Fourier's law from a chain of coupled anharmonic oscillators under energy-conserving noise

Linear and nonlinear optical absorption coefficients in InGaN/GaN quantum wells: Interplay between intense laser field and higher-order anharmonic potentials

This computational investigation delves into the electronic and optical attributes of InGaN/GaN nanostructures subjected to both harmonic and anharmonic confinement potentials, coupled with the influence of a nonresonant intense laser field (ILF). The theoretical framework incorporates higher-order anharmonic terms, specifically quartic and sextic terms. The solutions to the Schrödinger equation have been computed employing the finite element method and the effective mass theory. Moreover, linear and third-order nonlinear optical absorption coefficients are derived via a density matrix expansion. Our analysis reveals the feasibility of manipulating electronic and optical properties by adjusting confinement potential parameters, system attributes, and laser field intensity. In addition, the ILF induces remarkable modifications, characterized by reduced resonance peak amplitudes and a blue shift in absorption coefficients. Intriguingly, regardless of potential harmonicity, the impact of incident electromagnetic intensity is notably more pronounced in the absence of the ILF. These findings hold significant promise for advancing theoretical predictions, providing valuable insights into the intricate interplay between confinement potentials, laser fields, and their effects on electronic and optical behaviors within nanostructures.

Effects of Intense Laser Field on Electronic and Optical Properties of Harmonic and Variable Degree Anharmonic Oscillators

In this paper, we calculated the electronic and optical properties of the harmonic oscillator and single and double anharmonic oscillators, including higher-order anharmonic terms such as the quartic and sextic under the non-resonant intense laser field. Calculations are made within the effective mass and parabolic band approximations. We have used the diagonalization method by choosing a wave function based on the trigonometric orthonormal functions to find eigenvalues and eigenfunctions of the electron confined within the harmonic and anharmonic oscillator potentials under the non-resonant intense laser field. A two-level approach in the density matrix expansion is used to calculate the linear and third-order nonlinear optical absorption coefficients. Our results show that the electronic and optical properties of the structures we focus on can be adjusted to obtain a suitable response to specific studies or aims by changing the structural parameters such as width, depth, coupling between the wells, and applied field intensity.

Entropy production and heat transport in harmonic chains under time-dependent periodic drivings

Using stochastic thermodynamics, the properties of interacting linear chains subject to periodic drivings are investigated. The systems are described by Fokker-Planck-Kramers equation and exact solutions are obtained as functions of the modulation frequency and strength constants. Analysis will be carried out for short and long chains. In the former case, explicit expressions are derived for a chain of two particles, in which the entropy production is written down as a bilinear function of thermodynamic forces and fluxes, whose associated Onsager coefficients are evaluated for distinct kinds of periodic drivings. The limit of long chains is analyzed by means of a protocol in which the intermediate temperatures are self-consistently chosen and the entropy production is decomposed as a sum of two individual contributions, one coming from real baths (placed at extremities of lattice) and other from self-consistent baths. Whenever the former dominates for short chains, the latter contribution prevails for long ones. The thermal reservoirs lead to a heat flux according to Fourier's law.

Heat flux direction controlled by power-law oscillators under non-Gaussian fluctuations

Chains of particles coupled through anharmonic interactions and subject to non-Gaussian baths can exhibit paradoxical outcomes such as heat currents flowing from colder to hotter reservoirs. Aiming to explore the role of generic nonharmonicities in mediating the contributions of non-Gaussian fluctuations to the direction of heat propagation, we consider a chain of power-law oscillators, with interaction potential V(x)∝|x|^{α}, subject to Gaussian and Poissonian baths at its ends. Performing numerical simulations and addressing heuristic considerations, we show that a deformable potential has bidirectional control over heat flux.

