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The macroscopic hydrodynamic equations are derived for many-body systems in the local-equilibrium approach, using the Schr\"odinger picture of quantum mechanics. In this approach, statistical operators are defined in terms of microscopic densities associated with the fundamentally conserved quantities and other slow modes possibly emerging from continuous symmetry breaking, as well as macrofields conjugated to these densities. Functional identities can be deduced, allowing us to identify the reversible and dissipative parts of the mean current densities, to obtain general equations for the time evolution of the conjugate macrofields, and to establish the relationship to projection-operator methods. The entropy production is shown to be nonnegative by applying the Peierls-Bogoliubov inequality to a quantum integral fluctuation theorem. Using the expansion in the gradients of the conjugate macrofields, the transport coefficients are given by Green-Kubo formulas and the entropy production rate can be expressed in terms of quantum Einstein-Helfand formulas, implying its nonnegativity in agreement with the second law of thermodynamics. The results apply to multicomponent fluids and can be extended to condensed matter phases with broken continuous symmetries.

For the statistics of currents in quantum transport, microreversibility is shown to provide a way to obtain the statistical cumulants at the order n+1 from the measurement of the cumulants at the order n or lower. This fundamental result is based on relations generalizing the fluctuation-dissipation theorem and the Onsager-Casimir reciprocal relations from linear toward nonlinear transport properties, as a consequence of the time-reversal symmetry of the underlying microscopic Hamiltonian dynamics. The method is demonstrated in detail in the case of multiterminal Aharonov-Bohm rings. Within the independent electron approximation, the cumulant generating function, which fully specifies the statistics of the nonequilibrium currents, is obtained from the scattering matrix of these circuits. The time-reversal symmetry relations are explicitly shown to express the cumulants at equilibrium up to the fourth order in terms of lower-order cumulants and their nonequilibrium responses in the presence of an external magnetic field.

A stochastic approach for charge transport in diodes is developed in consistency with the laws of electricity, thermodynamics, and microreversibility. In this approach, the electron and hole densities are ruled by diffusion-reaction stochastic partial differential equations and the electric field generated by the charges is determined with the Poisson equation. These equations are discretized in space for the numerical simulations of the mean density profiles, the mean electric potential, and the current-voltage characteristics. Moreover, the full counting statistics of the carrier current and the measured total current including the contribution of the displacement current are investigated. On the basis of local detailed balance, the fluctuation theorem is shown to hold for both currents.

In biology, template-directed copolymerization is the fundamental mechanism responsible for the synthesis of DNA, RNA, and proteins. More than 50 years have passed since the discovery of DNA structure and its role in coding genetic information. Yet, the kinetics and thermodynamics of information processing in DNA replication, transcription, and translation remain poorly understood. Challenging issues are the facts that DNA or RNA sequences constitute disordered media for the motion of polymerases or ribosomes while errors occur in copying the template. Here, it is shown that these issues can be addressed and sequence heterogeneity effects can be quantitatively understood within a framework revealing universal aspects of information processing at the molecular scale. In steady growth regimes, the local velocities of polymerases or ribosomes along the template are distributed as the continuous or fractal invariant set of a so-called iterated function system, which determines the copying error probabilities. The growth may become sublinear in time with a scaling exponent that can also be deduced from the iterated function system.

Studies of phase transitions under pressure usually assume perfect hydrostatic conditions but it is far from being true in practice. Theoretical calculations based on a tight-binding model prove that nonhydrostatic conditions can significantly reduce the Si II to Si XI transition pressure. This distortion induced by nonhydrostaticity was already observed in high-pressure experiments (in the case of GaSb and InSb), and so this work is the theoretical confirmation of the possibility of such a phenomenon.

The local atomic order of semiconducting liquid GeTe is studied using first-principles molecular-dynamics simulations. Our work points out a high degree of alternating chemical order in the liquid and demonstrates the presence of a Peierls distortion close above the melting temperature. This distortion, absent in the high temperature crystalline structure of NaCl type, is a remnant of the atomic arrangement in the $A7$ low temperature crystalline phase. It disappears slowly with temperature, as the liquid evolves from a semiconducting to a metallic state.

