A closed system setting for quantum thermalisation in free fermions

summary

The gist

The gist: The study investigates thermalisation and the possible occurrence of the Mpemba effect in a closed quantum setting that mimics system coupling to thermal reservoirs, finding no Mpemba

In short

The study investigates thermalization in a quantum system where a central chain is suddenly connected to two semi-infinite chains acting as thermal baths at different temperatures. Using free-fermion models (XX and transverse-field Ising), the authors show that relaxation is fully characterized analytically, confirming no Mpemba effect occurs despite non-equilibrium dynamics. This demonstrates robust thermalization without anomalous acceleration.

Key concepts

Tripartite Quench Setup: A finite central chain is suddenly coupled to two infinite chains (reservoirs) at different temperatures. This mimics a system being suddenly exposed to external thermal environments, allowing researchers to study how the central system reaches equilibrium.
Frobenius Distance: This mathematical measure quantifies the distance between the actual state of the central subsystem over time and its final, equilibrium (thermal) state. It is used as a precise tool to track how quickly and accurately the system thermalizes.
Generalised Hydrodynamics (GHD): This framework uses free-fermion properties to predict relaxation dynamics in the long-time limit. It suggests that entanglement propagates ballistically, providing analytical predictions for how the Frobenius distance evolves during thermalization.

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This episode discusses

The paper

A closed system setting for quantum thermalisation in free fermions · Read on arXiv

Purvaash Panduranghan-Udhayashankar, Filiberto Ares, Pasquale Calabrese

SISSA and INFN

DOI: 10.1088/1742-5468/aea559

Transcript

Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: I'm Kai.

Mira: And I'm Mira, here with Lev.

Kai: Today's paper: "A closed system setting for quantum thermalisation in free fermions".

Mira: The gist: The study investigates thermalisation and the possible occurrence of the Mpemba effect in a closed quantum setting that mimics system coupling to thermal reservoirs,

Kai: First, who's behind it and why it matters.

Paper summary: Kai: So to recap this paper, "A closed system setting for quantum thermalisation in free fermions", they're looking at thermalization in a closed quantum system that mimics coupling to thermal reservoirs only at its boundaries Mira

Mira: The core idea is setting up this tripartite geometry with a finite chain initially prepared at one temperature connected to two semi-infinite chains of the same type but held at different temperatures acting as baths Kai

Lev: They are testing if this setup, which acts like a temperature quench in a closed system, can lead to an Mpemba effect that we saw classically Mira

Kai: They focus on two specific models, the XX chain and the transverse-field Ising chain because they show different behavior regarding global U(one) particle-number symmetry Lev <ref:2606.06362#pg1,the XX chain and the transverse-field Ising chain>

Mira: To probe how the system relaxes, they look at the Frobenius distance between the central subsystem's time evolution and its final thermal state at bath temperature Kai

Lev: They use a specific formula for this distance that relies on two-point correlation functions because both their initial states and their total Hamiltonian are quadratic Mira

Kai: Then they apply generalized hydrodynamics to this representation to get analytical predictions for the Frobenius distance in the hydrodynamic limit Lev

Mira: The main point they're making is that they investigate if an Mpemba effect occurs in this unitary evolution, and their conclusion is that no such effect arises Kai

Conclusion: Kai: So looking at the paper, "A closed system setting for quantum thermalisation in free fermions", we see they thoroughly analyzed this tripartite quench setup for both the XX chain and the transverse-field Ising chain Mira

Mira: They concluded that despite having genuine non-equilibrium dynamics in these systems, no Mpemba effect occurs here, which is a significant finding because it rules out one possible explanation for thermalization acceleration Kai

Lev: What this means is that for these specific free-fermion models under this kind of boundary coupling, the system relaxes in a very predictable way without any weird temperature-dependent speeding up Mira

Kai: The authors also pointed out that the time to relax actually increases as the temperature difference between the central chain and its baths gets larger Lev

Mira: So they're showing that for this class of boundary driven thermalization protocols, relaxation is fully characterized analytically and doesn't exhibit any anomalous acceleration Kai

Lev: It suggests that while we can model these free systems well with hydrodynamics, the way things happen when you move to more complicated, non-integrable systems might be different Mira

Kai: The paper confirms the absence of Mpemba effect for these two models across any external magnetic field and it lays out a clear picture of how relaxation works in this specific closed geometry Lev

Mira: It's important because it gives us a solid analytical framework for understanding thermalization in these boundary-driven quantum settings, even if the result is the absence of the effect we were hoping to find Kai

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