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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., 6 pages, 5 figures

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.

We study the statistical and dynamical properties of the quantum triangle map, whose classical counterpart can exhibit ergodic and mixing dynamics, but is never chaotic. Numerical results show that ergodicity is a sufficient condition for spectrum and eigenfunctions to follow the prediction of Random Matrix Theory, even though the underlying classical dynamics is not chaotic. On the other hand, dynamical quantities such as the out-of-time-ordered correlator (OTOC) and the number of harmonics, exhibit a growth rate vanishing in the semiclassical limit, in agreement with the fact that classical dynamics has zero Lyapunov exponent. Our finding show that, while spectral statistics can be used to detect ergodicity, OTOC and number of harmonics are diagnostics of chaos., 7 pages. 9 figures

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 work is a preliminary step in the understanding of statistical properties of infinite dimensional systems., 7 pages, 9 figures

The relaxation of out-of-time-ordered correlators (OTOCs) has been studied as a means to characterize the scrambling properties of a quantum system. We show that the presence of local conserved quantities typically results in, at the fastest, an algebraic relaxation of the OTOC provided (i) the dynamics is local and (ii) the system follows the eigenstate thermalization hypothesis. Our result relies on the algebraic scaling of the infinite-time value of OTOCs with system size, which is typical in thermalizing systems with local conserved quantities, and on the existence of finite speed of propagation of correlations for finite-range-interaction systems. We show that time independence of the Hamiltonian is not necessary as the above conditions (i) and (ii) can occur in time-dependent systems, both periodic or aperiodic. We also remark that our result can be extended to systems with power-law interactions.

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 non-chaotic systems [E.B. Rozenbaum et al., Phys. Rev. Lett. 125, 014101 (2020)], 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., 7 pages, 7 figures

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.

This paper shows that Onsager reciprocal relations remain valid even in presence of a generic magnetic field so that the time reversal symmetry is broken. The authors prove that breaking the time reversal symmetry does not remove the thermodynamic constraints imposed by the Onsager relations on heat to work conversion. In particular, the possibility of an engine operating at the Carnot efficiency with finite power is ruled out on purely thermodynamic grounds

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., 4+2 pages

We discuss the connection between the out-of-time-ordered correlator and the number of harmonics of the phase-space Wigner distribution function. In particular, we show that both quantities grow exponentially for chaotic dynamics, with a rate determined by the largest Lyapunov exponent of the underlying classical dynamics, and algebraically -- linearly or quadratically -- for integrable dynamics. It is then possible to use such quantities to detect in the time domain the integrability to chaos crossover in many-body quantum systems., Comment: 6 pages, 3 figures

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 cold enough temperature. For the numerically accessible chain lengths, we observe that the rectification increases with the system size. We gain insight in 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., 7 pages, 7 figures, Added 2 figures, 7 references and Appendix, Fixed typos

We study the rectification of spin current in $XXZ$ chains segmented in two parts, each with a different anisotropy parameter. Using exact diagonalization and a matrix product states 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 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 spectrum of magnon excitations between the two halves of the chain., Comment: 5 + 1 pages, 4 + 1 figures

© 2018 American Physical Society. 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.

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., Comment: 11 pages, 11 figures, added an illustrative example in two dimensions and discussed the bound on efficiency for a given cooling power

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., Comment: 6 pages, 5 figures

The time-periodic modulation of the self-interaction of a Bose--Einstein condensate or a nonlinear optics system has been recognized as an exciting tool to explore interesting physics that was previously unavailable. This tool is exploited here to examine the exotic dynamics of a nonlinear system described by the Gross--Pitaevskii equation. We observe three remarkable and closely related dynamical phenomena, exponentially localized profile of wave functions in momentum space with localization length exponentially increasing in time, exponential wave-packet spreading, and exponential sensitivity to initial conditions. A hybrid quantum-classical theory is developed to partly explain these findings. Time-periodic self-interaction modulation is seen to be a robust method to achieve superfast spreading and induce genuine chaos even in the absence of any external potential.

We study the coupled particle and energy transport in a prototype model of interacting one-dimensional system: the disordered hard-point gas, for which numerical data suggest that the thermoelectric figure of merit ZT diverges with the system size. This result is explained in terms of a microscopic mechanism, namely the local equilibrium is characterized by the emergence of a broad stationary "modified Maxwell-Boltzmann velocity distribution", of width much larger than the mean velocity of the particle flow., Comment: 18 pages, 4 figures

We discuss thermal rectification and thermoelectric energy conversion from the perspective of nonequilibrium statistical mechanics and dynamical systems theory. After preliminary considerations on the dynamical foundations of the phenomenological Fourier law in classical and quantum mechanics, we illustrate ways to control the phononic heat flow and design thermal diodes. Finally, we consider the coupled transport of heat and charge and discuss several general mechanisms for optimizing the figure of merit of thermoelectric efficiency.