We report a study of solutions of the defocusing nonlinear Schrodinger equation in a spatially periodic potential. The ground-state solution and the steady flows of the system are studied analytically. Above a critical current, a steady state no longer exists and time-dependent solutions are generated, which are numerically simulated and described.

The Mossbauer spectra of amorphous iron, prepared by using sonochemical methods, exhibit a broad magnetic hyperfine sextet at both 78 and 295 K. The spectra do not change with time if the amorphous iron is not exposed to oxygen or moisture. An analysis of the spectra with the method of Lines and Eibschutz yields average magnetic hyperfine fields of 29.1 and 25.9 T at 78 and 295 K, respectively. The corresponding moments of 1.9 mu(B), and 1.7 mu(B), agree well with values obtained from earlier magnetization studies and, further, provide strong experimental support for earlier calculations of the magnetic moments in amorphous iron. The observed average isomer shifts of 0.27 and 0.14 mm/s obtained at 78 and 295 K, respectively, correspond to a decrease in the s-electron density at the iron-57 nucleus as compared to that of alpha-iron, a decrease which is consistent with the decreased coordination number of amorphous iron. The similarity of the 295 K iron K-edge x-ray-absorption spectrum of amorphous iron and alpha-iron, up to 7130 eV, indicates that the d-electron density of states just above the Fermi level is similar in both forms of iron. The absence of structural details above 7130 eV in the spectrum of amorphous iron indicates, in agreement with multiple-scattering calculations, that long-range order does not extend beyond the third shell of neighbors in amorphous iron. Greatly reduced extended x-ray-absorption-fine-structure scattering is observed at the iron K edge of amorphous iron as compared to alpha-iron. An analysis of the weak observed scattering reveals both a decrease in the average coordination number from 14 in alpha-iron to 10 in amorphous iron, and an asymmetric radial distribution function of the iron neighbors in the first shell. This asymmetric distribution yields for amorphous iron a minimum iron-iron distance of 2.40 Angstrom and an average iron-iron distance of 2.92 Angstrom. [S0163-1829(98)08817-1].

Hydrodynamic modes of diffusion and the corresponding nonequilibrium steady states are studied as an eigenvalue problem for the Liouvillian dynamics of spatially extended suspension flows which are special continuous-time dynamical systems including billiards defined on the basis of a mapping. The infinite spatial extension is taken into account by spatial Fourier transforms which decompose the observables and probability densities into sectors corresponding to the different values of the wave number. The Frobenius-Perron operator ruling the time evolution in each wave number sector is reduced to a Frobenius-Perron operator associated with the mapping of the suspension flow. In this theory, the dispersion relation of diffusion is given as a Pollicott-Ruelle resonance of the Frobenius-Perron operator and the corresponding eigenstates are studied. Formulas are derived for the diffusion and the Burnett coefficients in terms of the mapping of the suspension flow. Nonequilibrium steady states are constructed on the basis of the eigenstates and are given by mathematical distributions without density functions, also referred to as singular measures. The nonequilibrium steady states are shown to obey Fick's law and to be related to Zubarev's local integrals of motion. The theory is applied to the regular Lorentz gas with a finite horizon. Generalizations to the nonequilibrium steady states associated with the other transport processes are also obtained.

The chaotic scattering theory is here extended to obtain escape-rate expressions for the transport coefficients appropriate for a simple classical fluid, or for a chemically reacting system. This theory allows various transport coefficients such as the coefficients of viscosity, thermal conductivity, etc., to be expressed in terms of the positive Lyapunov exponents and Kolmogorov-Sinai entropy of a set of phase space trajectories that take place on an appropriate fractal repeller. This work generalizes the previous results of Gaspard and Nicolis for the coefficient of diffusion of a particle moving in a fixed array of scatterers., Comment: 27 pages LaTeX, no figures

The structure of liquid and amorphous selenium has been investigated by a Monte Carlo computer simulation. The semiempirical model relies upon a tight-binding approximation of the cohesive energy. The excellent agreement of the pair correlation functions and structure factors computed at different temperatures with the experiments allows a detailed analysis of the structures. The fraction of twofold-coordinated atoms never exceeds 70%. This implies that, contrary to commonly reported ideas, the chains have to be quite short, of the order of five bonds per chain, forming a highly connected network.

