# Decay of phase-imprinted dark soliton in Bose-Einstein condensate at non-zero temperature

## TL;DR

This paper investigates how dark solitons in a Bose-Einstein condensate decay at non-zero temperatures, revealing that thermal fluctuations suppress the snake instability but still lead to a power-law decay in the soliton's stability.

## Contribution

It demonstrates the decay behavior of phase-imprinted dark solitons at finite temperatures using the projected Gross-Pitaevskii equation, highlighting the influence of thermal fluctuations.

## Key findings

- Snake instability is suppressed at non-zero temperature due to thermal fluctuations.
- Decay rate follows a power-law as a function of energy.
- The overlap integral's half width remains non-zero over time.

## Abstract

We study relaxation dynamics of dark soliton, created by a phase-imprinted method, in a two-dimensional trapped Bose-Einstein condensate at non-zero temperatures by using the projected Gross-Pitaevskii equation. At absolute zero temperature, a dark soliton is known to decay with a snake instability. At non-zero temperature, as we expected, we find that this snake instability cannot be clearly seen as in the absolute zero temperature case because of the presence of thermal fluctuations. However, we find that the decay rate, the half width of the overlap integral with respect to the phase-imprinted initial state, shows a power low decay as a function of the energy and finally remains a non-zero value.