Emmanuel Pereira

Thermal rectification in quantum graded mass systems

We show the existence of thermal rectification in the graded mass quantum chain of harmonic oscillators with self-consistent reservoirs. Our analytical study allows us to identify the ingredients leading to the effect. The presence of rectification in this effective, simple model (representing graded mass materials, systems that may be constructed in practice) indicates that rectification in graded mass quantum systems may be an ubiquitous phenomenon. Moreover, as the classical version of this model does not present rectification, our results show that, here, rectification is a direct result of the quantum statistics.

Graded anharmonic crystals as genuine thermal diodes: analytical description of rectification and negative differential thermal resistance.

We address the heat flow study starting from microscopic models of matter: we develop an approach and investigate some anharmonic graded mass crystals, with weak interparticle interactions. We calculate the thermal conductivity, and show the existence of rectification and negative differential thermal resistance. Our formalism allows us to understand the mechanism behind the phenomena, and shows that the properties of graded materials make them genuine thermal diodes.

Thermal rectification in graded materials

In order to identify the basic conditions for thermal rectification we investigate a simple model with nonuniform, 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 systems size is studied.

Sufficient conditions for thermal rectification in general graded materials.

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.

Nonequilibrium statistical mechanics of anharmonic crystals with self-consistent stochastic reservoirs.

We consider a d -dimensional crystal with an arbitrary harmonic interaction and an anharmonic on-site potential, with a 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 Fouriers 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.

A representation for the generating and correlation functions in the block field renormalization group formalism and asymptotic freedom

In this work the authors obtain a representation for the generating and correlation functions of finite lattice scalar field models in Z[sup d] with action 1/2([partial derivative][phi], [partial derivative][phi]) + V([phi]). The representation is in terms of the effective action generated after n applications of the block renormalization group transformation. In the thermodynamic and n [yields] [infinity] limit for infrared asymptotic-free theories the representation for correlation functions isolates the terms which give the correct long-distance behavior and can be used to obtain the subdominant contributions. It is shown in renormalization group perturbation theory up to second order and for d large, that correlation functions are determined by the limit of field derivatives of the effective action at zero field and by a sequence of approximate wavefunction renormalization constants. It is argued that these results hold in general, not just in perturbation theory. The relation between lattice wavelets and the block renormalization group is also shown. 13 refs.

Increasing thermal rectification: effects of long-range interactions.

In this paper, we study the effects of the interparticle interaction range on heat flow. We show that, by increasing the interaction range, we may amplify the thermal conductivity and even change the regime of heat transport. More importantly, considering a crucial problem of phononics, namely, the search of a suitable thermal diode, we investigate the range effects in some graded systems in which thermal rectification is a ubiquitous phenomenon. In such graded models, we show that long-range interactions may significatively increase the rectification power and may avoid its decay with the system size, thus solving relevant problems of the usual proposals of rectifiers. Our results indicate that graded materials are genuine candidates for the actual fabrication of thermal diodes.

Orthogonality between scales and wavelets in a representation for correlation functions. The lattice dipole gas and (∇φ)4 models

Exact formulas for the correlation functions of lattice scalar field models in Zd,d⩾3, such as the dipole gas and anharmonic crystal are derived in terms of the effective action generated aftern applications of the block renormalization group transformation. Utilizing the orthogonality between different momentum scales (relations due to the wavelets implicit in the structure of the block renormalization group transformation), the formulas are quite simple, isolate the dominant term, and, in the thermodynamic andn→∞ limits, reduce the analysis to local estimates of the effective action. Based on a large-small field analysis, the two-point function is determined and it is shown how to extend the results to general correlations. The results proved here show the usefulness of the “orthogonality-of-scales” property for the study of correlation functions.

Symmetry of heat conductivity in inhomogeneous quantum chains

We address the problem of the existence of thermal rectification in inhomogeneous (in particular, graded) chains. Searching for analytical results, we investigate the symmetry properties of the thermal conductivity of the quantum inhomogeneous harmonic chain of oscillators with self-consistent reservoirs, an analytically treatable effective anharmonic model (the inner reservoirs mimic the anharmonic on-site potentials). Considering the linear response regime, i.e., for the system submitted to a small gradient of temperature, we show that, even with quantum effects in the conductivity, there is no thermal rectification. Moreover, as a secondary result, we analyze an old expression derived for the thermal conductivity of pure harmonic chains (i.e., a chain with baths at the boundaries only), and prove that there is no thermal rectification in such inhomogeneous systems, as suggested by numerical simulations in previous works.

Noise-induced bound states

Abstract We investigate the presence of two-particle bound states in the stochastic dynamics generator of weakly coupled Ginzburg–Landau models, and study their dependence on the noise strength. For the space dimension d ⩽3, by analyzing the Bethe–Salpeter equation in the ladder approximation, we show that a bound state appears but disappears again at a higher value of the noise intensity. Furthermore, we show that in the case of the polynomial interaction with a negative quartic term the bound state appears and disappears for the noise intensity much smaller than that for the interaction with the quartic term positive. We also describe the curves giving the bound states masses in terms of the noise strength, which show the effect that, for a suitable noise intensity, the two-particle bound state mass becomes smaller than the one-particle mass.