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Semiclassical Description of Tunneling in Mixed Systems: The Case of the Annular Billiard  [PDF]
Eyal Doron,Steffen D. Frischat
Physics , 1995, DOI: 10.1103/PhysRevLett.75.3661
Abstract: We study quantum-mechanical tunneling between symmetry-related pairs of regular phase space regions that are separated by a chaotic layer. We consider the annular billiard, and use scattering theory to relate the splitting of quasi-degenerate states quantized on the two regular regions to specific paths connecting them. The tunneling amplitudes involved are given a semiclassical interpretation by extending the billiard boundaries to complex space and generalizing specular reflection to complex rays. We give analytical expressions for the splittings, and show that the dominant contributions come from {\em chaos-assisted}\/ paths that tunnel into and out of the chaotic layer.
Semiclassical Description of Wavepacket Revival  [PDF]
F. Toscano,R. O. Vallejos,D. A. Wisniacki
Physics , 2009, DOI: 10.1103/PhysRevE.80.046218
Abstract: We test the ability of semiclassical theory to describe quantitatively the revival of quantum wavepackets --a long time phenomena-- in the one dimensional quartic oscillator (a Kerr type Hamiltonian). Two semiclassical theories are considered: time-dependent WKB and Van Vleck propagation. We show that both approaches describe with impressive accuracy the autocorrelation function and wavefunction up to times longer than the revival time. Moreover, in the Van Vleck approach, we can show analytically that the range of agreement extends to arbitrary long times.
Semiclassical description of multiphoton processes  [PDF]
Gerd van de Sand,Jan M Rost
Physics , 2000, DOI: 10.1103/PhysRevA.62.053403
Abstract: We analyze strong field atomic dynamics semiclassically, based on a full time-dependent description with the Hermann-Kluk propagator. From the properties of the exact classical trajectories, in particular the accumulation of action in time, the prominent features of above threshold ionization (ATI) and higher harmonic generation (HHG) are proven to be interference phenomena. They are reproduced quantitatively in the semiclassical approximation. Moreover, the behavior of the action of the classical trajectories supports the so called strong field approximation which has been devised and postulated for strong field dynamics.
Semiclassical dynamical localization and the multiplicative semiclassical propagator  [PDF]
L. Kaplan
Physics , 1998, DOI: 10.1103/PhysRevLett.81.3371
Abstract: We describe an iterative approach to computing long-time semiclassical dynamics in the presence of chaos, which eliminates the need for summing over an exponentially large number of classical paths, and has good convergence properties even beyond the Heisenberg time. Long-time semiclassical properties can be compared with those of the full quantum system. The method is used to demonstrate semiclassical dynamical localization in one-dimensional classically diffusive systems, showing that interference between classical paths is a sufficient mechanism for limiting long-time phase space exploration.
Semiclassical Green Function in Mixed Spaces  [PDF]
Guangcan Yang
Physics , 1997, DOI: 10.1103/PhysRevA.58.2600
Abstract: A explicit formula on semiclassical Green functions in mixed position and momentum spaces is given, which is based on Maslov's multi-dimensional semiclassical theory. The general formula includes both coordinate and momentum representations of Green functions as two special cases of the form.
Semiclassical description of resonant tunneling  [PDF]
E. B. Bogomolny,D. C. Rouben
Physics , 1998, DOI: 10.1209/epl/i1998-00327-4
Abstract: We derive a semiclassical formula for the tunneling current of electrons trapped in a potential well which can tunnel into and across a wide quantum well. The calculations idealize an experimental situation where a strong magnetic field tilted with respect to an electric field is used. The resulting semiclassical expression is written as the sum over special periodic orbits which hit both walls of the quantum well and are perpendicular to the first wall.
Semiclassical description of spin ladders  [PDF]
D. Senechal
Physics , 1995, DOI: 10.1103/PhysRevB.52.15319
Abstract: The Heisenberg spin ladder is studied in the semiclassical limit, via a mapping to the nonlinear $\sigma$ model. Different treatments are needed if the inter-chain coupling $K$ is small, intermediate or large. For intermediate coupling a single nonlinear $\sigma$ model is used for the ladder. Its predicts a spin gap for all nonzero values of $K$ if the sum $s+\tilde s$ of the spins of the two chains is an integer, and no gap otherwise. For small $K$, a better treatment proceeds by coupling two nonlinear sigma models, one for each chain. For integer $s=\tilde s$, the saddle-point approximation predicts a sharp drop in the gap as $K$ increases from zero. A Monte-Carlo simulation of a spin 1 ladder is presented which supports the analytical results.
Short-distance wavefunction statistics in one-dimensional Anderson localization  [PDF]
H. Schomerus,M. Titov
Physics , 2003, DOI: 10.1140/epjb/e2003-00294-0
Abstract: We investigate the short-distance statistics of the local density of states nu in long one-dimensional disordered systems, which display Anderson localization. It is shown that the probability distribution function P(nu) can be recovered from the long-distance wavefunction statistics, if one also uses parameters that are irrelevant from the perspective of two-parameter scaling theory.
Effective quantum equations for the semiclassical description of the Hydrogen atom  [PDF]
Guillermo Chacón-Acosta,Héctor H. Hernández
Physics , 2011,
Abstract: We study the Hydrogen atom as a quantum mechanical system with a Coulomb like potential, with a semiclassical approach based on an effective description of quantum mechanics. This treatment allows us to describe the quantum state of the system as a system of infinite many classical equations for expectation values of configuration variables, their moments and quantum dispersions. It also provides a semiclassical description of the orbits and the evolution of observables and spreadings and their back-reaction on the evolution.
A Semiclassical Model for Molecular Localization in Ammonia  [PDF]
Sayan Chakraborti
Physics , 2007,
Abstract: The pedagogic two stste system of the ammonia molecule is used to illustrate the phenomenon of environment induced molecular localization in pyramidal molecules. A semiclassical model is used to describe a gas of pyramidal molecules interacting via hard ball collisions. This modifies the tunnelling dynamics between the classical equilibrium configurations of an isolated molecule. For sufficiently high pressures, the model explains molecular localization in these classical configurations. The decrease in the inversion line frequency of ammonia, noted upon increase in pressure, is also studied.
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