Related papers: Strong phase-space semiclassical asymptotics
The semiclassical Wigner function for a Bohr-quantized energy eigenstate is known to have a caustic along the corresponding classical closed phase space curve in the case of a single degree of freedom. Its Fourier transform, the…
We have developed a semiclassical approach to solving the Bogoliubov - de Gennes equations for superconductors. It is based on the study of classical orbits governed by an effective Hamiltonian corresponding to the quasiparticles in the…
We investigate the particle and kinetic-energy densities for a system of $N$ fermions bound in a local (mean-field) potential $V(\bfr)$. We generalize a recently developed semiclassical theory [J. Roccia and M. Brack, Phys. Rev.\ Lett. {\bf…
We consider discrete spectra of bound states for non-relativistic motion in attractive potentials V_{\sigma}(x) = -|V_{0}| |x|^{-\sigma}, 0 < \sigma \leq 2. For these potentials the quasiclassical approximation for n -> \infty predicts…
We study the relationship of the spectral form factor with quantum as well as classical probabilities to return. Defining a quantum return probability in phase space as a trace over the propagator of the Wigner function allows us to…
We examine in a semiclassical framework the deflection function of strong gravitational lensing, for static and spherically symmetric black holes, endowed with a photon sphere. From a first-order WKB analysis near the maximum of the…
We consider mixed quasi-free states describing $N$ fermions in the mean-field limit. In this regime, the time evolution is governed by the nonlinear Hartree equation. In the large $N$ limit, we study the convergence towards the classical…
It $d-$pends. Wigner's symmetry theorem implies that transformations that preserve transition probabilities of pure quantum states are linear maps on the level of density operators. We investigate the stability of this implication. On the…
We show that if the Wigner function of a (possibly mixed) quantum state decays toward infinity faster than any polynomial in the phase space variables $x$ and $p$, then so do all of its derivatives, i.e., it is a Schwartz function on phase…
We present a new generalization of the steepest descent method introduced by Deift and Zhou for matrix Riemann-Hilbert problems and use it to study the semiclassical limit of the focusing nonlinear Schroedinger equation with real analytic,…
In this paper, we study an L2 version of the semiclassical approximation of magnetic Schroedinger operators with invariant Morse type potentials on covering spaces of compact manifolds. In particular, we are able to establish the existence…
We address the homogenization of a semilinear hyperbolic stochastic partial differential equation with highly oscillating coefficients, in the context of ergodic algebras with mean value. To achieve our goal, we use a suitable variant of…
We present a complete derivation of the semiclassical limit of the coherent state propagator in one dimension, starting from path integrals in phase space. We show that the arbitrariness in the path integral representation, which follows…
Quantum mechanics has been formulated in phase space, with the Wigner function as the representative of the quantum density operator, and classical mechanics has been formulated in Hilbert space, with the Groenewold operator as the…
An adaptation of the WKB method in the deformation quantization formalism is presented with the aim to obtain an approximate technique of solving the eigenvalue problem for energy in the phase space quantum approach. A relationship between…
We present the application of variational-wavelet analysis to numerical/analytical calculations of Wigner functions in (nonlinear) quasiclassical beam dynamics problems. (Naive) deformation quantization and multiresolution representations…
We consider semiclassically scaled Schrodinger equations with an external potential and a highly oscillatory periodic potential. We construct asymptotic solutions in the form of semiclassical wave packets. These solutions are concentrated…
The Seiberg-Witten equations that have recently found important applications for four-dimensional geometry are the Euler-Lagrange equations for a functional involving a connection $A$ on a line bundle $L$ and a section $\phi$ of another…
The phase space representation for a q-deformed model of the quantum harmonic oscillator is constructed. We have found explicit expressions for both the Wigner and Husimi distribution functions for the stationary states of the…
This paper discusses the possibility of applying the velocity averaging theorems in [F. Golse, P.-L. Lions, B. Perthame, R. Sentis: J. Funct. Anal. 76(1):110--125, 1988] to the Wigner equation governing the quantum evolution of the Wigner…