Rectification of heat current in Corbino geometry.

We prove analytically the ballistic thermal rectification effect (BTRE) in the Corbino disk characterized by an annular shape. We derive the thermal rectification efficiency (RE) and show that it can be expressed as the product of two independent functions, the first dependent on the temperatures of the heat baths and the second on the system's geometry. It follows that a perfect BTRE can be reached with the increase of the ratios of the heat baths' temperatures and of the radius of the outer edge to the inner edge of the disk. We also show that, by introducing a potential barrier into the Corbino disk, the RE can be greatly improved. Quite remarkably, by an appropriate choice of parameters, the thermal diode effect can be reversed. Our results are robust under variation of the Corbino geometry, which may provide a flexible route to manipulate the heat flow at the nanoscale.

Curvature and van der Waals interface effects on thermal transport in carbon nanotube bundles.

A van der Waals (vdW) heterostructure, can be used in efficient heat management, due to its promising anisotropic thermal transport feature, with high heat conductance in one direction and low conductance in the rest. A carbon nanotube (CNT) bundle, can be used as one of the most feasible vdW heterostructures in a wide range of nanoscale devices. However, detailed investigations of heat transport in CNT bundles are still lacking. In this paper, we study heat transport in different CNT bundles-homogeneous bundles consisting of the one CNT radius (curvature) and inhomogeneous bundles constructed from different CNTs with different curvatures. We also investigate the comparison between two possible thermostatting configurations: the two ends connected (TEC) case in which there is at least a direct covalently connected path between the hot and cold heat baths, and the one end connected (OEC) case in which the system can be divided at least into two parts, by a vdW interacting interface. Nonequilibrium molecular dynamics simulations have been carried out for a wide range of configurations and curvature differences. We find that, in homogeneous bundles, by increasing the number of outer CNTs, the heat conductance increases. In inhomogeneous bundles, the total heat flux shows dependence on the difference between the curvature of the core and outer CNTs. The less the difference between the curvature of the core and the outer CNTs, the more the thermal conductance in the system. By investigating the spectral heat conductance (SHC) in the system, we found that a larger curvature difference between the core and outer CNTs leads to a considerable decrease in the contribution of 0-10 THz phonons in the bundled zone. These results provide an insightful understanding of the heat transport mechanism in vdW nano-heterostructures, more important for designing nanoelectronic devices as well as systems in which asymmetry plays a significant role.

Autonomous circular heat engine.

A dynamical model of a highly efficient heat engine is proposed, where an applied temperature difference maintains the motion of particles around the circuit consisting of two asymmetric narrow channels, in one of which the current flows against the applied thermodynamic forces. Numerical simulations and linear-response analysis suggest that, in the absence of frictional losses, the Carnot efficiency can be achieved in the thermodynamic limit.

Sublinear diffusion in the generalized triangle map.

Diffusion of the orbits in a nonchaotic area-preserving map called a generalized triangle map (GTM) is numerically and analytically investigated. We provide accurate empirical evidence that the mean-squared displacement of the momentum for generic perturbation parameter settings increases sublinearly in time, and that the distribution of the momentum obeys a time-fractional diffusion equation. We show that the diffusion properties in the GTM do not follow any of the known stochastic processes generating sublinear diffusion since two seemingly incompatible features, non-Markovian yet stationary, coexist in the dynamics.

Classical Physics and Blackbody Radiation.

We investigate the properties of the blackbody spectrum by direct numerical solution of the classical equations of motion of a one-dimensional model that contains the essential general features of the field-matter interaction. Our results, which do not rely on any statistical assumption, show that the classical blackbody spectrum exhibits remarkable properties: (i) a quasistationary state characterized by scaling properties, (ii) consistency with the Stefan-Boltzmann law, and (iii) a high-frequency cutoff. Our Letter is a preliminary step in the understanding of statistical properties of infinite-dimensional systems.

Quantum chaos and the correspondence principle.

The correspondence principle is a cornerstone in the entire construction of quantum mechanics. This principle has been recently challenged by the observation of an early-time exponential increase of the out-of-time-ordered correlator (OTOC) in classically nonchaotic systems [E. B. Rozenbaum et al., Phys. Rev. Lett. 125, 014101 (2020)PRLTAO0031-900710.1103/PhysRevLett.125.014101]. Here, we show that the correspondence principle is restored after a proper treatment of the singular points. Furthermore, our results show that the OTOC maintains its role as a diagnostic of chaotic dynamics.

Power, efficiency, and fluctuations in steady-state heat engines.

We consider the quality factor Q, which quantifies the trade-off between power, efficiency, and fluctuations in steady-state heat engines modeled by dynamical systems. We show that the nonlinear scattering theory, in both classical and quantum mechanics, sets the bound Q=3/8 when approaching the Carnot efficiency. On the other hand, interacting, nonintegrable, and momentum-conserving systems can achieve the value Q=1/2, which is the universal upper bound in linear response. This result shows that interactions are necessary to achieve the optimal performance of a steady-state heat engine.

Inverse Currents in Hamiltonian Coupled Transport.

The occurrence of an inverse current, where the sign of the induced current is opposite to the applied force, is a highly counterintuitive phenomenon. We show that inverse currents in coupled transport (ICC) of energy and particle can occur in a one-dimensional interacting Hamiltonian system when its equilibrium state is perturbed by coupled thermodynamic forces. This seemingly paradoxical result is possible due to the self-organization occurring in the system in response to the applied forces.

Heat current rectification in segmented XXZ chains.

