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Communications in mathematical physics, ISSN 1432-0916, 2007, Volume 274, Issue 1, pp. 187 - 216
... by Delta Impurities Justin Holmer, Jeremy Marzuola, Maciej Zworski Mathematics Department, Evans Hall, University of California, Berkeley, CA 94720, USA. E-mail... 
Quantum Computing, Information and Physics | Relativity and Cosmology | Mathematical and Computational Physics | Quantum Physics | Physics | Statistical Physics | Complexity | DYNAMICS | WAVES | PHYSICS, MATHEMATICAL | SCHRODINGER-EQUATION
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
Journal Article
Mathematical research letters, ISSN 1945-001X, 2012, Volume 19, Issue 2, pp. 309 - 324
A well-known result of Jaffard states that an arbitrary region on a torus controls, in the L-2 sense, solutions of the free stationary and dynamical... 
MATHEMATICS | RESOLVENT | EIGENFUNCTIONS
Journal Article
Physical Review Letters, ISSN 0031-9007, 04/2013, Volume 110, Issue 16, p. 164102
Symmetry reduced three-disk and five-disk systems are studied in a microwave setup. Using harmonic inversion the distribution of the imaginary parts of the... 
DENSITY | ZETA-FUNCTION | ANALYTIC CONTINUATION | DECAY | CAVITIES | PHYSICS, MULTIDISCIPLINARY | LIMIT SET | QUANTIZATION | QUANTUM RESONANCES | SCATTERING | CLASSICALLY CHAOTIC REPELLOR | Physics - Mesoscale and Nanoscale Physics | Mesoscopic Systems and Quantum Hall Effect | Condensed Matter | Physics
Journal Article
International Mathematics Research Notices, ISSN 1073-7928, 2008, Volume 2008, Issue 1
Journal Article
Annales de l'Institut Fourier, ISSN 0373-0956, 2016, Volume 66, Issue 2, pp. 455 - 475
We show that, in odd dimensions, any real valued, bounded potential of compact support has at least one scattering resonance. In dimensions 3 and greater this... 
Resonances | Scattering | Heat trace | GENERIC POTENTIALS | MATHEMATICS | NUMBER | heat trace | resonances | SCHRODINGER-OPERATORS
Journal Article
Physical Review Letters, ISSN 0031-9007, 2003, Volume 91, Issue 15, pp. 1541011 - 1541014
We present a conjecture relating the density of quantum resonances for an open chaotic system to the fractal dimension of the associated classical repeller.... 
DENSITY | PHYSICS, MULTIDISCIPLINARY | QUANTUM RESONANCES | SCATTERING | Physics - Chaotic Dynamics
Journal Article
Communications in Mathematical Physics, ISSN 0010-3616, 7/2011, Volume 305, Issue 2, pp. 363 - 425
... of Double Solitons for Perturbed mKdV Justin Holmer 1 , Galina Perelman 2 , Maciej Zworski 3 1 Department of Mathematics, Brown University, 151 Thayer Street... 
Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | EQUATIONS | EVOLUTION | SOLITARY WAVES | PHYSICS, MATHEMATICAL | STABILITY | PROPAGATION
Journal Article
Bulletin of the American Mathematical Society, ISSN 0273-0979, 07/2018, Volume 55, Issue 3, pp. 331 - 336
Immediately following the commentary below, this previously published article is reprinted in its entirety: Stephen Smale, ``Differentiable dynamical... 
ANOSOV-FLOWS | MATHEMATICS | MICROLOCAL ANALYSIS | ZETA-FUNCTIONS | SPACES
Journal Article
Journal of Nonlinear Science, ISSN 0938-8974, 8/2007, Volume 17, Issue 4, pp. 349 - 367
... Potentials J. Holmer, J. Marzuola, and M. Zworski Mathematics Department, University of California, Evans Hall, Berkeley, CA 94720, USA E-mail:{holmer,marzuola,zworski... 
