Nonequilibrium Energy Transport Research Articles

Nonequilibrium energy transport and nonclassical correlations of photons in a two-mode circuit quantum electrodynamic system

Nonequilibrium energy transport and nonclassical correlations of photons in a two-mode circuit quantum electrodynamic system

Thermal non-equilibrium natural convection in a trapezoidal porous cavity with heated cylindrical obstacles

Thermal and flow analysis is performed for natural convection in a porous trapezoidal cavity considering a non-equilibrium thermal energy transport model. The model study comprises a partially and fully heated bottom wall while obstacles are placed inside the cavity to examine the thermal behavior. However, governing energy and momentum equations exhibit an unsteady state, but the numerical outcomes are obtained after employing the steady-state condition. The physical problem is expressed in a mathematical model and numerically simulated using the finite difference scheme. The results are presented in graphical sets, while a comparative tabular analysis with existing literature is also reported. It is demonstrated that the parameters γ and H affect thermal non-equilibrium and that the isotherms and streamlines are symmetrically distributed around the obstacles. The local Nusselt number and average Nusselt numbers show a dominant enhancement for both fluids and solid phases assisted by Rayleigh numbers while decreased with an increase in the heating domains. The reported study will be useful in analyzing the natural convection thermal non-equilibrium models in curvilinear geometries.

Anomalous thermal phenomena in a temperature biased graphene-based N/I/p-wave SC junction

We investigate the nonequilibrium energy transport across a graphene-based unconventional superconductor (SC) hybrid structure with a barrier region sandwiched between normal and superconducting regions, which is evaluated within an extended Dirac Bogoliubov-de Gennes formalism. Three different scenarios of the hybrids having p-wave triplet SCs with (i) px-, (ii) py-, and (iii) unitary chiral px + ipy-parings, are involved. Between them, the thermal conductance, asymmetric Kapitza resistance, and negative differential thermal conductance, respectively, characteristic by much different anomalous thermal properties, are uncovered. More interestingly, thermal energies Klein tunneling also turns up.

Analysis of the thermalization dynamics of two-layer thin films irradiated by femtosecond laser

In this work, ultrafast thermalization dynamics was examined for a variety of two layer-thin films (Au/Si, Au/Ni, Au/W, Au/Al and Au/Pb). Non-equilibrium energy transport under laser irradiation was formulated for the electron and lattice sub-systems of the thin films. A significant reduction in the temperature of the electron and the lattice of the gold surface was observed especially for Au/Si and Au/Ni thin films due to their large G values. Next, the effects of laser power intensity and laser heating duration on the temperature distributions were examined for Au/Ni two-layer thin film. It was found that, as the laser intensity increased, the maximum electron temperature increased dramatically; on the other hand, as the pulse heating duration increased, the electron temperature gradually decreased. It was then concluded that thermal damage threshold of the gold surface can be improved by depositing gold layer on a substrate material with high electron-phonon coupling factor. Hence the thermal failure of thin films used in optical components of ultrafast laser systems or micro/nano electro mechanical systems can be prevented.

Mean field theory of thermal energy transport in molecular junctions.

Mean field theory is applied to nonequilibrium thermal energy transport in a model molecular junction. An approximation to the total time-dependent heat current in the junction is constructed using an ensemble of Ehrenfest trajectories, and the average heat current in the steady state is obtained. The accuracy of this treatment is verified through benchmark comparisons with exact quantum mechanical results and various approximate quantum transport theories for the nonequilibrium spin-boson model. The performance of the multitrajectory Ehrenfest approach is found to be quite robust, displaying good accuracy in intermediate cases that remain elusive to many perturbative approximations and in the strong coupling limit where many methods break down. Thus, mean field theory and related trajectory-based approximate quantum dynamics methods emerge as a promising toolkit for the study of transport properties in nanoscale systems.