Relaxation processes in collisionless dynamics lead to peculiar behavior in systems with long-range interactions such as self-gravitating systems, non-neutral plasmas, and wave-particle systems. These systems, adequately described by the Vlasov equation, present quasistationary states (QSS), i.e., long lasting intermediate stages of the dynamics that occur after a short significant evolution called ``violent relaxation.'' The nature of the relaxation, in the absence of collisions, is not yet fully understood. We demonstrate in this article the occurrence of stretching and folding behavior in numerical simulations of the Vlasov equation, providing a plausible relaxation mechanism that brings the system from its initial condition into the QSS regime. Area-preserving discrete-time maps with a mean-field coupling term are found to display a similar behavior in phase space as the Vlasov system.

The counting statistics of electron transport is theoretically studied in a system with two capacitively coupled parallel transport channels. Each channel is composed of a quantum dot connected by tunneling to two reservoirs. The nonequilibrium steady state of the system is controlled by two affinities or thermodynamic forces, each one determined by the two reservoirs of each channel. The status of a single-current fluctuation theorem is investigated starting from the fundamental two-current fluctuation theorem, which is a consequence of microreversibility. We show that the single-current fluctuation theorem holds in the limit of a large Coulomb repulsion between the two parallel quantum dots, as well as in the limit of a large current ratio between the parallel channels. In this latter limit, the symmetry relation of the single-current fluctuation theorem is satisfied with respect to an effective affinity that is much lower than the affinity determined by the reservoirs. This back-action effect is quantitatively characterized., Comment: 15 pages, 9 figures

The effect of ultrafast diffusion is studied on reaction-diffusion processes in heterogeneous media, as encountered in catalysis and field emission microscopy. The reaction-diffusion equations describe adsorption, desorption, and reaction processes for two adspecies, for instance, on a paraboloidal heterogeneous surface in the presence of an external electric field. Using multiscale analysis, we show that the fast adspecies rapidly reaches a quasiequilibrium spatial distribution, characterized by a nonequilibrium chemical potential of the fast adspecies. An ordinary differential equation is derived for the time evolution of the nonequilibrium chemical potential. Numerical simulations are performed under different conditions, which confirm the convergence of the dynamics for finite diffusion toward the ultrafast diffusion limit predicted by our multiscale analysis. The numerical simulations also demonstrate that electric fields may induce important diffusive currents on heterogeneous surfaces under the conditions of field emission microscopy.

Using Feynman path integrals and the stationary-phase method, we develop a semiclassical theory for quantum trace formulas in classically hyperbolic systems. In this way, we obtain corrections to the Gutzwiller-Selberg trace formula as an asymptotic series in powers of the Planck constant. The first coefficient of this series is given explicitly. We illustrate the theory with the calculation of complex-wave-number resonances for the two-disk scatterer and show that effects beyond the Gutzwiller leading approximation are at the origin of a lengthening of the resonance lifetimes at low energy

We present a calculation of the structure of liquid As and Sb obtained from the electronic structure described in the tight-binding approximation. We find pair correlation functions of liquid As and Sb in excellent agreement with the experimental data. We show that the structure of liquid As still shows a Peierls distortion whereas liquid Sb is no longer distorted. In our model, the difference between As and Sb can be attributed to a harder repulsive potential of Sb which penalizes the Peierls distortion.

We present an experimental and theoretical study of liquid ${\text{As}}_{2}{\text{Te}}_{3}$. This alloy exhibits a negative thermal expansion (NTE) in a 250 K range above the melting temperature ${T}_{m}=654\text{ }\text{K}$. We evidence the changes in ${\text{As}}_{2}{\text{Te}}_{3}$ structure by measuring neutron-diffraction spectra at five temperatures in the NTE range and perform first principles molecular dynamics simulations at the same temperatures and densities to study the local order evolution in the liquid. Our calculated structures show an increase in the coordination numbers and a symmetrization of the first neighbors shell around atoms when the temperature rises. To confirm these results, we performed inelastic neutron scattering to obtain the vibrational density of state (VDOS) along the NTE. We see a clear change in the VDOS, consisting in a redshift of the highest frequencies with temperature. Finally, electrical conductivity evolution was obtained from the simulated structures, to compare with the semiconductor to metal transition measured experimentally.

