Related papers: Arnold's potentials and quantum catastrophes II
In this paper we look at transmission through one-dimensional potential barriers that are piece wise constant. The Transfer Matrix approach is adopted and a new formula is derived for multiplying long matrix sequences that not only leads to…
We present a detailed comparison of the motion of a classical and of a quantum particle in the presence of trapping sites, within the framework of continuous-time classical and quantum random walk. The main emphasis is on the qualitative…
In this paper, the asymptotic behaviors of the transition probability for two-level avoided crossings are studied under the limit where two parameters (adiabatic parameter and energy gap parameter) tend to zero. This is a continuation of…
The charging of a quantum box connected to a lead by a single-mode point contact is solved for arbitrary temperatures, tunneling amplitudes, and gate voltages, using a variant of Wilson's numerical renormalization group. The charge inside…
In this paper, we have studied the Klein's paradox in the presence of both scalar and vector potential barriers. From the corresponding Dirac equation we have calculated the transmission and reflection coefficients. It is shown that the…
We develop a new numerical scheme which allows precise solution of coherent tunneling problems, i.e., problems with exponentially small transition amplitudes between quasidegenerate states. We explain how this method works for the…
We consider the scattering of particles by an obstacle which tunnels coherently between two positions. We show that the obstacle mimics two classical scatterers at fixed positions when the kinetic energy epsilon of the incident particles is…
Gutzwiller's trace formula for the semiclassical density of states diverges at the bifurcation points of periodic orbits and has to be replaced with uniform semiclassical approximations. We present a method to derive these expressions from…
The extremely small probability of quantum tunneling through an almost classical potential barrier may become not small under the action of the specially adapted nonstationary field. The tunneling rate has a sharp peak as a function of the…
We study the interplay between an inhomogeneous quantum quench of the external potential in a system of relativistic fermions in one dimension and the well-known Klein tunneling. We find that the large time evolution is characterized by…
Anderson localization of particles -- the complete halt of wave transport through multiple scattering and phase coherence -- is a paradigmatic manifestation of quantum interference in disordered media. In three dimensions, the scaling…
We use an one dimensional model of a square barrier embedded in an infinite potential well to demonstrate that tunneling leads to a complex behavior of the wave function and that the degree of complexity may be quantified by use of the…
It was proposed recently that the Schr\"odinger wave function can be reconstructed exactly from a discrete superposition of classical action branches weighted by associated classical densities, without semiclassical approximations. We…
The addition of tunnel barriers to open chaotic systems, as well as representing more general physical systems, leads to much richer semiclassical dynamics. In particular, we present here a complete semiclassical treatment for these…
We discuss a classical reinterpretation of quantum-mechanics-based analysis of classical Markov chains with detailed balance, that is based on the quantum-classical correspondence. The classical reinterpretation is then used to demonstrate…
Through a combination of rigorous analytical derivations and extensive numerical simulations, this work reports an exotic multifractal behavior, dubbed "logarithmic multifractality", in effectively infinite-dimensional systems undergoing…
A model for quantum tunnelling of a cluster comprising A identical particles, coupled by oscillator-type potential, through short-range repulsive potential barriers is introduced for the first time in the new symmetrized-coordinate…
We study transformations of conventional (`classical') probabilities induced by context transitions. It is demonstrated that the transition from one complex of conditions to another induces a perturbation of the classical rule for the…
Certain systems with slow driving and avalanche-like dissipation events are naturally close to a critical point when the ratio of two energy scales is large. The first energy scale is the threshold above which an avalanche is triggered, the…
We present new results on quantum tunneling between deep potential wells, in the presence of a strong constant magnetic field. We construct a family of double well potentials containing examples for which the low-energy eigenvalue splitting…