Topological analysis of chaotic transport through a ballistic atom pump

Abstract

We examine a system consisting of two reservoirs of particles connected by a channel. In the channel are two oscillating repulsive potential-energy barriers. It is known that such a system can transport particles from one reservoir to the other, even when the chemical potentials in the reservoirs are equal. We use computations and the theory of chaotic transport to study this system. Chaotic transport is described by passage around or through a heteroclinic tangle. Topological properties of the tangle are described using a generalization of homotopic lobe dynamics, which is a theory that gives some properties of intermediate-time behavior from properties of short-time behavior. We compare these predicted properties with direct computation of trajectories.

Matter, energy, and heat transfer in a classical ballistic atom pump

“…Studies that have been done in the context of mesoscopic pumps [28, 29] used a strictly quantum picture involving exchange of quasiparticles, and heat flow was shown to be outwards from the pump towards the reservoirs. The classical model discussed here is more appropriate for higher temperatures, and we show that the pump can heat or cool one or both reservoirs.Summary of results: In previous papers [26,30,31] we have shown that two-barrier pumps have the following properties when at least one barrier oscillates. (1) These so-called "quantum pumps" provide nice models of classical chaotic scattering, and their behavior is governed by a heteroclinic tangle.(2) Quantum theory shows that monoenergetic particles incident on periodically oscillating barriers have final energies equal to E n = E i + n ω, where E i is their initial energy and ω is the frequency of the pump; classical and semiclassical theories are needed to understand the range of n and the heights of the peaks.(3) Net pumping of particles from one reservoir to another can occur if monoenergetic particles approach the pump from both sides.…”

Using Invariant Manifolds to Construct Symbolic Dynamics for Three-Dimensional Volume-Preserving Maps

“…The objective of this paper is to extend the homotopic lobe dynamics approach of Refs. [9,[39][40][41][42][43]47] to continuous maps acting on a three-dimensional space. Our approach is applicable to volume-preserving maps, though volume preservation is not a requirement.…”

“…Due to the rotational symmetry, this tangle can be analyzed within a cross-sectional plane. We shall carry out this 2D analysis using the homotopic lobe dynamics technique developed previously [9,[39][40][41][42][43]47]. The present description of the 2D HLD analysis differs in some significant ways from earlier references; the purpose here is to set the stage for the 3D asymmetric case to come in Sect.…”

Ballistic atom pumps

“…However, above this range, all particles approaching from the left transmit, while some approaching from the right are trapped between the barriers until |p i | 2.5. The complete description of particle transport through the barrier region lies outside the scope of this paper, but a detailed topological analysis is given in [61]. Fig.…”