Mechanics | Economic Theory | Mathematics | Analysis | Mathematical and Computational Physics | Appl.Mathematics/Computational Methods of Engineering | DYNAMICS | MATHEMATICS, APPLIED | MECHANICS | NONLINEAR SCHRODINGER-EQUATION | PHYSICS, MATHEMATICAL | Mathematics - Analysis of PDEs
Journal Article
SIAM Review, ISSN 0036-1445, 3/2005, Volume 47, Issue 1, pp. 43 - 49
Quantum ergodicity for classically chaotic systems has been studied extensively both theoretically and experimentally in mathematics and physics. Despite this... 
Ergodic theory | Pool tables | Billiards | Mathematical theorems | Chaos theory | Rectangles | Quantum mechanics | Eigenfunctions | Problems and Techniques | Physics | Quantum ergodicity | eigenfunctions | UNIQUE ERGODICITY | MATHEMATICS, APPLIED | quantum ergodicity | SINGULARITIES | BOUNDARY-VALUE-PROBLEMS | billiards | Models | Quantum theory
Journal Article
Inventiones mathematicae, ISSN 0020-9910, 4/1999, Volume 136, Issue 2, pp. 353 - 409
Journal Article
Communications on Pure and Applied Mathematics, ISSN 0010-3640, 03/2004, Volume 57, Issue 3, pp. 384 - 415
The pseudo-spectra (or spectral instability) of non-selfadjoint operators is a topic of current interest in applied mathematics. For example, in computational... 
MATHEMATICS | MATHEMATICS, APPLIED | HARMONIC-OSCILLATOR | QUASIMODES | EQUATIONS | PSEUDODIFFERENTIAL OPERATORS | RESONANCES | principal type | non-selfadjoint operators | Naturvetenskap | semiclassical operators | Mathematics | Natural Sciences | Matematik | pseudospectrum
Journal Article
Journal of Spectral Theory, ISSN 1664-039X, 2015, Volume 5, Issue 3, pp. 599 - 615
We show how the presence of resonances close to the real axis implies exponential lower bounds on the norm of the cut-off resolvent on the real axis. 
Resolvent estimates | Semiclassical analysis | Scattering resonances | MATHEMATICS | RANGE SCHRODINGER-OPERATORS | MATHEMATICS, APPLIED | scattering resonances | LIMIT | semiclassical analysis | SCATTERING | Mathematics - Analysis of PDEs
Journal Article
Nonlinearity, ISSN 0951-7715, 06/2009, Volume 22, Issue 6, pp. 1259 - 1301
... and Maciej Zworski 2 1 Department of Mathematics, Brown University, 151 Thayer Street, Providence, RI 02912, USA 2 Mathematics Department, University of California... 
SCHRODINGER-EQUATIONS | MATHEMATICS, APPLIED | INSTABILITY | PHYSICS, MATHEMATICAL | SOLITON DYNAMICS
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
Journal Article
Journal of the European Mathematical Society, ISSN 1435-9855, 2013, Volume 15, Issue 5, pp. 1597 - 1628
For the Schrodinger equation (i partial derivative(t) + Delta)u = 0 on a torus, an arbitrary non-empty open set Omega provides control and observability of the... 
MATHEMATICS | MATHEMATICS, APPLIED | CONTROLLABILITY | EQUATION | UNIQUE CONTINUATION
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 10/2001, Volume 129, Issue 10, pp. 2955 - 2957
We explain the existence of open sets of complex quasi-modes in terms of Hörmander's commutator condition. 
Commutators
Journal Article
Communications in Mathematical Physics, ISSN 0010-3616, 1/2007, Volume 269, Issue 2, pp. 311 - 365
... of Resonances for Open Quantum Maps Stéphane Nonnenmacher 1 , Maciej Zworski 2 1 Service de Physique Théorique, CEA/DSM/PhT, Unité de Recherche Associée au CNRS, CEA/Saclay... 
Quantum Computing, Information and Physics | Relativity and Cosmology | Mathematical and Computational Physics | Quantum Physics | Physics | Statistical Physics | Complexity | TRANSFORMATION | LIFETIMES | ZETA-FUNCTION | STATISTICS | DIMENSION | SEMICLASSICAL QUANTIZATION | SYSTEMS | CHAOTIC SCATTERING | BAKERS MAPS | PHYSICS, MATHEMATICAL | SURFACES | Mathematical Physics | Dynamical Systems | Mathematics
Journal Article
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
Journal Article
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