Related papers: Uniform Semiclassical Wavepacket Propagation and E…
We define and prove some properties of the semi-classical wavefront set. We also define and study semi-classical Fourier integral operators, of which we give a complete characterization. Lastly, we prove a generalization of the…
Propagation of the Wigner function is studied on two levels of semiclassical propagation, one based on the van-Vleck propagator, the other on phase-space path integration. Leading quantum corrections to the classical Liouville propagator…
Resonance states in quantum chaotic scattering systems have a multifractal structure that depends on their decay rate. We show how classical dynamics describes this structure for all decay rates in the semiclassical limit. This result for…
We study smooth, caustic-free, chaotic semiclassical dynamics on two-dimensional phase space and find that the dynamics can be approached by an iterative procedure which constructs an approximation to the exact long-time semiclassical…
In the scalar light model given by Helmholtz' equation in R^{1+d} , we consider the transformation of an initial scene (a hologram) in {0}xR^d by an arbitrary affine transformation (which can be viewed as a propagation into a tilted…
We discuss the propagation dynamics of nonspreading wave packets. We decompose the Hamiltonian into two parts. The first part is such that wave packets is its instantaneous eigenstate and is therefore irrelevant to the propagation of the…
A trajectory segment in an energy shell, which combines to form a closed curve with a segment in another canonically driven energy shell, adds an oscillatory semiclassical contribution to the smooth classical background of the quantum…
We use a continuous-time path integral to obtain the semiclassical propagator for minimal-spread spin coherent states. We pay particular attention to the ``extra phase'' discovered by Solari and Kochetov, and show that this correction is…
We study the propagation of wavepackets along curved interfaces between topological, magnetic materials. Our Hamiltonian is a massive Dirac operator with a magnetic potential. We construct semiclassical wavepackets propagating along the…
We describe a semiclassical method to calculate universal transport properties of chaotic cavities. While the energy-averaged conductance turns out governed by pairs of entrance-to-exit trajectories, the conductance variance, shot noise and…
Semiclassical (stochastic) wave equations are proposed for the coupled dynamics of atomic quantum states and semiclassical radiation field. All relevant predictions of standard unitary quantum dynamics are exactly reproducible in the…
We study the dynamics of a quantum particle in R^(n+m) constrained by a strong potential force to stay within a distance of order hbar (in suitable units) from a smooth n-dimensional submanifold M. We prove that in the semiclassical limit…
It is shown that the semiclassical coherent state propagator takes its simplest form when the quantum mechanical Hamiltonian is replaced by its Weyl symbol in defining the classical action, in that there is then no need of a Solari-Kochetov…
We analyze the propagation of coherent states through general systems of pseudodifferential form associated with Hamiltonian presenting codimension one eigen-value crossings. In particular, we calculate precisely the non adiabatic effects…
The standard semiclassical calculation of transmission correlation functions for chaotic systems is severely influenced by unitarity problems. We show that unitarity alone imposes a set of relationships between cross sections correlation…
We study the resonance (or Gamow) eigenstates of open chaotic systems in the semiclassical limit, distinguishing between left and right eigenstates of the non-unitary quantum propagator, and also between short-lived and long-lived states.…
We consider quantum decay and photofragmentation processes in open chaotic systems in the semiclassical limit. We devise a semiclassical approach which allows us to consistently calculate quantum corrections to the classical decay to high…
The statistical properties of a Hamiltonian $H_0$ perturbed by a localized scatterer are considered. We prove that when $H_0$ describes a bounded chaotic motion, the universal part of the spectral statistics are not changed by the…
We present a semiclassical approach to eigenfunction statistics in chaotic and weakly disordered quantum systems which goes beyond Random Matrix Theory, supersymmetry techniques, and existing semiclassical methods. The approach is based on…
Wave equations are fundamental to describing a vast array of physical phenomena, yet their simulation in inhomogeneous media poses a computational challenge due to the highly oscillatory nature of the solutions. To overcome the high costs…