We study the rectification of heat current in an XXZ chain segmented in two parts. We model the effect of the environment with Lindblad heat baths. We show that in our system, rectification is large for strong interactions in half of the chain and if one bath is at a cold enough temperature. For the numerically accessible chain lengths, we observe that the rectification increases with the system size. We gain insight into the rectification mechanism by studying two-time correlations in the steady state. The presence of interactions also induces a strong nonlinear response to the temperature difference, resulting in superlinear and negative differential conductance regimes.

Thermodynamic Bound on Heat-to-Power Conversion.

In systems described by the scattering theory, there is an upper bound, lower than Carnot, on the efficiency of steady-state heat-to-work conversion at a given output power. We show that interacting systems can overcome such bound and saturate, in the thermodynamic limit, the much more favorable linear-response bound. This result is rooted in the possibility for interacting systems to achieve the Carnot efficiency at the thermodynamic limit without delta-energy filtering, so that large efficiencies can be obtained without greatly reducing power.

Perfect Diode in Quantum Spin Chains.

We study the rectification of the spin current in XXZ chains segmented in two parts, each with a different anisotropy parameter. Using exact diagonalization and a matrix product state algorithm, we find that a large rectification (of the order of 10^{4}) is attainable even using a short chain of N=8 spins, when one-half of the chain is gapless while the other has a large enough anisotropy. We present evidence of diffusive transport when the current is driven in one direction and of a transition to an insulating behavior of the system when driven in the opposite direction, leading to a perfect diode in the thermodynamic limit. The above results are explained in terms of matching of the spectrum of magnon excitations between the two halves of the chain.

Efficient thermal diode with ballistic spacer.

Thermal rectification is of importance not only for fundamental physics, but also for potential applications in thermal manipulations and thermal management. However, thermal rectification effect usually decays rapidly with system size. Here, we show that a mass-graded system, with two diffusive leads separated by a ballistic spacer, can exhibit large thermal rectification effect, with the rectification factor independent of system size. The underlying mechanism is explained in terms of the effective size-independent thermal gradient and the match or mismatch of the phonon bands. We also show the robustness of the thermal diode upon variation of the model's parameters. Our finding suggests a promising way for designing realistic efficient thermal diodes.

Minimal motor for powering particle motion from spin imbalance.

We introduce a minimalistic quantum motor for coupled energy and particle transport. The system is composed of two spins, each coupled to a different bath and to a particle which can move on a ring consisting of three sites. We show that the energy flowing from the baths to the system can be partially converted to perform work against an external driving, even in the presence of moderate dissipation. We also analytically demonstrate the necessity of coupling between the spins. We suggest an experimental realization of our model using trapped ions or quantum dots.

One-Dimensional Self-Organization and Nonequilibrium Phase Transition in a Hamiltonian System.

Self-organization and nonequilibrium phase transitions are well known to occur in two- and three-dimensional dissipative systems. Here, instead, we provide numerical evidence that these phenomena also occur in a one-dimensional Hamiltonian system. To this end, we calculate the heat conductivity by coupling the two ends of our system to two heat baths at different temperatures. It is found that when the temperature difference is smaller than a critical value, the heat conductivity increases with the system size in power law with an exponent considerably smaller than 1. However, as the temperature difference exceeds the critical value, the system's behavior undergoes a transition and the heat conductivity tends to diverge linearly with the system size. Correspondingly, an ordered structure emerges. These findings suggest a new direction for exploring the transport problems in one dimension.

Thermoelectricity of interacting particles: a numerical approach.

A method for computing the thermopower in interacting systems is proposed. This approach, which relies on Monte Carlo simulations, is illustrated first for a diatomic chain of hard-point elastically colliding particles and then in the case of a one-dimensional gas with (screened) Coulomb interparticle interaction. Numerical simulations up to N>10^{4} particles confirm the general theoretical arguments for momentum-conserving systems and show that the thermoelectric figure of merit increases linearly with the system size.

Classical dynamical localization.

We consider classical models of the kicked rotor type, with piecewise linear kicking potentials designed so that momentum changes only by multiples of a given constant. Their dynamics display quasilocalization of momentum, or quadratic growth of energy, depending on the arithmetic nature of the constant. Such purely classical features mimic paradigmatic features of the quantum kicked rotor, notably dynamical localization in momentum, or quantum resonances. We present a heuristic explanation, based on a classical phase space generalization of a well-known argument, that maps the quantum kicked rotor on a tight-binding model with disorder. Such results suggest reconsideration of generally accepted views that dynamical localization and quantum resonances are a pure result of quantum coherence.

Nonintegrability and the Fourier heat conduction law.

We study in momentum-conserving systems, how nonintegrable dynamics may affect thermal transport properties. As illustrating examples, two one-dimensional (1D) diatomic chains, representing 1D fluids and lattices, respectively, are numerically investigated. In both models, the two species of atoms are assigned two different masses and are arranged alternatively. The systems are nonintegrable unless the mass ratio is one. We find that when the mass ratio is slightly different from one, the heat conductivity may keep significantly unchanged over a certain range of the system size and as the mass ratio tends to one, this range may expand rapidly. These results establish a new connection between the macroscopic thermal transport properties and the underlying dynamics.

Nonergodicity and localization of invariant measure for two colliding masses.

We show evidence, based on extensive and carefully performed numerical experiments, that the system of two elastic hard-point masses in one dimension is not ergodic for a generic mass ratio and consequently does not follow the principle of energy equipartition. This system is equivalent to a right triangular billiard. Remarkably, following the time-dependent probability distribution in a suitably chosen velocity direction space, we find evidence of exponential localization of invariant measure. For nongeneric mass ratios which correspond to billiard angles which are rational, or weak irrational multiples of π, the system is ergodic, consistent with existing rigorous results.