Nonequilibrium functional renormalization group for interacting quantum systems

We propose a nonequilibrium version of functional renormalization within the Keldysh formalism by introducing a complex-valued flow parameter in the Fermi or Bose functions of each reservoir. Our cutoff scheme provides a unified approach to equilibrium and nonequilibrium situations. We apply it to nonequilibrium transport through an interacting quantum wire coupled to two reservoirs and show that the nonequilibrium occupation induces new power law exponents for the conductance.     

Gibbs–Jaynes Entropy Versus Relative Entropy

The maximum entropy formalism developed by Jaynes determines the relevant ensemble in nonequilibrium statistical mechanics by maximising the entropy functional subject to the constraints imposed by the available information. We present an alternative derivation of the relevant ensemble based on the Kullback–Leibler divergence from equilibrium. If the equilibrium ensemble is already known, then calculation of the relevant ensemble is considerably simplified. The constraints must be chosen with care in order to avoid contradictions between the two alternative derivations. The relative entropy functional measures how much a distribution departs from equilibrium. Therefore, it provides a distinct approach to the calculation of statistical ensembles that might be applicable to situations in which the formalism presented by Jaynes performs poorly (such as non-ergodic dynamical systems).     

Theoretical evidence for a reentrant phase diagram in ortho-para mixtures of solid H2 at high pressure

We develop a multiorder parameter mean-field formalism for systems of coupled quantum rotors. The scheme is developed to account for systems where ortho-para distinction is valid. We apply our formalism to solid H2 and D2. We find an anomalous reentrant orientational phase transition for both systems at thermal equilibrium. The correlation functions of the order parameter indicate short-range order at low temperatures. As the temperature is increased the correlation increases along the phase boundary. We also find that even extremely small odd-J concentrations (1%) can trigger short-range orientational ordering.     

Theory of Non-Equilibrium Heat Transport in Anharmonic Multiprobe Systems at High Temperatures

We consider the problem of heat transport by vibrational modes between Langevin thermostats connected by a central device. The latter is anharmonic and can be subject to large temperature difference and thus be out of equilibrium. We develop a classical formalism based on the equation of motion method, the fluctuation–dissipation theorem and the Novikov theorem to describe heat flow in a multi-terminal geometry. We show that it is imperative to include a quartic term in the potential energy to insure stability and to properly describe thermal expansion. The latter also contributes to leading order in the thermal resistance, while the usually adopted cubic term appears in the second order. This formalism paves the way for accurate modeling of thermal transport across interfaces in highly non-equilibrium situations beyond perturbation theory.     

Quasi-Maxwell interpretation of the spin–curvature coupling

We write the Mathisson-Papapetrou equations of motion for a spinning particle in a stationary spacetime using the quasi-Maxwell formalism and give an interpretation of the coupling between spin and curvature. The formalism is then used to compute equilibrium positions for spinning particles in the NUT spacetime. This work was partially supported by FCT/POCTI/FEDER.     

Nonequilibrium electromagnetic fluctuations: heat transfer and interactions

The Casimir force between arbitrary objects in equilibrium is related to scattering from individual bodies. We extend this approach to heat transfer and Casimir forces in nonequilibrium cases where each body, and the environment, is at a different temperature. The formalism tracks the radiation from each body and its scatterings by the other objects. We discuss the radiation from a cylinder, emphasizing its polarized nature, and obtain the heat transfer between a sphere and a plate, demonstrating the validity of proximity transfer approximation at close separations and arbitrary temperatures.     

Extremal properties of distribution function and statistical operator in equilibrium and nonequilibrium thermodynamics

It is shown that the distribution function and the statistical operator, in the case that the considered system is close to the equilibrium state, can be received by the method relying upon minimizing the information gain, which is connected with the transition of the system from a nonequilibrium state to the equilibrium state. For the systems far from equilibrium the nonequilibrium distribution function or the nonequilibrium statistical operator can be derived using a variational principle based on Jaynes' maximum entropy formalism including memory effects.     

