Dynamics of kicked particles in a double-barrier structure

Abstract

We study the classical and quantum dynamics of periodically kicked particles placed initially within an open double-barrier structure. This system does not obey the Kolmogorov-Arnold-Moser (KAM) theorem and displays chaotic dynamics. The phase-space features induced by non-KAM nature of the system lead to dynamical features such as the nonequilibrium steady state, classically induced saturation of energy growth and momentum filtering. We also comment on the experimental feasibility of this system as well as its relevance in the context of current interest in classically induced localization and chaotic ratchets.

Eigenstate thermalization: Deutsch’s approach and beyond

“…More recently, the seminal paper by Rigol et al [26] introduced the term ETH, pinpointed its importance for thermalization, and stimulated numerous, predominantly numerical studies on the validity of ETH for a large variety of specific models (mostly spin-chain-or Hubbard-like), initial conditions (often involving some quantum quench), and observables (mainly few-body or local), see e.g. [27][28][29][30][31][32][33][34][35][36][37][38][39][40].…”

Classically induced suppression of energy growth in a chaotic quantum system

“…Suppose a particle follows a quasiperiodic orbit C 1 (μ 1 ) with winding number μ 1 before it encounters the boundary at x w and, emerges out in the region x > x w + b on an orbit C 2 (μ 2 ) with winding number μ 2 . It can be shown that as b → 0, μ 1 → μ 2 [9]. In this situation, trajectories of the particles crossing the double-barrier structure without suffering any reflection resemble the invariant tori of the corresponding standard map.…”

“…In this section, we show that, if < 1, the presence of both the KAM-type and non-KAM type classical dynamical structures in the phase space leads to saturation of the mean energy of the system [9]. Though the complete arrest of energy growth can occur only as n → ∞, the time at which the energy growth effectively saturates is finite when measured in the units of T .…”

“…, B k respectively. Depending on energy E of the particle being E > V 0 or E < V 0 , each of these k encounters could either be a reflection (sign of the momentum changes) or refraction (magnitude of the momentum changes) at B i ∈ B, i = 1, 2, ..., k. The explicit forms for the operatorsR i can be obtained from [9] and we do not pursue that in this paper.…”

“…Thus, the system is equivalent to a kicked rotor subjected to the stationary potential V sq . The dynamics of H is mainly governed by that of H 0 in addition to being subjected to the discontinuities in V sq which are incorporated through appropriate boundary conditions [9]. Going by this approach, we obtain the following map:…”