Related papers: Tunnelings as Catastrophes
Quantum mechanics predicts an exponentially small probability that a particle with energy greater than the height of a potential barrier will nevertheless reflect from the barrier in violation of classical expectations. This process can be…
We study the dynamics of a quantum particle in a constricted two-dimensional channel and analyze how the onset of quantum corrections impacts the (semi-)classical high-temperature behaviour, as temperature is lowered. We characterize both…
One of the most fundamental difference between classical and quantum mechanics is observed in the particle tunneling through a localized potential: the former predicts a discontinuous transmission coefficient ($T$) as a function in incident…
Following our work [Phys. Rev. Lett. 125, 020401 (2020)], we discuss a semiclassical description of one-dimensional quantum tunneling through multibarrier potentials in terms of complex time. We start by defining a complex-extended…
We study the interplay between coherent transport by tunneling and diffusive transport through classically chaotic phase-space regions, as it is reflected in the Floquet spectrum of the periodically driven quartic double well. The tunnel…
Path-integral approach in imaginary and complex time has been proven successful in treating the tunneling phenomena in quantum mechanics and quantum field theories. Latest developments in this field, the proper valley method in imaginary…
By adding generalizations involving translations, the machinery of the quantum theory of free fields leads to the semiclassical equations of motion for a charged massive particle in electromagnetic and gravitational fields. With the…
It is shown that the probability of quantum-mechanical transmission across a phase space bottleneck can be compactly approximated using an operator derived from a complex Poincar\'e return map. This result uniformly incorporates tunnelling…
In physics, one is often misled in thinking that the mathematical model of a system is part of or is that system itself. Think of expressions commonly used in physics like "point" particle, motion "on the line", "smooth" observables, wave…
The new method for the simulation of nonstationary quantum processes is proposed. The method is based on the tomography representation of quantum mechanics, {\it i.e.}, the state of the system is described by the {\it nonnegative} function…
A standard approach to analyzing tunneling processes in various physical contexts is to use instanton or imaginary time path techniques. For systems in which the tunneling takes place in a time dependent setting, the standard methods are…
We demonstrate how rate equations can be employed to find analytical expressions for the sequential tunneling current through a quantum dot as a function of the tunnel rates, for an arbitrary number of states involved. We apply this method…
The interplay between chaotic tunneling and dynamical localization in mixed phase space is investigated. Semiclassical analysis using complex classical orbits reveals that tunneling through torus regions and transport in chaotic regions are…
Any particular classical system and its quantum version are normally viewed as separate formulations that are strictly distinct. Our goal is to overcome the two separate languages and create a smooth and common procedure that provides a…
In superconducting qubits the lifetime of quantum states cannot be prolonged arbitrarily by decreasing temperature. At low temperature quasiparticles tunneling between electromagnetic environment and superconducting islands takes the…
Chaotic tunneling in a driven double-well system is investigated in absence as well as in the presence of dissipation. As the constitutive mechanism of chaos-assisted tunneling, we focus on the dynamics in the vicinity of three-level…
The problem of inter-band tunneling in a semiconductor (Zener breakdown) in a nonstationary and homogeneous electric field is solved exactly. Using the exact analytical solution, the approximation based on classical trajectories is studied.…
We examine the quantum tunneling of magnetization in molecular spin in weak interaction with a bath subject to Redfield master equation. By designing a microscopic model for a multilevel spin system using only a generic Hamiltonian and…
In this paper we show an approach to electron transport in double barrier structures which unifies the well known sequential and resonant tunneling models in the widest range of transport regimes, from completely coherent to completely…
In the well known Thom's classification, every classical catastrophe is assigned a Lyapunov function. In the one-dimensional case, due to V. I. Arnold, these functions have polynomial form $V_{(k)}(x)= x^{k+1} + c_1x^{k-1} + \ldots$. A…