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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
Communications in Mathematical Physics, ISSN 0010-3616, 5/2011, Volume 304, Issue 1, pp. 1 - 48
Journal Article
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
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
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
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
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
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
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
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
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
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
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
Journal Article
Letters in Mathematical Physics, ISSN 0377-9017, 8/2007, Volume 81, Issue 2, pp. 107 - 117
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
Journal Article
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