Time Evolution of Heat Conduction in a Generalized Model of Brownian Motion

• URL: http://arxiv.org/abs/2606.08839v1
• Date: Sun, 07 Jun 2026 21:08:47 GMT
• Title: Time Evolution of Heat Conduction in a Generalized Model of Brownian Motion
• Abstract summary: We investigate the properties of heat conduction in a network of harmonic oscillators interacting with heat baths.<n>We derive an analytical expression for the steady-state heat flow based on an extended framework of corresponding energetics.<n>We show that the heat current exhibits characteristic transient behavior when the inter-particle interaction is switched on.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We investigate the properties of heat conduction in a network of harmonic oscillators interacting with heat baths, described by a generalized model of Brownian motion. This model includes noise and dissipation terms in both the momentum and position equations. This generalization is motivated by the requirement of consistency with the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) equation. Because standard definitions of heat current based on velocity become mathematically inconsistent in this framework, we derive an analytical expression for the steady-state heat flow based on an extended framework of stochastic energetics. We confirm that Fourier's law (linear thermal response) is satisfied and that the model naturally captures microscopic thermal boundary resistance, analogous to Kapitza resistance. This demonstrates that our generalized model functions as a valid phenomenological framework for simulating non-equilibrium processes, marking a crucial step toward a unified formulation of stochastic and quantum thermodynamics. Furthermore, we analyze the time evolution of heat conduction by numerically solving the corresponding differential equations for the correlation functions. Unlike standard Brownian motion, the generalized model generates continuous and nowhere differentiable trajectories for both momentum and position (as is characteristic of overdamped dynamics). Finally, we show that the heat current exhibits characteristic transient behavior when the inter-particle interaction is switched on. Specifically, an instantaneous heat flow emerges, whose direction is strictly governed by whether the interaction is attractive or repulsive, significantly differing from the predictions of the standard model.

Related papers

• Scaled Caldeira-Leggett Dynamics: Deterministic Trajectories and the Classical Limit [0.0]
  The dynamics of an open quantum system in the high-temperature regime of the Caldeira-Leggett model is investigated.<n>The effective potential does not vanish in the classical limit and cannot, in general, be decomposed into simple additive quantum and thermal contributions.<n>As a consequence, the resulting temperature-dependent trajectories remain deterministic even in the presence of a thermal environment.
  arXiv  Detail & Related papers  (2026-08-03T10:50:58Z)
• Breakdown of Thermalization from Real-Time Dynamics in the Two-Dimensional Hubbard Model [37.56003520528009]
  Thermalization in strongly correlated fermionic systems remains a central open problem in quantum many-body physics.<n>In this work, we investigate the real-time dynamics and the approach to thermalization in the two-dimensional Hubbard model.
  arXiv  Detail & Related papers  (2026-06-03T18:00:05Z)
• Impossibility of Refrigeration and Engine Operation in Minimal Qubit Repeated-Interaction Models [39.146761527401424]
  We investigate the operation of a qubit as a quantum thermal device within the repeated interaction framework.<n>We analyze two minimal models: an alternating-coupling setup, and a simultaneous-coupling setup.<n>Our results establish fundamental limitations on qubit-based quantum thermal machines operating under Markovian repeated interactions.
  arXiv  Detail & Related papers  (2026-02-20T15:53:52Z)
• First-order friction models with bristle dynamics: lumped and distributed formulations [1.453612836743437]
  This paper introduces a class of first-order dynamic friction models that approximate the dynamics of a bristle element by inverting the friction characteristic.<n>A specific formulation closely resembling the LuGre model is derived using a simple rheological equation for the bristle element.<n>A distributed version, formulated as a hyperbolic partial differential equation (PDE), is presented, which enables the modeling of frictional processes commonly encountered in rolling contact phenomena.
  arXiv  Detail & Related papers  (2026-02-10T05:49:16Z)
• Eigenstate Thermalization Hypothesis correlations via non-linear Hydrodynamics [0.0]
  We provide a prediction for the late-time behavior of time-ordered free cumulants in the thermodynamic limit.<n>Good agreement is observed in both infinite and finite-temperature regimes.
  arXiv  Detail & Related papers  (2025-05-11T06:35:16Z)
• Equilibrium and nonequilibrium steady states with the repeated interaction protocol: Relaxation dynamics and energetic cost [44.99833362998488]
  We study the dynamics of a qubit system interacting with thermalized bath-ancilla spins via a repeated interaction scheme.<n>Our key finding is that deterministic system-ancilla interactions do not typically result in the system thermalizing to the thermal state of the ancilla.
  arXiv  Detail & Related papers  (2025-01-09T17:35:36Z)
• Quantum thermodynamics of the Caldeira-Leggett model with non-equilibrium Gaussian reservoirs [0.0]
  We introduce a non-equilibrium version of the Caldeira-Leggett model in which a quantum particle is strongly coupled to a set of engineered reservoirs. Strongly displaced/squeezed reservoirs can be used to generate an effective time dependence in the system Hamiltonian. We show the quantum-classical correspondence between the heat statistics in the non-equilibrium Caldeira-Leggett model and the statistics of a classical Langevin particle under the action of squeezed and displaced colored noises.
  arXiv  Detail & Related papers  (2024-04-30T21:41:34Z)
• Quantum Effects on the Synchronization Dynamics of the Kuramoto Model [62.997667081978825]
  We show that quantum fluctuations hinder the emergence of synchronization, albeit not entirely suppressing it. We derive an analytical expression for the critical coupling, highlighting its dependence on the model parameters.
  arXiv  Detail & Related papers  (2023-06-16T16:41:16Z)
• Photoinduced prethermal order parameter dynamics in the two-dimensional large-$N$ Hubbard-Heisenberg model [77.34726150561087]
  We study the microscopic dynamics of competing ordered phases in a two-dimensional correlated electron model. We simulate the light-induced transition between two competing phases.
  arXiv  Detail & Related papers  (2022-05-13T13:13:31Z)
• Quantum-classical correspondence principle for heat distribution in quantum Brownian motion [5.096938986357835]
  We study the heat distribution of a relaxation process in the quantum Brownian motion model. Our research brings justification for the definition of the quantum fluctuating heat via two-point measurements.
  arXiv  Detail & Related papers  (2021-11-22T15:19:49Z)
• Analog cosmological reheating in an ultracold Bose gas [58.720142291102135]
  We quantum-simulate the reheating-like dynamics of a generic cosmological single-field model in an ultracold Bose gas. Expanding spacetime as well as the background oscillating inflaton field are mimicked in the non-relativistic limit. The proposed experiment has the potential of exploring the evolution up to late times even beyond the weak coupling regime.
  arXiv  Detail & Related papers  (2020-08-05T18:00:26Z)
• Probing eigenstate thermalization in quantum simulators via fluctuation-dissipation relations [77.34726150561087]
  The eigenstate thermalization hypothesis (ETH) offers a universal mechanism for the approach to equilibrium of closed quantum many-body systems. Here, we propose a theory-independent route to probe the full ETH in quantum simulators by observing the emergence of fluctuation-dissipation relations. Our work presents a theory-independent way to characterize thermalization in quantum simulators and paves the way to quantum simulate condensed matter pump-probe experiments.
  arXiv  Detail & Related papers  (2020-07-20T18:00:02Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.