Change of entropy for the one-dimensional ballistic heat equation: Sinusoidal initial perturbation

This work presents a thermodynamic analysis of the ballistic heat equation from two viewpoints: classical irreversible thermodynamics (CIT) and extended irreversible thermodynamics (EIT). A formula for calculating the entropy within the framework of EIT for the ballistic heat equation is derived. The entropy is calculated for a sinusoidal initial temperature perturbation by using both approaches. The results obtained from CIT show that the entropy is a non-monotonic function and that the entropy production can be negative. The results obtained for EIT show that the entropy is a monotonic function and that the entropy production is nonnegative. A comparison between the entropy behaviors predicted for the ballistic, for the ordinary Fourier-based, and for the hyperbolic heat equation is made. A crucial difference of the asymptotic behavior of the entropy for the ballistic heat equation is shown. It is argued that mathematical time reversibility of the partial differential ballistic heat equation is not consistent with its physical irreversibility. The processes described by the ballistic heat equation are irreversible because of the entropy increase.

Quantum thermal transistor based on qubit-qutrit coupling

A quantum thermal transistor is designed by the strong coupling between one qubit and one qutrit which are in contact with three heat baths with different temperatures. The thermal behavior is analyzed based on the master equation by both the numerical and the approximately analytic methods. It is shown that the thermal transistor, as a three-terminal device, allows a weak modulation heat current (at the modulation terminal) to switch on and off and effectively modulate the heat current between the other two terminals. In particular, the weak modulation heat current can induce the strong heat current between the other two terminals with the multiple-region amplification of heat current. Furthermore, the heat currents are quite robust to the temperature (current) fluctuation at the lower-temperature terminal within a certain range of temperature, and so it can behave as a heat current stabilizer.

Heat transport along a chain of coupled quantum harmonic oscillators

I study the heat transport properties of a chain of coupled quantum harmonic oscillators in contact at its ends with two heat reservoirs at distinct temperatures. My approach is based on the use of an evolution equation for the density operator which is a canonical quantization of the classical Fokker-Planck-Kramers equation. I set up the evolution equation for the covariances and obtain the stationary covariances at the stationary states from which I determine the thermal conductance in closed form when the interparticle interaction is small. The conductance is finite in the thermodynamic limit implying an infinite thermal conductivity.

Role of the range of the interactions in thermal conduction

We investigate thermal transport along a one-dimensional lattice of classical inertial rotators, with attractive couplings that decrease with distance as r^{-α} (α≥0), subject at its ends to Brownian heat reservoirs at different temperatures with average value T. By means of numerical integration of the equations of motion, we show the effects of the range of the interactions in the temperature profile and energy transport and determine the domain of validity of Fourier's law in this context. We find that Fourier's law, as signaled by a finite κ in the thermodynamic limit, holds only for sufficiently short-range interactions, with α>α_{c}(T). For α<α_{c}(T), a kind of insulator behavior emerges at any T.

Nonequilibrium quantum chains under multisite Lindblad baths

We study a quantum XX chain coupled to two heat reservoirs that act on multiple sites and are kept at different temperatures and chemical potentials. The baths are described by Lindblad dissipators, which are constructed by direct coupling to the fermionic normal modes of the chain. Using a perturbative method, we are able to find analytical formulas for all steady-state properties of the system. We compute both the particle or magnetization current and the energy current, both of which are found to have the structure of Landauer's formula. We also obtain exact formulas for the Onsager coefficients. All properties are found to differ substantially from those of a single-site bath. In particular, we find a strong dependence on the intensity of the bath couplings. In the weak-coupling regime, we show that the Onsager reciprocal relations are satisfied.

Stretch diffusion and heat conduction in one-dimensional nonlinear lattices

For heat conduction in one-dimensional (1D) nonlinear Hamiltonian lattices, it has been known that conserved quantities play an important role in determining the actual heat conduction behavior. In closed or microcanonical Hamiltonian systems, the total energy and stretch are always conserved. Depending on the existence of external on-site potential, the total momentum can be conserved or not. All the momentum-conserving lattices have anomalous heat conduction except the 1D coupled rotator lattice. It was recently claimed that "whenever stretch (momentum) is not conserved in a 1D model, the momentum (stretch) and energy fields exhibit normal diffusion." The stretch in a coupled rotator lattice was also argued to be nonconserved due to the requirement of a finite partition function, which enables the coupled rotator lattice to fulfill this claim. In this work, we will systematically investigate stretch diffusion and heat conduction in terms of energy diffusion for typical 1D nonlinear lattices. Contrary to what was claimed, no clear connection between conserved quantities and heat conduction can be established. The actual situation might be more complicated than what was proposed.