Nonlinear transport equations in statistical mechanics

A simple projection operator method is developed for computing nonequilibrium ensemble averages for systems that are close to a state of local equilibrium. The formalism used here is a straight-forward generalization of the Mori-Zwanzig techniques used in linear response theory and it avoids many of the technical difficulties associated with time-dependent projection operators. The method is used here to derive gradient expansions for nonequibrium average values about their values in local equilibrium. This is used to derive the nonlinear hydrodynamic equations for a pure fluid, to Burnett order.     

Quantum statistical mechanics as a construction of an embedding scheme

The aim of the present paper is to show that the formalism of equilibrium quantum statistical mechanics can fully be incorporated into Ludwig's embedding scheme for classical theories in many-body quantum mechanics. A construction procedure based on a recently developed reconstruction procedure for the so-called macro-observable is presented which leads to the explicit determination of the set of classical ensembles compatible with the embedding scheme.     

Equilibrium free energies from nonequilibrium metadynamics

In this Letter we propose a new formalism to map history-dependent metadynamics in a Markovian process. We apply this formalism to model Langevin dynamics and determine the equilibrium distribution of a collection of simulations. We demonstrate that the reconstructed free energy is an unbiased estimate of the underlying free energy and analytically derive an expression for the error. The present results can be applied to other history-dependent stochastic processes, such as Wang-Landau sampling.     

On the generation and annealing of dangling bond defects in hydrogenated amorphous silicon

We show that, through the diffusive re-arrangement of Si-H bonds, the a-SiH lattice is able to establish thermal equilibrium between the densities of band tail trapped charge carriers and dangling bond defects. When this equilibrium is disturbed by changes in temperature, carrier injection or illumination, dangling bond defects have to be generated or annealed out via H-diffusion processes. Based on the concept of charge-induced bond breaking, we develop a mathematical formalism for the diffusive re-arrangement of Si-H bonds and show that our formalism can account for a variety of observations that have been made in the context of defect-generation and annealing experiments.     

Thermodynamic Formalism for Systems with Markov Dynamics

The thermodynamic formalism allows one to access the chaotic properties of equilibrium and out-of-equilibrium systems, by deriving those from a dynamical partition function. The definition that has been given for this partition function within the framework of discrete time Markov chains was not suitable for continuous time Markov dynamics. Here we propose another interpretation of the definition that allows us to apply the thermodynamic formalism to continuous time. We also generalize the formalism—a dynamical Gibbs ensemble construction—to a whole family of observables and their associated large deviation functions. This allows us to make the connection between the thermodynamic formalism and the observable involved in the much-studied fluctuation theorem. We illustrate our approach on various physical systems: random walks, exclusion processes, an Ising model and the contact process. In the latter cases, we identify a signature of the occurrence of dynamical phase transitions. We show that this signature can already be unraveled using the simplest dynamical ensemble one could define, based on the number of configuration changes a system has undergone over an asymptotically large time window.     

An approach to the nonequilibrium theory of highly excited semiconductors

We present an investigation of the optical properties of semiconductors, which are excited by a strong laser pulse. On the basis of a nonequilibrium Green's function technique (Keldysh formalism) we study the system of electrons and holes, interacting among themselves and with the exciting pulse. A set of coupled equations for the one-particle Green's function and the transverse and longitudinal polarizability is derived, which is valid for arbitrary excitation conditions. For an initially prepared state, which is not too far from a quasiequilibrium state of the excited system, the theory is elaborated in detail, using a screened Hartree-Fock approximation scheme. Within this approximation earlier results of various theoretical approaches are found to be special cases of the equilibrium limit of the present theory.     

A Time-Dependent Nonequilibrium Calculational Scheme towards the Study of Temperature Fluctuations

A new perturbative scheme for interacting nonequilibrium thermal quantum fields using thermo field dynamics is outlined by explicitly considering the temporal change of the thermal vacuum as it moves through many inequivalent state vector spaces. One is then naturally led to two sources of time dependence, one from the dynamics and the other from the change of thermal vacuum, which are taken care of by the Hamiltonian and the thermal generator, respectively. To obtain a practical scheme we restrict ourselves by the demand that a spectral representation for the full propagator exists. This leads to a time dependent temperature. The addition of a diagonalization condition for the quasi-particle Hamiltonian provides the master equation for the number density. We show that our formalism is equivalent to an extended form of the path-ordering method. This formalism is a first step towards the study of the origin of heat and temperature in high-energy heavy ion collisions.     

