In order to identify the basic conditions for thermal rectification we investigate a simple model with non-uniform, graded mass distribution. The existence of thermal rectification is theoretically predicted and numerically confirmed, suggesting that thermal rectification is a typical occurrence in graded systems, which are likely to be natural candidates for the actual fabrication of thermal diodes. In view of practical implications, the dependence of rectification on the asymmetry and system's size is studied. The study of the underlying dynamical mechanisms which determine the macroscopic properties of heat conduction has opened the fascinating possibility to control the heat current. In particular a model of a thermal rectifier has been proposed [1] and since then, the phenomenon of thermal rectification has been intensively investigated [2][3][4][5][6][7][8][9] in order to analyze and improve the rectification effect, including experimental realizations [10].However, as correctly pointed out in Ref.[3], most recurrent proposals of a thermal diode, based on the sequential coupling of two or three segments with different anharmonic potentials, are difficult to be experimentally implemented and the rectification power typically decays to zero with increasing the system size. In addition, most investigations so far have been based on numerical simulations and a much better theoretical understanding is highly desirable both for fundamental reasons as well as for obtaining useful hints for the actual realization of devices with satisfactory rectification power.Along these lines, graded materials are attracting more and more interest: Papers with numerical [5][6][7], analytical [8,9] and even experimental [10] studies have appeared recently in the literature.The present paper addresses the fundamental dynamical mechanisms that lead to rectification. Our strategy is to consider a simple model that contains the minimal ingredients we theoretically judge to be necessary to rectification, and compare the numerical results with the theoretical predictions. As the features of our model are also shared by more realistic models such as anharmonic chains of oscillators, we conjecture that the obtained results may have practical implications as well. Our study allows us to understand the basic ingredients behind rectification, to describe non-trivial and important properties of the heat flow, and to show that rectification in graded materials could be a ubiquitous phenomenon.We consider a chain [11] of elastically colliding particles of two kinds referred to, in the following, as "bars" L R FIG. 1: (Color online)The schematic plot of our model. Dotted lines divide elementary unit cells. In each cell there is a bar which is subjected to elastic collisions with both cell boundaries and with neighboring bullets. The first (last) cell is coupled to a heat bath at temperature τL (τR).and "bullets", respectively. (See Fig. 1.) Each bar is confined inside a cell of unit length; that is, besides elastic collisions with its neighbor...

In this work, with focus on the energy transport properties in quantum, low dimensional, graded materials, we address the investigation of the energy (and spin) current in XXZ open chains with graded inner structures and driven out of equilibrium by magnetization pumping applied at the ends. We study several types of graded structures in different situations in order to show a ubiquitous occurrence of energy rectification, even for the system under a homogeneous magnetic field. Due to technical difficulties, we carry out the computation for small chains, but we present arguments which indicate the extension of some results to larger systems. Recalling the generic existence of energy rectification in classical, graded materials, which are described by anharmonic chains of oscillators, and recalling also the anharmonicity of these XXZ models, which involve quartic terms in more transparent representation in terms of fermionic creation and annihilation operators, we may say that our results extend the ubiquity of energy rectification occurrence in classical graded materials to the case of quantum systems.

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We address a fundamental problem for the advance of phononics: the search of a feasible thermal diode. We establish sufficient conditions for the existence of thermal rectification in general graded materials. By starting from simple assumptions satisfied by the usual anharmonic models that describe heat conduction in solids, we derive an expression for the rectification. The analytical formula shows how to increase the rectification, and the conditions to avoid its decay with the system size, a problem present in the recurrent model of diodes given by the sequential coupling of two or three different parts. Moreover, for these graded systems, we show that the regimes of nondecaying rectification and of normal conductivity do not overlap. Our results indicate the graded systems as optimal materials for a thermal diode, the basic component of several devices of phononics.

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.

We consider a d-dimensional crystal with an arbitrary harmonic interaction and an anharmonic on-site potential, with stochastic Langevin heat bath at each site. We develop an integral formalism for the correlation functions that is suitable for the study of their relaxation (time decay) as well as their behavior in space. Furthermore, in a perturbative analysis, for the one-dimensional system with weak coupling between the sites and small quartic anharmonicity, we investigate the steady state and show that the Fourier's law holds. We also obtain an expression for the thermal conductivity (for arbitrary next-neighbor interactions) and give the temperature profile in the steady state.

We address the detailed study of the energy current and its components, heat and work, in the boundary-driven one-dimensional XXZ quantum model. We carry out the investigation by considering two different approaches present in the literature. First, we take the repeated interaction scheme and derive the expressions for the currents of heat and work, exchanged between system and baths. Then we perform the derivation of the energy current by means of a Lindblad master equation together with a continuity equation, another approach which is recurrently used. A comparison between the obtained expressions allows us to show the consistency of both approaches, and, in the latter expression derived from the Lindblad equation, it allows us to split the energy, which comes from the baths to the system, into heat and work. The recognition of work in the process, which is recurrently ignored in studies of transport, enables us to understand thermodynamical aspects and to solve some imbroglios in the physics behind the energy current in the XXZ spin chain.

We study the existence of bound states in the generator of the stochastic dynamics associated to weakly coupled lattice Landau-Ginzburg models. By analyzing the Bethe-Salpeter kernel in the ladder approximation, these states are shown to exist if the polynomial interaction has a negative quartic term and the lattice dimension is smaller than 3. Asymptotic values for the masses are also obtained, giving precise relaxation rates for even correlations. ͓S1063-651X͑99͒05203-4͔