# A Chain, a Bath, a Sink and a Wall

## TL;DR

This paper studies out-of-equilibrium processes in a nonlinear chain coupled to heat and dissipation sources, revealing regimes with negative temperatures, breather-induced thermal walls, and intermittent energy flux with large deviations.

## Contribution

It uncovers the emergence of negative temperature regions and breather dynamics in a nonlinear chain under thermal and dissipative influences, highlighting new out-of-equilibrium phenomena.

## Key findings

- Temperature profiles can be non-monotonous and enter negative temperature regions.
- Discrete breathers act as thermal walls, inhibiting energy transport at higher temperatures.
- Breather lifetimes follow a stretched-exponential distribution.

## Abstract

We investigate out-of-equilibrium stationary processes emerging in a Discrete Nonlinear Schroedinger chain in contact with a heat reservoir (a bath) at temperature $T_L$ and a pure dissipator (a sink) acting on opposite edges. We observe two different regimes. For small heat-bath temperatures $T_L$ and chemical-potentials, temperature profiles across the chain display a non-monotonous shape, remain remarkably smooth and even enter the region of negative absolute temperatures. For larger temperatures $T_L$, the transport of energy is strongly inhibited by the spontaneous emergence of discrete breathers, which act as a thermal wall. A strongly intermittent energy flux is also observed, due to the irregular birth and death events of the breathers. The corresponding statistics exhibits the typical signature of rare events of processes with large deviations. In particular, the breather lifetime is found to be ruled by a stretched-exponential law.