# Scale-invariant relaxation dynamics in two-component Bose-Einstein condensates with large particle-number imbalance

## TL;DR

This paper investigates the scale-invariant relaxation dynamics in segregating two-component Bose-Einstein condensates with large particle-number imbalance, revealing the role of droplet random walk and deriving scaling laws through simulations and analytical models.

## Contribution

It introduces a novel random walk model for droplets that explains the scale-invariant relaxation and predicts crossover phenomena in two-component Bose-Einstein condensates.

## Key findings

- Emergence of dynamical scaling in correlation functions.
- Derivation of 1/3 and 1/2 power laws for scaling exponents.
- Identification of a crossover in the scaling behavior.

## Abstract

We theoretically study the scale-invariant relaxation dynamics in segregating two-component Bose-Einstein condensates with large particle-number imbalance, and uncover that random walk of droplet for the minor component plays a fundamental role in the relaxation process. Our numerical simulations based on the binary Gross-Pitaevskii model reveal the emergence of the dynamical scaling during the relaxation, which is a hallmark of scale-invariant dynamics, in a correlation function for the minor condensate. Tracking exponents characterizing the dynamical scaling in time, we find out a crossover phenomenon that features the change in power exponents of the correlation length. To understand the fundamental mechanism inherent in the scale-invariant relaxation dynamics, we construct a random walk model for droplets. Employing the model, we analytically derive the $1/3$ and $1/2$ power laws and predict the crossover of the scaling. These exponents are in reasonable agreement with the values obtained in the numerical calculations. We also discuss a possible experimental setup for observing the scale-invariant dynamics.