Abstract

We Study The Statistical Mechanics And The Dynamical Relaxation Process Of Modulationally Unstable One-Dimensional Quantum Droplets Described By A Modified Gross-Pitaevskii Equation. To Determine The Classical Partition Function Thereof, We Leverage The Semi-Analytical Transfer Integral Operator (TIO) Technique. The Latter Predicts A Distribution Of The Observed Wave-Function Amplitudes And Yields Two-Point Correlation Functions Providing Insights Into The Emergent Dynamics Involving Quantum Droplets. We Compare The Ensuing TIO Results With The Probability Distributions Obtained At Large Times Of The Modulationally Unstable Dynamics As Well As With The Equilibrium Properties Of A Suitably Constructed Langevin Dynamics. We Find That The Instability Leads To The Spontaneous Formation Of Quantum Droplets Featuring Multiple Collisions And Which Are Found To Coalesce At Large Evolution Times. Our Results From The Distinct Methodologies Are In Good Agreement Aside From The Case Of Low Temperatures In The Special Limit Where The Droplet Widens. In This Limit, The Distribution Acquires A Pronounced Bimodal Character, Exhibiting A Deviation Between The TIO Solution And The Langevin Dynamics.

Department(s)

Physics

Comments

Universität Hamburg, Grant PHY-2110030

International Standard Serial Number (ISSN)

2469-9934; 2469-9926

Document Type

Article - Journal

Document Version

Final Version

File Type

text

Language(s)

English

Rights

© 2024 American Physical Society, All rights reserved.

Publication Date

01 Sep 2021

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Physics Commons

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