We suggest an insight into level dynamics of classically nonintegrable quantum systems. When several nonintegrability parameters are varied in a Hamiltonian, the desymmetrized energy spectrum generally exhibits degeneracies. In this case the fundamental equation of level dynamics is altered as follows: (i) Euclidean ``space-time'' coordinates are needed instead of a single ``time'' coordinate; (ii) gauge structures around diabolical degenerate points are incorporated into level dynamics. With these changes we obtain an alternative field-theoretical model for interacting energy surfaces.

We consider a dynamic entropy of a Rayleigh-B\'enard flow which varies with the characteristic scales \ensuremath{\epsilon} of the process. Such an \ensuremath{\epsilon} entropy is used to distinguish and classify the different dynamic regimes recently observed in this system: oscillation, chaos, and soft, hard, and developed turbulences. Moreover, data analysis of an experimental time series reveals a scaling behavior of the \ensuremath{\epsilon} entropy in a hard turbulent regime, demonstrating that this notion of entropy is suitable to describe dynamic processes with a heirarchy of characteristic instabilities.

Negative thermal expansion (NTE) in tellurium based liquid alloys (${\mathrm{GeTe}}_{6}$ and ${\mathrm{GeTe}}_{12}$) is analyzed through the atomic vibrational properties. Using neutron inelastic scattering, we show that the structural evolution resulting in the NTE is due to a gain of vibrational entropy that cancels out the Peierls distortion. In the NTE temperature range, these competing effects give rise to noticeable changes in the vibrational density of states spectra. Additional first principles molecular dynamics simulations emphasize the role of the temperature dependance of the Ge atomic environment in this mechanism. For comparison, we extended our study to ${\mathrm{Ge}}_{2}{\mathrm{Sb}}_{2}{\mathrm{Te}}_{5}$ and ${\mathrm{Ge}}_{1}{\mathrm{Sb}}_{2}{\mathrm{Te}}_{4}$ phase-change materials.

We present a first-principles study of heat conduction in a class of models which exhibit a new multi-step local thermalization mechanism which gives rise to Fourier's law. Local thermalization in our models occurs as the result of binary collisions among locally confined gas particles. We explore the conditions under which relaxation to local equilibrium, which involves no energy exchange, takes place on time scales shorter than that of the binary collisions which induce local thermalization. The role of this mechanism in multi-phase material systems such as aerogels is discussed., 4 pages, 3 color figures, to appear in Physical Review Letters

We study the spectral properties of infinite rectangular quantum graphs in the presence of a magnetic field. We study how these properties are affected when three-dimensionality is considered, in particular, the chaological properties. We then establish the quantization of the Hall transverse conductivity for these systems. This quantization is obtained by relating the transverse conductivity to topological invariants. The different integer values of the Hall conductivity are explicitly computed for an anisotropic diffusion system which leads to fractal phase diagrams., 15 pages, 9 figures

By using projection superoperators, we present a new derivation of the quantum master equation first obtained by the Authors in Phys. Rev. E {\bf 68}, 066112 (2003). We show that this equation describes the dynamics of a subsystem weakly interacting with an environment of finite heat capacity and initially described by a microcanonical distribution. After applying the rotating wave approximation to the equation, we show that the subsystem dynamics preserves the energy of the total system (subsystem plus environment) and tends towards an equilibrium state which corresponds to equipartition inside the energy shell of the total system. For infinite heat capacity environments, this equation reduces to the Redfield master equation for a subsystem interacting with a thermostat. These results should be of particular interest to describe relaxation and decoherence in nanosystems where the environment can have a finite number of degrees of freedom and the equivalence between the microcanonical and the canonical ensembles is thus not always guaranteed., 8 pages, 0 figures; v2: typos in eq 42 and 43 corrected; v3: submitted to Phys.Rev.E; v4: accepted in Phys.Rev.E

Solid bromine has been studied by x-ray absorption spectroscopy experiments up to a maximum pressure of 75 GPa. The data analysis of the extended fine structure reveals that the intramolecular distance first increases, reaching its maximum value at 25+/-5 GPa. From this value the intramolecular distance abruptly begins to decrease evidencing a nonpreviously observed phase transformation taking place at 25+/-5 GPa. A maximum variation of 0.08 A is observed at 65+/-5 GPa where again a phase transition occurs. This last transformation could correspond with the recently observed change to an incommensurate modulated phase. We discuss the possible generalization of the observed new phase transition at 25+/-5 GPa to the case of the other halogens.

