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arXiv:2409.17609 · Europhysics Letters (EPL)

Enhanced correlations due to ballistic transport

Damiano De Angelis, Jacopo De Nardis, Stefano Scopa

Published Dec 1, 2024• 1 citation
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Abstract

Abstract We investigate the nature of density-density correlations in a 1D gas of hard-core particles initially prepared at equilibrium (either at zero or finite temperature) on a semi-infinite line and subsequently let to expand into the other (initially empty) half of the system. Using a combination of analytical techniques based on exact methods and asymptotic hydrodynamic approaches, we discuss the behavior of the gas as its initial temperature varies, and back up our derivations with numerical exact diagonalization of the model. Our findings reveal that, irrespective of the initial temperature, the non-equilibrium behavior of density-density correlations at sufficiently large times is characterized by algebraic decay. Furthermore, we provide analytical results based on quantum generalized hydrodynamics that match with the numerical data both at zero and finite temperature.

DOI
10.1209/0295-5075/ad99fa

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Describing the collective behavior of many body interacting systems is a central challenge in coldatom physics. Systems confined in one dimension are particularly interesting due to the fact thatin many cases they are integrable. In this work, we focus on such systems—specifically, Bose gasessolvable via the Bethe Ansatz. We begin the thesis by preparing the background, the tools and themotivation needed in the following, inlcuding a review of the Lieb-Liniger gas, it's Bethe Ansatz andthe recent advancements in the experimental realization of it. We include a brief introduction of thetheory of Generalized Hydrodynamics as well as effective field theoretical methods, such as theLuttinger liquid theory, used to compute correlation functions in ground states of low dimensionalsystems. We then turn to the study of lattice hard core bosons out- of euqilibrium. By computing analyticalresults for the one particle density matrix of a freely expanding system of hard-core bosons from aninitial double domain wall potential we provide a fully analytical treatment of the phenomenon ofdynamical quasicondensation and discuss the emergence of off-diagonal long range order. Next, we investigate the dynamics of hard-core bosons released from a domain wall initial statein the presence of two conformal defects. The observed density profile differs from the Euler-scalehydrodynamic description due to quantum interference effects. By analyzing boson propagators, weshow that repeated scattering on the defects leads to interference patterns that cannot be capturedby the hydrodynamic approach. We derive an analytic expression for the density profile during freeexpansion and demonstrate that a modified semi-classical scattering framework is required for thedescription of systems with such conformal defects. The final part of thesis deals with the calculation of the one particle density matrix of Lieb-Lingergas in smooth trapping potentials at finite temperature and interaction strengths. We introduce amethod to obtain such correlation functions by combining long-distance asymptotics with knownshort distance expansions. For the limits of weak and strong interactions we derive analytical re-sults, as well as a general protocol for computing one-particle correlations at any arbitrary repulsiveinteraction strengths. We include a detailed explanation of the numerical method used to computeGreen's functions of field of the effective theory needed as an input to our procedure. We benchmarkour results by comparing them to exact numerical calculations and to recent experimental findings.
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