Phase diagram of the dissipative quantum particle in a box

TL;DR

This paper investigates how dissipation affects a quantum particle in a finite box, revealing a phase transition from a localized to a degenerate phase as dissipation increases, using analytical and numerical methods.

Contribution

It provides a detailed phase diagram of a dissipative quantum particle in a finite chain, highlighting the transition to a degenerate phase at high dissipation levels.

Findings

Small dissipation narrows the density distribution and shifts it to the center.

Large dissipation induces a phase transition to a doubly degenerate phase.

The study combines analytical and numerical techniques for comprehensive analysis.

Abstract

We analyze the phase diagram of a quantum particle confined to a finite chain, subject to a dissipative environment described by an Ohmic spectral function. Analytical and numerical techniques are employed to explore both the perturbative and non-perturbative regime of the model. For small dissipation the coupling to the environment leads to a narrowing of the density distribution, and to a displacement towards the center of the array of accessible sites. For large values of the dissipation, we find a phase transition to a doubly degenerate phase which reflects the formation of an inhomogeneous effective potential within the array.