The structure of liquid GeSb2Te4 alloys is investigated using first-principles molecular dynamics at three densities: the experimental one and two other densities, 7% and 15% lower, respectively. Contrary to what has been reported for amorphous phases, no departure from an octahedral local environment, with bond angles around 90 degrees-95 degrees, is observed. Expanding the liquid results in an increasing distortion of the local environment by a Peierls-like mechanism.

The structure of liquid ${\mathrm{Ge}}_{0.15}{\mathrm{Te}}_{0.85}$ alloys that exhibit a density anomaly between $633\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ and $733\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ at ambient pressure was investigated using x-ray absorption spectroscopy at the Ge $K$ edge. Using a reverse Monte Carlo method to combine the present results with neutron scattering data, we show that the volume contraction is associated with an increase of the first neighbor coordination number around both Ge and Te by about one atom. The coordination number of Ge increases from $3\ifmmode\pm\else\textpm\fi{}0.3$ to $4.1\ifmmode\pm\else\textpm\fi{}0.3$. These results support an interpretation of the density anomaly in terms of the same Peierls-like distortion mechanism acting in the liquid state and in the neighboring (pure Te and GeTe compound) phases.

We study the emergence of diffusion for a quantum particle moving in a finite and translationally invariant one-dimensional subsystem described by a tight-binding Hamiltonian with a single energy band and interacting with its environment by an interaction energy proportional to some coupling parameter. We show that there exists a crossover between a nondiffusive relaxation regime for small sizes or low values of the coupling parameter and a diffusive regime above a critical size or for higher values of the coupling parameter. In the nondiffusive regime, the relaxation is characterized by oscillations decaying at rates independent of the size and proportional to the square of the coupling parameter and the temperature of the environment. In the diffusive regime, the damped oscillations have disappeared and the relaxation rate is inversely proportional to the square of the size. The diffusion coefficient is proportional to the square of the energy bandwidth of the subsystem and inversely proportional to the temperature of the environment and the square of the coupling parameter. The critical size where the crossover happens is obtained analytically.

We report the study of a random Lorentz gas with a reaction of isomerization $A\rightleftharpoons B$ between the two colors of moving particles elastically bouncing on hard disks. The reaction occurs when the moving particles collide on catalytic disks which constitute a fraction of all the disks. Under the dilute-gas conditions, the reaction-diffusion process is ruled by two coupled Boltzmann-Lorentz equations for the distribution functions of the colors. The macroscopic reaction-diffusion equations with cross-diffusion terms induced by the chemical reaction are derived from the kinetic equations. We use a $H$-theorem of the kinetic theory in order to derive a macroscopic entropy depending on the gradients of color densities and which has a non-negative entropy production in agreement with the second law of thermodynamics., 14 pages, 3 eps-figures

It is our aim to study the dynamics of a two-level atom immersed in the modified radiation field of a photonic band-gap material using non-Markovian stochastic Schr\"odinger equations. Up to now, such methodology has only been applied to toy models and not to physically realistic systems as the one presented here. In order to check its validity, we shall study several of the physical phenomena already described in the literature within non-Markovian master equations, such as the long-time-limit residual population in the excited level of the atom and the population inversion which occurs in the atomic system when applying an external laser field. In addition to the stochastic equation, we propose a non-Markovian master equation derived from the stochastic formalism, which in contrast to the current models of master equation preserves positivity. We propose a correlation function for the radiation field (environment) that captures many of the physically relevant aspects of the problem and describes the short-time behavior in a more accurate way than previously proposed ones. This characteristic permits a correct description of the fluctuations of the electromagnetic field, which in the stochastic formalism are represented by the noise, and a better description of the non-Markovian effects in the atomic dynamics. The methodology presented in this paper to apply stochastic Schr\"odinger equations can be followed to study more complex systems, like many-level atoms embedded in more complicated photonic band-gap structures.

