Related papers: Tunnelings as Catastrophes
We use path-integrals to derive a general expression for the semiclassical approximation to the partition function of a one-dimensional quantum-mechanical system. Our expression depends solely on ordinary integrals which involve the…
We have revealed that the barrier-tunneling process in non-integrable systems is strongly linked to chaos in complex phase space by investigating a simple scattering map model. The semiclassical wavefunction reproduces complicated features…
We describe a computational investigation of tunneling at finite energy in a weakly coupled quantum mechanical system with two degrees of freedom. We compare a full quantum mechanical analysis to the results obtained by making use of a…
We adapt the semiclassical technique, as used in the context of instanton transitions in quantum field theory, to the description of tunneling transmissions at finite energies through potential barriers by complex quantum mechanical…
Process of quantum tunneling of particles in various physical systems can be effectively controlled even by a weak and slow varying in time electromagnetic signal if to adapt specially its shape to a particular system. During an…
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…
Time evolution of tunneling phenomena in medium is studied using a standard model of environment interaction. A semiclassical formula valid at low, but finite temperatures is derived in the form of integral transform for the reduced Wigner…
Based on the general form of the master equation for open quantum systems the tunneling is considered. Using the path integral technique a simple closed form expression for the tunneling rate through a parabolic barrier is obtained. The…
We study the quantum tunnel effect through a potential barrier employing a semiclassical formulation of quantum mechanics based on expectation values of configuration variables and quantum dispersions as dynamical variables. The evolution…
It was found recently that processes of multidimensional tunneling are generally described at high energies by unstable semiclassical trajectories. We study two observational signatures related to the instability of trajectories. First, we…
The time dependent density matrix of a system with potential barrier is studied using path integrals. The characterization of the initial state, which is assumed to be restricted to one side of the barrier, and the time evolution of the…
We develop the semiclassical method of complex trajectories in application to chaotic dynamical tunneling. First, we suggest a systematic numerical technique for obtaining complex tunneling trajectories by the gradual deformation of the…
We consider the problem of a semiclassical description of quantum chaotic transport, when a tunnel barrier is present in one of the leads. Using a semiclassical approach formulated in terms of a matrix model, we obtain transport moments as…
We show that the pattern of tunnelling rates can display a vivid and regular pattern when the classical dynamics is of mixed chaotic/regular type. We consider the situation in which the dominant tunnelling route connects to a stable…
Quantum transitions are described semiclassically as motions of systems along (complex) trajectories. We consider the cases when the semiclassical trajectories are unstable and find that durations of the corresponding transitions are large.…
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…
We derive a prediction of dynamical tunneling rates from regular to chaotic phase-space regions combining the direct regular-to-chaotic tunneling mechanism in the quantum regime with an improved resonance-assisted tunneling theory in the…
We use a semiclassical approximation to derive the partition function for an arbitrary potential in one-dimensional Quantum Statistical Mechanics, which we view as an example of finite temperature scalar Field Theory at a point. We rely on…
Some tunneling phenomena are described, in the semiclassical approximation, by unstable complex trajectories. We develop a systematic procedure to stabilize the trajectories and to calculate the tunneling probability, including both the…
We investigate the semiclassical mechanism of tunneling process in non-integrable systems. The significant role of complex-phase-space chaos in the description of the tunneling process is elucidated by studying a simple scattering map…