Journal Article

Acta Mathematica, ISSN 0001-5962, 12/2009, Volume 203, Issue 2, pp. 149 - 233

We study quantum scattering on manifolds equivalent to the Euclidean space near infinity, in the semiclassical regime. We assume that the corresponding...

Mathematics, general | Mathematics | LAPLACIAN | DENSITY | MATHEMATICS | RESOLVENT | BOUNDS | MANIFOLDS | RESONANCES | AXIOM | Spectral Theory | Mathematical Physics | Physics

Mathematics, general | Mathematics | LAPLACIAN | DENSITY | MATHEMATICS | RESOLVENT | BOUNDS | MANIFOLDS | RESONANCES | AXIOM | Spectral Theory | Mathematical Physics | Physics

Journal Article

Inventiones mathematicae, ISSN 0020-9910, 10/2017, Volume 210, Issue 1, pp. 211 - 229

We show that the Ruelle zeta function for a negatively curved oriented surface vanishes at zero to the order given by the absolute value of the Euler...

Mathematics, general | Mathematics | DIFFEOMORPHISMS | MATHEMATICS | SOBOLEV SPACES | MAPS | DYNAMICAL-SYSTEMS | ANALYTIC-TORSION | HYPERBOLIC MANIFOLDS | SPECTRUM | CONTACT ANOSOV-FLOWS | RESONANCES | FREDHOLM DETERMINANTS

Mathematics, general | Mathematics | DIFFEOMORPHISMS | MATHEMATICS | SOBOLEV SPACES | MAPS | DYNAMICAL-SYSTEMS | ANALYTIC-TORSION | HYPERBOLIC MANIFOLDS | SPECTRUM | CONTACT ANOSOV-FLOWS | RESONANCES | FREDHOLM DETERMINANTS

Journal Article

Annales Scientifiques de l'Ecole Normale Superieure, ISSN 0012-9593, 2016, Volume 49, Issue 3, pp. 543 - 577

The purpose of this paper is to give a short microlocal proof of the meromorphic continuation of the Ruelle zeta function for C-infinity Anosov flows. More...

DIFFEOMORPHISMS | MATHEMATICS | SOBOLEV SPACES | NUMBER | POLLICOTT-RUELLE RESONANCES | RIEMANN SURFACES | SYSTEMS | HYPERBOLIC MANIFOLDS | SPECTRUM | OPERATORS | FREDHOLM DETERMINANTS

DIFFEOMORPHISMS | MATHEMATICS | SOBOLEV SPACES | NUMBER | POLLICOTT-RUELLE RESONANCES | RIEMANN SURFACES | SYSTEMS | HYPERBOLIC MANIFOLDS | SPECTRUM | OPERATORS | FREDHOLM DETERMINANTS

Journal Article

Inventiones mathematicae, ISSN 0020-9910, 4/2003, Volume 152, Issue 1, pp. 89 - 118

Journal Article

SIAM Journal on Mathematical Analysis, ISSN 0036-1410, 2018, Volume 50, Issue 5, pp. 5362 - 5379

We consider the Kramers-Smoluchowski equation at a low temperature regime and show how semiclassical techniques developed for the study of the Witten Laplacian...

Witten Laplacian | Semiclassical analysis | Kramers-Smoluchowski equation | CHEMICAL-REACTIONS | MATHEMATICS, APPLIED | DIFFUSION | ASYMPTOTICS | semiclassical analysis | Analysis of PDEs | Mathematics

Witten Laplacian | Semiclassical analysis | Kramers-Smoluchowski equation | CHEMICAL-REACTIONS | MATHEMATICS, APPLIED | DIFFUSION | ASYMPTOTICS | semiclassical analysis | Analysis of PDEs | Mathematics

Journal Article

Annales Henri Poincaré, ISSN 1424-0637, 1/2017, Volume 18, Issue 1, pp. 1 - 35

We prove a local trace formula for Anosov flows. It relates Pollicott–Ruelle resonances to the periods of closed orbits. As an application, we show that the...

Mathematical Methods in Physics | Theoretical, Mathematical and Computational Physics | Quantum Physics | Dynamical Systems and Ergodic Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | DIFFEOMORPHISMS | NUMBER | ZETA-FUNCTIONS | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | AXIOM | DYNAMICAL-SYSTEMS | BOUNDS | POLLICOTT-RUELLE RESONANCES | POLES | SPECTRUM | OPERATORS | PHYSICS, PARTICLES & FIELDS

Mathematical Methods in Physics | Theoretical, Mathematical and Computational Physics | Quantum Physics | Dynamical Systems and Ergodic Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | DIFFEOMORPHISMS | NUMBER | ZETA-FUNCTIONS | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | AXIOM | DYNAMICAL-SYSTEMS | BOUNDS | POLLICOTT-RUELLE RESONANCES | POLES | SPECTRUM | OPERATORS | PHYSICS, PARTICLES & FIELDS

Journal Article

Physical Review D - Particles, Fields, Gravitation and Cosmology, ISSN 1550-7998, 10/2013, Volume 88, Issue 8

We present dynamical properties of linear waves and null geodesics valid for Kerr and Kerr-de Sitter black holes and their stationary perturbations. The two...