Generalized hydrodynamics, quasiparticle diffusion, and anomalous local relaxation in random integrable spin chains

We study the nonequilibrium dynamics of random spin chains that remain integrable (i.e., solvable via Bethe ansatz): because of correlations in the disorder, these systems escape localization and feature ballistically spreading quasiparticles. We derive a generalized hydrodynamic theory for dynamics in such random integrable systems, including diffusive corrections due to disorder, and use it to study non-equilibrium energy and spin transport. We show that diffusive corrections to the ballistic propagation of quasiparticles can arise even in noninteracting settings, in sharp contrast with clean integrable systems. This implies that operator fronts broaden diffusively in random integrable systems. By tuning parameters in the disorder distribution, one can drive this model through an unusual phase transition, between a phase where all wavefunctions are delocalized and a phase in which low-energy wavefunctions are quasi-localized (in a sense we specify). Both phases have ballistic transport; however, in the quasi-localized phase, local autocorrelation functions decay with an anomalous power law, and the density of states diverges at low energy.

Non-equilibrium energy transport and entropy production due to laser short-pulse irradiation

Laser short-pulse heating of a nano-size wire is considered and entropy generation rate is predicted during the heating pulse. The analytical solution of the heat equation is obtained using the Lie point symmetry for the laser short-pulse heating. The nano-size wire is assumed to be symmetric along its y-axis. Laser pulse intensity is considered to be Gaussian at the irradiated surface while the exponential decay of the laser pulse is incorporated in the time domain. It is found that surface temperature variation in the lattice subsystem almost follows the laser pulse intensity distribution at the surface. Entropy generation rate attains low values along the symmetry axis and it increases considerably in the region of the nano-size wire edges. This behavior is associated with the temperature gradient, which attains high values in the region close to the nano-size wire edge.

Erratum: “Curl flux, coherence, and population landscape of molecular systems: Nonequilibrium quantum steady state, energy (charge) transport, and thermodynamics” [J. Chem. Phys. 140, 245101 (2014)

Erratum: “Curl flux, coherence, and population landscape of molecular systems: Nonequilibrium quantum steady state, energy (charge) transport, and thermodynamics” [J. Chem. Phys. 140, 245101 (2014)

Non-equilibrium energy transport in a thin metallic film: Analytical solution for radiative transport equation

Non-equilibrium energy transfer in thin aluminum film is examined and analytical solution for the radiative transport equation is presented for the electron and lattice subsystems. Electron–phonon coupling is incorporated in the radiative transport equation to account for the energy exchange between the electron and the lattice sub-systems during their thermal communications. The radiative transport equations are reduced to a system of integral equations in the form of Fredholm integral equation of the second kind and they are solved analytically through the integral transformations technique. The analytical solution for temperature distribution in lattice and electron sub-systems is simulated for various film thicknesses. The analytical solution of two-equation model is also presented to compare the findings of the radiative transport in the film. The analytical solution of the radiative transport equation is validated through the numerical predictions. It is found that numerical predictions agree well with the findings of the analytical solution. Lattice site and electron temperatures obtained from the analytical solution differ from those resulted from the two-equation model for the aluminum film thickness of 0.1µm because of the ballistic behavior of the phonons emitted at high temperature edge of the film.

Curl flux, coherence, and population landscape of molecular systems: nonequilibrium quantum steady state, energy (charge) transport, and thermodynamics.

We established a theoretical framework in terms of the curl flux, population landscape, and coherence for non-equilibrium quantum systems at steady state, through exploring the energy and charge transport in molecular processes. The curl quantum flux plays the key role in determining transport properties and the system reaches equilibrium when flux vanishes. The novel curl quantum flux reflects the degree of non-equilibriumness and the time-irreversibility. We found an analytical expression for the quantum flux and its relationship to the environmental pumping (non-equilibriumness quantified by the voltage away from the equilibrium) and the quantum tunneling. Furthermore, we investigated another quantum signature, the coherence, quantitatively measured by the non-zero off diagonal element of the density matrix. Populations of states give the probabilities of individual states and therefore quantify the population landscape. Both curl flux and coherence depend on steady state population landscape. Besides the environment-assistance which can give dramatic enhancement of coherence and quantum flux with high voltage at a fixed tunneling strength, the quantum flux is promoted by the coherence in the regime of small tunneling while reduced by the coherence in the regime of large tunneling, due to the non-monotonic relationship between the coherence and tunneling. This is in contrast to the previously found linear relationship. For the systems coupled to bosonic (photonic and phononic) reservoirs the flux is significantly promoted at large voltage while for fermionic (electronic) reservoirs the flux reaches a saturation after a significant enhancement at large voltage due to the Pauli exclusion principle. In view of the system as a quantum heat engine, we studied the non-equilibrium thermodynamics and established the analytical connections of curl quantum flux to the transport quantities such as energy (charge) transfer efficiency, chemical reaction efficiency, energy dissipation, heat and electric currents observed in the experiments. We observed a perfect transfer efficiency in chemical reactions at high voltage (chemical potential difference). Our theoretical predicted behavior of the electric current with respect to the voltage is in good agreements with the recent experiments on electron transfer in single molecules.

