Towards a dynamical approach to the calculation of the figure of merit of thermoelectric nanoscale devices

Research on thermoelectrical energy conversion, the reuse of waste heat produced by some mechanical or chemical processes to generate electricity, has recently gained some momentum. The calculation of the electronic parameters entering the figure of merit of this energy conversion, and therefore the discovery of efficient materials, is usually performed starting from the Landauer's approach to quantum transport coupled with the Onsager's linear response theory. As it is well known, that approach suffers of certain serious drawbacks. Here, we discuss alternative dynamical methods that can go beyond the validity of the Landauer's/Onsager's approach for electronic transport. They can be used to validate the predictions of the Landauer's/Onsager's approach and to investigate systems for which that approach has shown to be unsatisfactory.Comment: 9 pages, no figures, Late

A stochastic approach to open quantum systems

Stochastic methods are ubiquitous to a variety of fields, ranging from Physics to Economy and Mathematics. In many cases, in the investigation of natural processes, stochasticity arises every time one considers the dynamics of a system in contact with a somehow bigger system, an environment, that is considered in thermal equilibrium. Any small fluctuation of the environment has some random effect on the system. In Physics, stochastic methods have been applied to the investigation of phase transitions, thermal and electrical noise, thermal relaxation, quantum information, Brownian motion etc. In this review, we will focus on the so-called stochastic Schr\"odinger equation. This is useful as a starting point to investigate the dynamics of open quantum systems capable of exchanging energy and momentum with an external environment. We discuss in some details the general derivation of a stochastic Schr\"odinger equation and some of its recent applications to spin thermal transport, thermal relaxation, and Bose-Einstein condensation. We thoroughly discuss the advantages of this formalism with respect to the more common approach in terms of the reduced density matrix. The applications discussed here constitute only a few examples of a much wider range of applicability.Comment: 43 pages, 9 figures, iopart style, published in Journal of Physics: Condensed Matte

Foundations of stochastic time-dependent current-density functional theory for open quantum systems: Potential pitfalls and rigorous results

We clarify some misunderstandings on the time-dependent current density functional theory for open quantum systems we have recently introduced [M. Di Ventra and R. D'Agosta, Phys. Rev. Lett. {\bf 98}, 226403 (2007)]. We also show that some of the recent formulations attempting to improve on this theory suffer from some inconsistencies, especially in establishing the mapping between the external potential and the quantities of interest. We offer a general argument about this mapping, showing that it must fulfill certain "dimensionality" requirements.Comment: 9 pages, Latex, no figures. arXiv admin note: substantial text overlap with arXiv:0911.393

Transport properties of a two-dimensional electron liquid at high magnetic field

The chiral Luttinger liquid model for the edge dynamics of a two-dimensional electron gas in a strong magnetic field is derived from coarse-graining and a lowest Landau level projection procedure at arbitrary filling factors $\nu<1$ -- without reference to the quantum Hall effect. Based on this model, we develop a formalism to calculate the Landauer-B\"uttiker conductances in generic experimental set-ups including multiple leads and voltage probes. In the absence of tunneling between the edges the "ideal" Hall conductances ($G_{ij}= \frac{e^2 \nu}{h}$ if lead $j$ is immediately upstream of lead $i$, and $G_{ij}=0$ otherwise) are recovered. Tunneling of quasiparticles of fractional charge $e^*$ between different edges is then included as an additional term in the Hamiltonian. In the limit of weak tunneling we obtain explicit expressions for the corrections to the ideal conductances. As an illustration of the formalism we compute the current- and temperature-dependent resistance $R_{xx}(I,T)$ of a quantum point contact localized at the center of a gate-induced constriction in a quantum Hall bar. The exponent $\alpha$ in the low-current relation $R_{xx}(I,0) \sim I^{\alpha -2}$ shows a nontrivial dependence on the strength of the inter-edge interaction, and its value changes as $e^*V_H$, where $V_H = \frac{h I}{\nu e^2}$ is the Hall voltage, falls below a characteristic crossover energy $\frac{\hbar c}{d}$, where $c$ is the edge wave velocity and $d$ is the length of the constriction. The consequences of this crossover are discussed vis-a-vis recent experiments in the weak tunneling regime.Comment: 20 pages, 8 figures, Revtex4, adjourned with referee's comments, added references and typos correcte

Relaxation in Time-Dependent Current-Density-Functional Theory

URL:http://link.aps.org/doi/10.1103/PhysRevLett.96.016405 DOI:10.1103/PhysRevLett.96.016405We apply the time-dependent current-density-functional theory to the study of the relaxation of a closed many-electron system evolving from a nonequilibrium initial state. We show that the self-consistent unitary time evolution generated by the exchange-correlation vector potential irreversibly drives the system to equilibrium. We also show that the energy dissipated in the Kohn-Sham system, i.e., the noninteracting system whose particle and current densities coincide with those of the physical system under study, is related to the entropy production in the real system.We acknowledge financial support from NSF Grant No. DMR-0313681 and the kind hospitality of the Scuola Normale Superiore in Pisa, where part of this work was completed

Temperature Dependence of the Tunneling Amplitude between Quantum Hall Edges

URL:http://link.aps.org/doi/10.1103/PhysRevLett.94.086801 DOI:10.1103/PhysRevLett.94.086801Recent experiments have studied the tunneling current between the edges of a fractional quantum Hall liquid as a function of temperature and voltage. The results of the experiment are puzzling because at “high” temperature (600-900 mK) the behavior of the tunneling conductance is consistent with the theory of tunneling between chiral Luttinger liquids, but at low temperature it strongly deviates from that prediction dropping to zero with decreasing temperature. In this Letter we suggest a possible explanation of this behavior in terms of the strong temperature dependence of the tunneling amplitude.We are grateful to S. Roddaro, V. Pellegrini, and F. Beltram for useful discussions and the use of their experimental data. We kindly acknowledge the hospitality of the Max Planck Institute for the Physics of Complex Systems in Dresden where part of this work was completed. This research was supported by NEST-INFM PRA-Mesodyf and NSF DMR-0313681. R. D'A. acknowledges the financial support by NEST-INFM PRA-Mesodyf