arXiv subjects

Jianjun Dong

Publications and source records attributed to Jianjun Dong.

3 recordsLinked to original sources

arXiv2025

Unified Statistical Theory of Heat Conduction in Nonuniform Media

Using the Zwanzig projection-operator formalism, we derive a causal two-point spatiotemporal kernel for heat conduction, defined microscopically as a space-resolved equilibrium heat-flux time-correlation function, that encodes temporal memory, spatial nonlocality, and material heterogeneity on equal footing. Classical diffusion, nonlocal transport, and hydrodynamic models emerge as controlled asymptotic limits of this kernel, providing a unified constitutive description across diffusive, quasi-ballistic, and hydrodynamic regimes. Interfacial heat transfer is incorporated through a spatially resolved kernel formulation, in which the conventional Kapitza resistance arises as a coarse-grained limit. The kernel admits a spatiotemporal Green--Kubo representation and can, in principle, be evaluated from atomistic simulations for bulk media, providing a direct connection between microscopic dynamics and continuum transport without empirical closure. For crystalline solids, we derive explicit kernel forms in the hydrodynamic and attenuated-streaming limits and introduce a hybrid reduction that captures the coexistence of collective and quasi-ballistic transport. For disordered harmonic solids, the framework recovers a spatial diffusion kernel consistent with the Allen--Feldman limit. To illustrate the theory, we construct the kernel for silicon at room temperature within the relaxation-time approximation and apply it to transient thermal grating configurations. Spatial nonlocality associated with the phonon mean-free-path distribution is the primary source of deviation from Fourier transport under these conditions, while temporal memory mainly influences short-time dynamics. These findings identify the spatiotemporal kernel as a unifying constitutive descriptor whose coarse-grained limits recover conventional transport coefficients.

cond-mat.mtrl-sci↗

arXiv2024

Theory of Transient Heat Conduction

Ultrafast and nanoscale heat conduction demands a unified theoretical framework that rigorously bridges macroscopic transport equations with microscopic material properties derived from statistical physics.Existing empirical generalizations of Fourier's law often lack a solid microscopic foundation, failing to connect observed non-Fourier behavior with underlying atomic scale mechanisms. In this work, we present a time-domain theory of transient heat conduction rooted in Zwanzig's statistical theory of irreversible processes. Central to this framework is the time-domain transport function, Z(t), defined through equilibrium time-correlation functions of heat fluxes. This function generalizes the conventional concept of steady-state thermal conductivity, governing the transition of conduction dynamics from onset second sound type wave propagation at finite speeds to diffusion-dominated behavior across broad temporal and spatial scales. Unlike phonon hydrodynamic models that rely on mesoscopic constructs such as phonon drift velocity, our approach provides a quantitative and microscopic description of intrinsic memory effects in transient heat fluxes and applies universally to bulk materials at any temperature or length scale. By integrating atomistic-scale first-principles calculations with continuum-level macroscopic equations, this framework offers a robust foundation for numerical simulations of transient temperature fields. Furthermore, it facilitates the interpretation and design of transient thermal grating experiments using nanometer-scale heat sources and ultrafast laser systems in the extreme ultraviolet and x-ray wavelength ranges, advancing our understanding of heat dissipation dynamics.

cond-mat.mtrl-sci↗

arXiv2018

The Fokker-Planck Equation for Lattice Vibration: Stochastic Dynamics and Thermal Conductivity

We propose a Fokker-Planck equation (FPE) theory to describe stochastic fluctuation and relaxation processes of lattice vibration at a wide range of conditions, including those beyond the phonon gas (PG) limit. Using the time-dependent, multiple state-variable probability function of a FPE, we first derive time-correlation functions of lattice heat currents in terms of correlation functions among multiple vibrational modes, and subsequently predict the thermal conductivity based on the Green-Kubo formalism. When the kinetic transport theories are valid, this FPE not only predicts a thermal conductivity that is identical to the one predicted by the phonon Boltzmann transport equation, but also provides additional microscopic details on the multiple-mode correlation functions. More importantly, when the kinetic theories become insufficient due to the breakdown of the PG approximation, this FPE theory remains valid to study the correlation functions among vibrational modes in highly anharmonic lattices with significant mode-mode interactions and/or in disordered lattices with strongly localized modes. At the limit of weak mode-mode interactions, we can adopt quantum perturbation theories to derive the drift/diffusion coefficients based on the anharmonicity data derived from first-principles methods. As temperature elevates to the classical regime, we can perform molecular dynamics simulations to directly compute the coefficients. Because these coefficients are defined as ensemble averages at the short time limit, we can implement massive parallel simulation algorithms to take full advantage of the paralleled high-performance computing platforms. A better understanding of the temperature-dependent coefficients up to melting temperatures will provide new insights on microscopic mechanisms that govern the heat conduction through anharmonic and/or disordered lattices beyond the PG model.

cond-mat.stat-mech↗