An open question: Are topological arguments helpful in setting initial conditions for transport problems in condensed matter physics?

TL;DR

This paper explores the application of topological arguments to set initial conditions in transport problems within condensed matter physics, specifically using wavefunctional approaches to tunneling Hamiltonians in driven sine-Gordon systems.

Contribution

It introduces a generalized tunneling Hamiltonian framework for charge density wave transport, incorporating topological charge considerations to inform wavefunctional coefficients.

Findings

Derived I-E curves match experimental Zenier curves.

Wavefunctionals are consistent with the false vacuum hypothesis.

Open question on topological charge's role in coefficient selection.

Abstract

The tunneling Hamiltonian is a proven method to treat particle tunneling between different states represented as wavefunctions in many-body physics. Our problem is how to apply a wave functional formulation of tunneling Hamiltonians to a driven sine-Gordon system. We apply a generalization of the tunneling Hamiltonian to charge density wave (CDW) transport problems in which we consider tunneling between states that are wavefunctionals of a scalar quantum field. We present derived I-E curves that match Zenier curves used to fit data experimentally with wavefunctionals congruent with the false vacuum hypothesis. THe open question is whether the coefficients picked in both the wavefunctionals and the magnitude of the coefficents of the driven sine Gordon physical system should be picked by topological charge arguements that in principle appear to assign values that have a tie in with the false vacuum hypothesis first presented by Sidney Coleman