arXiv subjects

A. G. Panin

Publications and source records attributed to A. G. Panin.

23 records · Page 2Linked to original sources

arXiv2009

Long quantum transition times due to unstable semiclassical dynamics

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. In addition, we show that the probability distributions over transition times have unusual asymmetric form in cases of unstable trajectories. We investigate in detail three types of processes related to unstable semiclassical dynamics. First, we analyze recently proposed mechanism of multidimensional tunneling where transitions proceed by formation and subsequent decay of classically unstable "states." The second class of processes includes one-dimensional activation transitions due to energy dispersion. In this case the semiclassical transition-time distributions have universal form. Third, we investigate long-time asymptotics of transition-time distributions in the case of over-barrier wave packet transmissions. We show that behavior of these asymptotics is controlled by unstable semiclassical trajectories which linger near the barrier top.

quant-ph↗

arXiv2009

Signatures of unstable semiclassical trajectories in tunneling

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 find an additional power-law dependence of the tunneling probability on the semiclassical parameter as compared to the standard case of potential tunneling. The second signature is substantial widening of the probability distribution over final-state quantum numbers. These effects are studied using modified semiclassical technique which incorporates stabilization of the tunneling trajectories. The technique is derived from first principles. We obtain expressions for the inclusive and exclusive tunneling probabilities in the case of unstable semiclassical trajectories. We also investigate the "phase transition" between the cases of stable and unstable trajectories across certain "critical" value of energy. Finally, we derive the relation between the semiclassical probabilities of tunneling from the low-lying and highly excited initial states. This puts on firm ground a conjecture made previously in the semiclassical description of collision-induced tunneling in field theory.

quant-ph↗

arXiv2007

Unstable Semiclassical Trajectories in Tunneling

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 suppression exponent and prefactor. We find that the instability of tunneling solutions modifies the power-law dependence of the prefactor on h as compared to the case of stable solutions.

quant-ph↗

arXiv2007

Complex trajectories in chaotic dynamical tunneling

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 classical ones. This provides a natural classification of the tunneling solutions. Second, we present a heuristic procedure for sorting out the least suppressed trajectory. As an illustration, we apply our technique to the process of chaotic tunneling in a quantum mechanical model with two degrees of freedom. Our analysis reveals rich dynamics of the system. At the classical level, there exists an infinite set of unstable solutions forming a fractal structure. This structure is inherited by the complex tunneling paths and plays the central role in the semiclassical study. The process we consider exhibits the phenomenon of optimal tunneling: the suppression exponent of the tunneling probability has a local minimum at a certain energy which is thus (locally) the optimal energy for tunneling. We test the proposed method by comparison of the semiclassical results with the results of the exact quantum computations and find a good agreement.

nlin.CD↗

arXiv2007

On the over-barrier reflection in quantum mechanics with multiple degrees of freedom

We present an analytic example of two dimensional quantum mechanical system, where the exponential suppression of the probability of over-barrier reflection changes non-monotonically with energy. The suppression is minimal at certain "optimal" energies where reflection occurs with exponentially larger probability than at other energies.

quant-ph↗