ENERGY | DECAY | COLLAPSE | QUASI-NORMAL MODES | ASTRONOMY & ASTROPHYSICS | RESONANCES | SCALAR | SCATTERING | PHYSICS, PARTICLES & FIELDS | Physics - General Relativity and Quantum Cosmology

ENERGY | DECAY | COLLAPSE | QUASI-NORMAL MODES | ASTRONOMY & ASTROPHYSICS | RESONANCES | SCALAR | SCATTERING | PHYSICS, PARTICLES & FIELDS | Physics - General Relativity and Quantum Cosmology

Journal Article

Annales Henri Poincaré, ISSN 1424-0637, 11/2011, Volume 12, Issue 7, pp. 1349 - 1385

We give pole free strips and estimates for resolvents of semiclassical operators which, on the level of the classical flow, have normally hyperbolic smooth...

Mathematical Methods in Physics | Theoretical, Mathematical and Computational Physics | Quantum Physics | Dynamical Systems and Ergodic Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | DENSITY | DECAY | PHYSICS, MULTIDISCIPLINARY | BOUNDS | WAVE-EQUATION | SEMICLASSICAL RESONANCES | TRACE FORMULA | MANIFOLDS | PHYSICS, MATHEMATICAL | LOCAL ENERGY | SCATTERING | PHYSICS, PARTICLES & FIELDS

Mathematical Methods in Physics | Theoretical, Mathematical and Computational Physics | Quantum Physics | Dynamical Systems and Ergodic Theory | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | DENSITY | DECAY | PHYSICS, MULTIDISCIPLINARY | BOUNDS | WAVE-EQUATION | SEMICLASSICAL RESONANCES | TRACE FORMULA | MANIFOLDS | PHYSICS, MATHEMATICAL | LOCAL ENERGY | SCATTERING | PHYSICS, PARTICLES & FIELDS

Journal Article

Annals of Mathematics, ISSN 0003-486X, 1/2014, Volume 179, Issue 1, pp. 179 - 251

We study a semiclassical quantization of Poincaré maps arising in scattering problems with fractal hyperbolic trapped sets. The main application is the proof...

Maps | Mathematical theorems | Invertibility | Coordinate systems | Fractals | Mathematical functions | Resonance | Trajectories | Lagrangian function | MATHEMATICS | ZETA-FUNCTION | NUMBER | SET | SCATTERING POLES | LOWER BOUNDS | RESOLVENT | SPACES | GROWTH | SEMICLASSICAL RESONANCES | Chaotic Dynamics | Mathematics | Nonlinear Sciences | Mathematical Physics | Analysis of PDEs | Physics

Maps | Mathematical theorems | Invertibility | Coordinate systems | Fractals | Mathematical functions | Resonance | Trajectories | Lagrangian function | MATHEMATICS | ZETA-FUNCTION | NUMBER | SET | SCATTERING POLES | LOWER BOUNDS | RESOLVENT | SPACES | GROWTH | SEMICLASSICAL RESONANCES | Chaotic Dynamics | Mathematics | Nonlinear Sciences | Mathematical Physics | Analysis of PDEs | Physics

Journal Article

Journal of the American Mathematical Society, ISSN 0894-0347, 4/2004, Volume 17, Issue 2, pp. 443 - 471

Journal Article

Nonlinearity, ISSN 0951-7715, 01/2013, Volume 26, Issue 1, pp. 35 - 52

Quantum ergodicity theorem states that for quantum systems with ergodic classical flows, eigenstates are, on average, uniformly distributed on energy surfaces....

MATHEMATICS, APPLIED | SUBMANIFOLDS | EIGENFUNCTIONS | PHYSICS, MATHEMATICAL | BILLIARDS | Geometry | Constrictions | Nonlinearity | Theorems | Quantum theory | Ergodic processes

MATHEMATICS, APPLIED | SUBMANIFOLDS | EIGENFUNCTIONS | PHYSICS, MATHEMATICAL | BILLIARDS | Geometry | Constrictions | Nonlinearity | Theorems | Quantum theory | Ergodic processes

Journal Article

Ergodic Theory and Dynamical Systems, ISSN 0143-3857, 2014, Volume 34, Issue 4, pp. 1168 - 1183

We give a sharp polynomial bound on the number of Pollicott-Ruelle resonances. These resonances, which are complex numbers in the lower half-plane, appear in...

DENSITY | MATHEMATICS | TRANSFER OPERATORS | MATHEMATICS, APPLIED | SOBOLEV SPACES | SCATTERING POLES | MAPS | SYSTEMS | CONTACT ANOSOV-FLOWS | Correlation analysis | Scattering | Polynomials | Complex numbers | Correlation | Upper bounds | Dynamical systems | Ergodic processes | Contact

DENSITY | MATHEMATICS | TRANSFER OPERATORS | MATHEMATICS, APPLIED | SOBOLEV SPACES | SCATTERING POLES | MAPS | SYSTEMS | CONTACT ANOSOV-FLOWS | Correlation analysis | Scattering | Polynomials | Complex numbers | Correlation | Upper bounds | Dynamical systems | Ergodic processes | Contact

Journal Article

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