Heat conduction and energy diffusion in momentum-conserving one-dimensional full-lattice ding-a-ling model

The ding-a-ling model is a kind of half lattice and half hard-point-gas (HPG) model. The original ding-a-ling model proposed by Casati et al. does not conserve total momentum and has been found to exhibit normal heat conduction behavior. Recently, a modified ding-a-ling model which conserves total momentum has been studied and normal heat conduction has also been claimed. In this work, we propose a full-lattice ding-a-ling model without hard point collisions where total momentum is also conserved. We investigate the heat conduction and energy diffusion of this full-lattice ding-a-ling model with three different nonlinear inter-particle potential forms. For symmetrical potential lattices, the thermal conductivities diverges with lattice length and their energy diffusions are superdiffusive signaturing anomalous heat conduction. For asymmetrical potential lattices, although the thermal conductivity seems to converge as the length increases, the energy diffusion is definitely deviating from normal diffusion behavior indicating anomalous heat conduction as well. No normal heat conduction behavior can be found for the full-lattice ding-a-ling model.

Thermal rectification in anharmonic chains under an energy-conserving noise

Systems in which the heat flux depends on the direction of the flow are said to present thermal rectification. This effect has attracted much theoretical and experimental interest in recent years. However, in most theoretical models the effect is found to vanish in the thermodynamic limit, in disagreement with experiment. The purpose of this paper is to show that the rectification may be restored by including an energy-conserving noise which randomly flips the velocity of the particles with a certain rate λ. It is shown that as long as λ is nonzero, the rectification remains finite in the thermodynamic limit. This is illustrated in a classical harmonic chain subject to a quartic pinning potential (the Φ(4) model) and coupled to heat baths by Langevin equations.

Temperature-dependent thermal conductivities of one-dimensional nonlinear Klein-Gordon lattices with a soft on-site potential

The temperature-dependent thermal conductivities of one-dimensional nonlinear Klein-Gordon lattices with soft on-site potential (soft-KG) are investigated systematically. Similarly to the previously studied hard-KG lattices, the existence of renormalized phonons is also confirmed in soft-KG lattices. In particular, the temperature dependence of the renormalized phonon frequency predicted by a classical field theory is verified by detailed numerical simulations. However, the thermal conductivities of soft-KG lattices exhibit the opposite trend in temperature dependence in comparison with those of hard-KG lattices. The interesting thing is that the temperature-dependent thermal conductivities of both soft- and hard-KG lattices can be interpreted in the same framework of effective phonon theory. According to the effective phonon theory, the exponents of the power-law dependence of the thermal conductivities as a function of temperature are only determined by the exponents of the soft or hard on-site potentials. These theoretical predictions are consistently verified very well by extensive numerical simulations.

Fourier's law from a chain of coupled planar harmonic oscillators under energy-conserving noise

We study the transport of heat along a chain of particles interacting through a harmonic potential and subject to heat reservoirs at its ends. Each particle has two degrees of freedom and is subject to a stochastic noise that produces infinitesimal changes in the velocity while keeping the kinetic energy unchanged. This is modeled by means of a Langevin equation with multiplicative noise. We show that the introduction of this energy-conserving stochastic noise leads to Fourier's law. By means of an approximate solution that becomes exact in the thermodynamic limit, we also show that the heat conductivity κ behaves as κ = aL/(b + λL) for large values of the intensity λ of the energy-conserving noise and large chain sizes L. Hence, we conclude that in the thermodynamic limit the heat conductivity is finite and given by κ = a/λ.