Non-Equilibrium Heating of a Solid Surface by a Short-Pulse Laser: A Closed-Form Solution Including Thermo-Mechanical Coupling

A closed-form solution for temperature and stress fields is presented for short-pulse laser heating of the metal surface. Thermo-mechanical coupling between the heat and stress equations is incorporated in the analysis. The lattice site heat equation based on the non-equilibrium energy transport is used to account for the thermal field due to short-pulse heating. The Lie symmetry method is adopted to obtain the solution for the heat equation with the appropriate boundary conditions. In the analysis, stress wave dissipation is omitted in space due to mathematical simplifications. It is found that thermal displacement is negative in the early heating period and it becomes positive as the heating period progresses, which is attributed to thermo-mechanical coupling.

Anomalous energy transport across topological insulator superconductor junctions

We study the nonequilibrium energy transport across a topological insulator/superconductor junction, by deriving an interfacial heat current formula through scattering wave approach. Several anomalous thermal properties are uncovered, such as thermal energy's Klein tunneling, asymmetric Kapitza resistance and negative differential thermal resistance. We expect these findings could have potential applications for the energy control in various hybridized mesoscopic systems.

Phonon and electron transport in aluminum thin film: Influence of film thickness on electron and lattice temperatures

Abstract Influence of film thickness on non-equilibrium energy transport in the aluminum thin film is examined. The solutions of Boltzmann equation and the modified two-equation model are presented to predict electron and phonon temperatures in the film for various film thicknesses. It is found that electron and phonon temperatures predicted from the Boltzmann equation differ from the solution of two-equation model in the film for small film thickness. As the film thickness increases, this difference becomes negligibly small. Two-equation model predicts higher electron and phonon temperatures than those obtained from the solutions of the Boltzmann equation in the vicinity of the high temperature edge. This becomes opposite in the region of the low temperature edge.

Laser short-pulse heating of silicon-aluminum thin films

Energy transport in silicon-aluminum thin films is examined during the laser short-pulse irradiation subjected to the silicon film. The silicon film is considered to be at the top of the aluminum film. Thermal boundary resistance at the interface of the films is incorporated in the analysis. The absorption of laser radiation in the silicon and aluminum films is modeled using the transfer matrix method. Since the silicon film is dielectric, the phonon radiative transport basing the Boltzmann transport equation is incorporated to determine equivalent equilibrium temperature in the film while modified two-equation model is used to account for the non-equilibrium energy transport due to thermal separation of electron and phonon sub-systems in the aluminum film during the laser short-pulse heating process.

Thermal Boundary Resistance Effect on Non-Equilibrium Energy Transport in Metal-Dielectric Thin Films Heated by Femtosecond Pulse Lasers

The aim of this study is to investigate the effect of interfacial thermal boundary resistance (TBR) at a metal-dielectric interface on nonequilibrium energy transport in Au/SiO2 films heated by femtosecond pulse lasers. In this paper we suggest a combined set of numerical models that include the two-temperature model (TTM) for a metal side and the heat conduction equation for a dielectric layer. In addition, the TBRs between metal and nonmetal layers are calculated using thermal conductance, which is closely associated with the electron-phonon resistance and phonon-phonon resistance. Herein we present the transient and spatial distributions of TBR for a Au/SiO2 film irradiated by a 100-fs pulse laser with a 1053 nm wavelength, which are substantially affected by the phonon temperature and electron-phonon coupling. We also discuss the effect of laser fluence on the TBR and energy transport. The TBR rapidly increases the thermal conductivity at the interface, and becomes dominant at an early stage of laser irradiation over a very short period and then drastically decreases with time. Moreover, the TBR is substantially affected by the electron-phonon coupling and it should be considered for more accurate prediction of the lattice temperature drop at the interface. [doi:10.2320/matertrans.M2011021]