The Onsager-Casimir relations revisited

We study the fate of the Onsager-Casimir reciprocity relations for a continuous system when some of its variables are eliminated adiabatically. Just as for discrete systems, deviations appear in correction terms to the reduced evolution equation that are of higher order in the time scale ratio. The deviations are not removed by including correction terms to the coarse-grained thermodynamic potential. However, via a reformulation of the theory, in which the central role of the thermodynamic potential is taken over by an associated Lagrangian-type expression, we arrive at a modified form of the Onsager-Casimir relations that survives the adiabatic elimination procedure. There is a simple relation between the time evolution of the redefined thermodynamic forces and that of the basic thermodynamic variables; this relation also survives the adiabatic elimination. The formalism is illustrated by explicit calculations for the Klein-Kramers equation, which describes the phase space distribution of Brownian particles, and for the corrected Smoluchowski equation derived from it by adiabatic elimination of the velocity variable. The symmetry relation for the latter leads to a simple proof that the reality of the eigenvalues of the simple Smoluchowski equation is not destroyed by the addition of higher order corrections, at least not within the framework of a formal perturbation expansion in the time scale ratio.     

Spintronic devices as quantum networks

We explore spintronics from a quantum information (QI) perspective. We show that QI specific methods can be an effective tool in designing new devices. Using the formalism of quantum gates acting on spin and mode degrees of freedom, we provide a solution to a reverse engineering problem, namely, how to design a device performing a given transformation between input and output. Among these, we describe an orientable Stern-Gerlach device and a new scheme to entangle two spins by transferring the entanglement from orbital to spin degrees of freedom. Finally, we propose a simple scheme to produce hyperentangled electrons, i.e., particles entangled in both the spin and mode degrees of freedom.     

Anomalous sensitivity to initial conditions and entropy production in standard maps: Nonextensive approach

We perform a throughout numerical study of the average sensitivity to initial conditions and entropy production for two symplectically coupled standard maps focusing on the control-parameter region close to regularity. Although the system is ultimately strongly chaotic (positive Lyapunov exponents), it first stays lengthily in weak-chaotic regions (zero Lyapunov exponents). We argue that the nonextensive generalization of the classical formalism is an adequate tool in order to get nontrivial information about the first stage of this crossover phenomenon. Within this context we analyze the relation between the power-law sensitivity to initial conditions and the entropy production.     

Nodes versus minima in the energy gap of iron pnictide superconductors from field-induced anisotropy

We develop the formalism for computing the oscillations of the specific heat and thermal transport under rotated magnetic field in multiband superconductors with anisotropic gap and apply it to iron-based materials. We show that these oscillations change sign at low temperatures and fields, which strongly influences the experimental conclusions about the gap structure. We find that recent measurements of the specific heat oscillations indicate that the iron-based superconductors possess an anisotropic gap with deep minima or nodes close to the line connecting electron and hole pockets. We predict the behavior of the thermal conductivity that will help distinguish between these cases.     

Covariant Wigner function approach to the relativistic quantum electron gas in a strong magnetic field

This paper is concerned with a unified approach to some equilibrium properties of the relativistic quantum electron plasma embedded in a strong external magnetic field. This unified approach rests on the systematic use of a covariant Wigner function. The equilibrium Wigner function of the noninteracting gas is derived and its main properties are studied. In particular, it satisfies equations that are the complete analog of the usual Liouville equation and thus can be termed “relativistic quantum Liouville equation” whose properties are considered. The equations of state are rederived in this formalism and the results obtained earlier by Canuto and Chiu are found anew. Also, the covariant Wigner funetion of the magnetized vacuum is derived: it is needed, in this formalism, in order to obtain, e.g., the vacuum polarization tensor. Since we are also interested in the plasma modes, the fluctuations of one-particle quantities—and their spectrum—(in particular, of the four current) are calculated in view of their use in the fluctuation-dissipation theorem. We also outline a microscopic proof of this theorem, on the basis of a BBGKY hierarchy for the covariant Wigner functions, and point out the existence of an effective plasma frequency.