Non-Fourier heat transport in metal-dielectric core-shell nanoparticles under ultrafast laser pulse excitation

Relaxation dynamics of embedded metal nanoparticles after ultrafast laser pulse excitation is driven by thermal phenomena of different origins the accurate description of which is crucial for interpreting experimental results: hot electron gas generation, electron-phonon coupling, heat transfer to the particle environment and heat propagation in the latter. Regardingthis last mechanism, it is well known that heat transport in nanoscale structures and/or at ultrashort timescales may deviate from the predictions of the Fourier law. In these cases heat transport may rather be described by the Boltzmann transport equation. We present a numerical model allowing us to determine the electron and lattice temperature dynamics in a spherical gold nanoparticle core under subpicosecond pulsed excitation, as well as that of the surrounding shell dielectric medium. For this, we have used the electron-phonon coupling equation in the particle with a source term linked with the laser pulse absorption, and the ballistic-diffusive equations for heat conduction in the host medium. Either thermalizing or adiabatic boundary conditions have been considered at the shell external surface. Our results show that the heat transfer rate from the particle to the matrix can be significantly smaller than the prediction of Fourier's law. Consequently, the particle temperature rise is larger and its cooling dynamics might be slower than that obtained by using Fourier's law. This difference is attributed to the nonlocal and nonequilibrium heat conduction in the vicinity of the core nanoparticle. These results are expected to be of great importance for analyzing pump-probe experiments performed on single nanoparticles or nanocomposite media

Asymptotic-Preserving Monte Carlo methods for transport equations in the diffusive limit

We develop a new Monte Carlo method that solves hyperbolic transport equations with stiff terms, characterized by a (small) scaling parameter. In particular, we focus on systems which lead to a reduced problem of parabolic type in the limit when the scaling parameter tends to zero. Classical Monte Carlo methods suffer of severe time step limitations in these situations, due to the fact that the characteristic speeds go to infinity in the diffusion limit. This makes the problem a real challenge, since the scaling parameter may differ by several orders of magnitude in the domain. To circumvent these time step limitations, we construct a new, asymptotic-preserving Monte Carlo method that is stable independently of the scaling parameter and degenerates to a standard probabilistic approach for solving the limiting equation in the diffusion limit. The method uses an implicit time discretization to formulate a modified equation in which the characteristic speeds do not grow indefinitely when the scaling factor tends to zero. The resulting modified equation can readily be discretized by a Monte Carlo scheme, in which the particles combine a finite propagation speed with a time-step dependent diffusion term. We show the performance of the method by comparing it with standard (deterministic) approaches in the literature

Implicit-Explicit Runge-Kutta schemes for hyperbolic systems and kinetic equations in the diffusion limit

We consider Implicit-Explicit (IMEX) Runge-Kutta (R-K) schemes for hyperbolic systems with stiff relaxation in the so-called diffusion limit. In such regime the system relaxes towards a convection-diffusion equation. The first objective of the paper is to show that traditional partitioned IMEX R-K schemes will relax to an explicit scheme for the limit equation with no need of modification of the original system. Of course the explicit scheme obtained in the limit suffers from the classical parabolic stability restriction on the time step. The main goal of the paper is to present an approach, based on IMEX R-K schemes, that in the diffusion limit relaxes to an IMEX R-K scheme for the convection-diffusion equation, in which the diffusion is treated implicitly. This is achieved by an original reformulation of the problem, and subsequent application of IMEX R-K schemes to it. An analysis on such schemes to the reformulated problem shows that the schemes reduce to IMEX R-K schemes for the limit equation, under the same conditions derived for hyperbolic relaxation. Several numerical examples including neutron transport equations confirm the theoretical analysis

Landau-Khalatnikov two-fluid hydrodynamics of a trapped Bose gas

Starting from the quantum kinetic equation for the non-condensate atoms and the generalized Gross-Pitaevskii equation for the condensate, we derive the two-fluid hydrodynamic equations of a trapped Bose gas at finite temperatures. We follow the standard Chapman-Enskog procedure, starting from a solution of the kinetic equation corresponding to the complete local equilibrium between the condensate and the non-condensate components. Our hydrodynamic equations are shown to reduce to a form identical to the well-known Landau-Khalatnikov two-fluid equations, with hydrodynamic damping due to the deviation from local equilibrium. The deviation from local equilibrium within the thermal cloud gives rise to dissipation associated with shear viscosity and thermal conduction. In addition, we show that effects due to the deviation from the diffusive local equilibrium between the condensate and the non-condensate (recently considered by Zaremba, Nikuni and Griffin) can be described by four frequency-dependent second viscosity transport coefficients. We also derive explicit formulas for all the transport coefficients. These results are used to introduce two new characteristic relaxation times associated with hydrodynamic damping. These relaxation times give the rate at which local equilibrium is reached and hence determine whether one is in the two-fluid hydrodynamic region.Comment: 26 pages, 3 postscript figures, submitted to PR