We provide convincing empirical evidence that long range interactions strongly enhance the rectification effect which takes place in mass graded systems. Even more importantly the rectification does not decrease with the increase of the system size. Large rectification is obtained also for the equal mass case and with graded on-site potential. These results allow to overcome current limitations of the rectification mechanism and open the way for a realistic implementation of efficient thermal diodes., 5 pages, 6 figures

We study heat transport in a nonequilibrium steady state of a quantum interacting spin chain. We provide clear numerical evidence of the validity of Fourier law. The regime of normal conductivity is shown to set in at the transition to quantum chaos., Comment: 4 pages, 5 figures, RevTeX

We discuss the stability of quantum motion under system's perturbations in the light of the corresponding classical behavior. In particular we focus our attention on the so called "fidelity" or Loschmidt echo, its relation with the decay of correlations, and discuss the quantum-classical correspondence. We then report on the numerical simulation of the double-slit experiment, where the initial wave-packet is bounded inside a billiard domain with perfectly reflecting walls. If the shape of the billiard is such that the classical ray dynamics is regular, we obtain interference fringes whose visibility can be controlled by changing the parameters of the initial state. However, if we modify the shape of the billiard thus rendering classical (ray) dynamics fully chaotic, the interference fringes disappear and the intensity on the screen becomes the (classical) sum of intensities for the two corresponding one-slit experiments. Thus we show a clear and fundamental example in which transition to chaotic motion in a deterministic classical system, in absence of any external noise, leads to a profound modification in the quantum behavior.

We show that in an isolated model of quantum computer the residual short-range inter-qubit couplings and fluctuations in individual qubit energies can lead to quantum chaos and quantum ergodicity of eigenstates. The onset of chaos results in the interaction induced dynamical thermalization and the occupation numbers well described by the Fermi–Dirac distribution. This thermalization destroys the noninteracting qubit structure and sets serious requirements for the quantum computer operability. We also show that a quantum computer operating with a small number of qubits can simulate the dynamical localization of classical chaos in a system described by the quantum sawtooth map model. The dynamics of the system is computed efficiently up to a time t ≥ l , and then the localization length l can be obtained with accuracy ν by means of order 1/ν 2 computer runs, followed by coarse grained projective measurements on the computational basis.

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., 8 pages, 6 figures

The concept of the effective quasi-Hamiltonian of a quantum map is proposed. It is shown, using Chirikov's standard map as an example, how such a Hamiltonian is constructed in the form of a power expansion near the points of the quantum resonances. In these points, the evolution is connected to continuous gauge transformations from the unitary unimodular group. Within some domain near a resonance of the order q , the evolution turns out to be equivalent to the regular conservative motion along a circle in a ( q 2 −1)-component inhomogeneous “magnetic” field of a particle with q intrinsic degrees of freedom described by the SU ( q ) group.

We study analytically as well as numerically the dynamics of a quantum map near a quantum resonance of an order q. The map is embedded into a continuous unitary transformation generated by a time-independent quasi-Hamiltonian. Such a Hamiltonian generates at the very point of the resonance a local gauge transformation described the unitary unimodular group SU(q). The resonant energy growth of is attributed to the zero Liouville eigenmodes of the generator in the adjoint representation of the group while the non-zero modes yield saturating with time contribution. In a vicinity of a given resonance, the quasi-Hamiltonian is then found in the form of power expansion with respect to the detuning from the resonance. The problem is related in this way to the motion along a circle in a (q^2-1)-component inhomogeneous "magnetic" field of a quantum particle with $q$ intrinsic degrees of freedom described by the SU(q) group. This motion is in parallel with the classical phase oscillations near a non-linear resonance. The most important role is played by the resonances with the orders much smaller than the typical localization length, q << l. Such resonances master for exponentially long though finite times the motion in some domains around them. Explicit analytical solution is possible for a few lowest and strongest resonances., 28 pages (LaTeX), 11 ps figures, submitted to PRE

The quantum kicked rotor map is embedded into a continuous unitary transformation generated by a time-independent quasi Hamiltonian. In some vicinity of a quantum resonance of order q, we relate the problem to the regular motion along a circle in a (q(2)-1) component inhomogeneous "magnetic" field of a quantum particle with q intrinsic degrees of freedom described by the SU(q) group. This motion is in parallel with the classical phase oscillations near a nonlinear resonance.

We study fluctuations of survival probability in an open quantum system classically described by a map with a mixed phase space. Our results provide the first numerical support to theoretical predictions that such fluctuations have a fractal structure, quantitatively related to the algebraic decay of the classical survival probability.

We present numerical evidence which strongly suggests that irrational triangular billiards (all angles irrational with $\pi$) are mixing. Since these systems are known to have zero Kolmogorov-Sinai entropy, they may play an important role in understanding the statistical relaxation process., Comment: 4 pages in RevTeX with 4 eps-figures

We study quantum chaos in open dynamical systems and show that it is characterized by quantum fractal eigenstates located on the underlying classical strange repeller. The states with longest life times typically reveal a scars structure on the classical fractal set.

The statistical properties of a classical electromagnetic field in interaction with matter are numerically investigated on a one-dimensional model of a radiant cavity, conservative and with finite total energy. Our results suggest a trend towards equipartition of energy, with the relaxation times of the normal modes of the cavity increasing with the mode frequency according to a law, the form of which depends on the shape of the charge distribution., Comment: revtex, 4 pages, 3 figures, to be published in Europhys. Lett

We show that quantum effects modify the decay rate of Poincar\'e recurrences P(t) in classical chaotic systems with hierarchical structure of phase space. The exponent p of the algebraic decay P(t) ~ 1/t^p is shown to have the universal value p=1 due to tunneling and localization effects. Experimental evidence of such decay should be observable in mesoscopic systems and cold atoms., Comment: revtex, 4 pages, 4 figures

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.

We numerically analyze the transmission through a thin disordered wire of finite length attached to perfect leads, by making use of banded random Hamiltonian matrices. We compare the Landauer and the Thouless conductances, and find that they are proportional to each other in the diffusive regime, while in the localized regime the Landauer conductance is approximately proportional to the square of the Thouless one. Fluctuations of the Landauer conductance were also numerically computed; they are shown to slowly approach the theoretically predicted value., Comment: 11 latex preprint pages with 6 ps figures, to appear in Journal de Physique I, May (1997)