Comparison of Theoretical Models of Electron-Phonon Coupling in Thin Gold Films Irradiated by Femtosecond Pulse Lasers

This study reports on a comparison of theoretical models for electron-phonon coupling that is substantially associated with nonequilibrium energy transport in thin gold films irradiated by femtosecond pulse lasers. Three published electron-phonon coupling models were analyzed with the use of a well-established two-temperature model to describe non-equilibrium energy transport between electrons and phonons. Based on the numerical results, at lower fluence, all models showed nearly similar tendencies, whereas at higher fluence, constant electronphonon coupling forced unrealistically long electron-phonon equilibration times and spatially long diffusive regions as it failed to intrinsically consider the effect of a high number density of excited d-band electrons. Even at higher fluence, however, both Lin’s and Chen’s models yielded physically reasonable results, showing converging electron-phonon equilibration times and steep gradients in the spatial lattice temperature profiles at higher laser fluence. In particular, Lin’s model predicts nonlinear characteristics of heat capacity and lattice temperature with respect to laser fluence better than Chen’s model. Moreover, the electron-phonon relaxation time increased with laser fluence, whereas at laser fluence greater than 0.05 J/cm 2 , the thermal equilibrium time was nearly independent of the laser fluence. Thus, it was concluded that Lin’s model better predicted the electron-phonon coupling phenomena in thin metal films irradiated by ultra-short pulse lasers. [doi:10.2320/matertrans.M2010396]

Analytical solution for electron and lattice site temperatures due to laser-induced non-equilibrium energy transport in metals

The present study describes the modeling of short-pulse laser heating of gold and copper materials. The energy transport due to a laser short pulse is formulated using the electron kinetic theory approach. Electron and lattice temperature distributions inside the substrate material during the laser short pulse are formulated analytically. In the analysis, the Laplace transformation technique is used. The results obtained from the analytical solutions are compared with numerical predictions and experimental data. It is found that the results obtained from the numerical and analytical solutions for temperature distributions are in good agreement with the experimental data.

Non-equilibrium energy transport in nano-layer gold coating onto silica

The non-equilibrium energy transport in a metallic material with two layered structure having different material properties results in thermal separation of electrons and lattice sub-systems during a laser short-pulse irradiation. In this case, electron and lattice site temperature distributions become material properties and thickness of each layer dependent. In the present study, energy transport in a nanometer scale gold coating onto silica due to laser short-pulse irradiation is examined. The Seebeck coefficient in the gold coating is predicted and compared to the results obtained from the previous formulation. It is found that the maximum value of electron temperature in the gold coating increases with increasing coating thickness and lattice site temperature results in a peak in the silica in the region close to the coating silica interface. The Seebeck coefficient predicted agrees well with the results of the previous formulation.

Improved formulation of electron kinetic theory approach for laser shortpulse heating: Thermal stress consideration

Nonequilibrium energy transport between excited electrons and lattice site is re-formulated after considering the ballistic contribution of the electron energy to the energy transport process. The improved formulation of the electron kinetic theory predictions are compared with the previously obtained electron kinetic and two-equation models. Thermal stress developed in the region irradiated by a laser beam is formulated during the heating pulse. Copper with variable properties is used in the simulations. It is found that improved electron kinetic theory model predicts less temperature rise than that corresponding to previously formulated electron kinetic theory and two equation models in the surface region; in this case, electron temperature attains high values. Thermal stress developed is compressive and attains the maximum at some depth below the surface. The thermal stress level is well below the yielding limit of the substrate material.

Numerical Investigation of Opto-Energy Phenomena in Thin Gold Films Irradiated by Femtosecond Pulse Laser Considering Quantum Effects

Nonequilibrium energy transport and optical characteristics in thin gold film structures irradiated by a femtosecond pulse laser are examined numerically. With the use of a two-temperature model, the quantum effect is considered to determine various thermo-optical properties such as electron heat capacity, electron thermal conductivity, collision frequencies, reflectivity, and absorption rates. As a result, estimation on the electron temperature considering the quantum effect is in better agreement with measurements than those without considering quantum effect. During a femtoseond laser pulse, it is found that the electron and lattice are in nonequilibrium, the electron thermal conductivity changes rapidly with time, and reflectivity decreases substantially because of the changes in dielectric function and refractive index of gold films.