Dynamical chaos is studied in the Hamiltonian motion of ions confined in a Penning trap and forming so-called microplasmas. The dynamical chaos of the ion motion is characterized by the maximum Lyapunov exponent. Results are reported on the dependence of this exponent on the energy of the system, on the number of ions, as well as on the geometry of the trap. Different dynamical regimes are characterized from the crystalline state to a strongly chaotic regime, and to quasiharmonic motion in the external potential of the trap. Across these regimes, the Lyapunov exponent increases, reaches a maximum value, and decreases as a function of energy. Besides, the maximum value of the Lyapunov exponent increases as a function of the number of ions.

This paper presents an analysis of the structural changes undergone by liquid ${\mathrm{Ge}}_{15}{\mathrm{Te}}_{85}$ alloys in a 150 K temperature range above the eutectic temperature. This structural change is characterized by strong and anomalous variations of thermodynamic quantities among which are the density, the heat capacity, and the isothermal compressibility. The total structure factors were measured by neutron scattering on the D4B spectrometer at the ILL (Grenoble). The analysis of the thermodynamic and neutron scattering data suggests that the structural change undergone by the liquid mainly consists in a modification of the first-neighbor shell of the Ge atoms. With increasing temperature an increasingly large number of GeTe bonds become shorter, leading to a more compact local environment with a smaller atomic volume. The relation with the $\ensuremath{\alpha}\ensuremath{\rightleftharpoons}\ensuremath{\beta}$ transition of the solid GeTe compound is discussed.

We examine the local atomic order as well as some dynamic properties of the semiconducting liquid GeTe. We employ hot-neutron two-axis diffraction at three temperatures above the melting point and compare these results with ab initio molecular dynamics simulations. The simulations were based on interatomic forces derived from pseudopotentials constructed within density functional theory. At the melting temperature, the Peierls distortion responsible for the lower-temperature crystal phase is shown to manifest itself within the liquid structure. At higher temperatures in the liquid, increasing disorder in the Ge environment determines the eventual semiconductor-metal transition. The calculated kinematic viscosity of the liquid is found to agree with the experimental value and is shown to arise from the small diffusion coefficient of the Te atoms.

We analyze the structure and dynamics of semiconducting liquid GeSe using ab initio molecular-dynamics simulations. We show the local order of the liquid to be close to that of the low-temperature crystalline phase, \ensuremath{\alpha}-GeSe. In particular, we show that the Peierls distortion, which defines the \ensuremath{\alpha} phase and vanishes in the high-temperature \ensuremath{\beta} crystalline phase, reenters GeSe in the melt. Examining the distance histograms allows one to analyze the Ge environment as consisting of a ${\mathrm{GeSe}}_{3}$ unit and having one Ge-Ge defective bond. Evidence is presented that Peierls distortion is directly responsible for the semiconducting behavior of the melt. The calculated viscosity and electrical conductivity are in agreement with the experiment. An additional neutron-diffraction experiment indicates that this liquid structure is unmodified 200 K above the melting point.

The tight-binding scheme has been largely used in the description of the electronic properties of disordered systems. Several direct-space techniques of calculation have been developed in order to compute the density of electronic states; among those the moments method and the recursion scheme have become popular. We discuss both of them and we propose a new method that interpolates between these two techniques. It is based on the calculations of generalized moments. We show that the generalized-moments method shares the advantages of both methods and avoids their difficulties.

A neutron-diffraction experiment (\ensuremath{\lambda}=0.704 A\r{}) has been performed for the first time on liquid arsenic above the triple point. The coordination number (Z=3) does not change through the semimetal-to-semiconductor transition on melting. This is in sharp contrast to the elemental semiconductors (Si,Ge) that undergo a semiconductor-to-metal transition upon melting, accompanied by an increase (4\ensuremath{\rightarrow}6.4) of the coordination number. The nonmetallic behavior of As, which has a half-filled p band, can be understood as a Peierls distortion in the p-bonding mechanism (three p-p bonds are reinforced; the others are considerably weakened).

Exact one-soliton and two-soliton solutions of generalized Calogero-Moser (cCM) equations are presented. We explain how these solutions describe the origin of the successive avoided crossings observed in the energy-level structure of bounded systems when a parameter is varied. A new statistical description, based on the grand-canonical ensemble for the gCM system, is developed for the study of the parametric properties of irregular spectra. The relationship with random-matrix theory is discussed