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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

A quantum-mechanical framework is set up to describe the full counting statistics of particles flowing between reservoirs in an open system under time-dependent driving. A symmetry relation is obtained which is the consequence of microreversibility for the probability of the nonequilibrium work and the transfer of particles and energy between the reservoirs. In some appropriate long-time limit, the symmetry relation leads to a steady-state quantum fluctuation theorem for the currents between the reservoirs. On this basis, relationships are deduced which extend the Onsager-Casimir reciprocity relations to the nonlinear response coefficients., Comment: 19 pages

We here present the complete analysis of experiments on driven Brownian motion and electric noise in a $RC$ circuit, showing that thermodynamic entropy production can be related to the breaking of time-reversal symmetry in the statistical description of these nonequilibrium systems. The symmetry breaking can be expressed in terms of dynamical entropies per unit time, one for the forward process and the other for the time-reversed process. These entropies per unit time characterize dynamical randomness, i.e., temporal disorder, in time series of the nonequilibrium fluctuations. Their difference gives the well-known thermodynamic entropy production, which thus finds its origin in the time asymmetry of dynamical randomness, alias temporal disorder, in systems driven out of equilibrium., to be published in : Journal of Statistical Mechanics: theory and experiment

A previously reported method for shaping electromagnetic field pulses to achieve chemical selectivity is extended and applied to a simple multiple level model system. The pulse shaping approach is based on optimal control theory, where both the time‐dependent Schrodinger equation and the constant pulse energy are used as constraints on the variational scheme. A conjugate gradient direction method is used to direct the convergence of the iterative process used to calculate the optimum pulse shape. The method is applied to a five‐level system interacting with an optical (laser) field. Results demonstrating selectivity and stability are compared to those of other recent related investigations.

Several experimental results1,2,3,4,5 suggest that stable quasicrystals are Hume- Rothery phases6. The singularly continuous character of the total density of states (DOS) of one dimensional quasiperiodic systems makes difficult to calculate the total energies E and occupation numbers n needed to study their stability. Reported calculations of the DOS of Fibonacci chains by decimation7,8,9,10 are not exact and give wrong results regarding the stability. In this paper we obtain by decimation exact results for n(eF) and E(eF) for periodic approximants that converge rapidly to the true Fibonacci chain. It is shown that the maxima of stability fulfils the Hume-Rothery rule. The effect of disorder is also studied.

In this paper, we study the structural properties of liquid group-V elements (and a compound InSb) and we analyse the differences with their room temperature crystalline phases. Neutron diffraction experiments are performed using short-wavelength neutrons (0.7 A). We show different melting behaviours of a light element (As) and a heavy element (Sb) under study. Whereas As keeps its coordination three upon melting, Sb is six-coordinated in the melt. Similarly, InSb has a coordination number increasing from 4 to about 6 upon melting. Large entropies of melting are related to important structural variations.

We report studies of classical models of unimolecular fragmentation of van der Waals complexes using the methodologies of Hamiltonian mappings and flows. The effect of frequency mismatch between harmonic molecular vibrations of a host molecule and the van der Waals bond‐stretching motion is shown to dominate vibrational energy redistribution and fragmentation. Our results show that a crossover exists when the frequency mismatch is increased from a stochastic regime of resonances between the nonlinear oscillators to a regular regime where the system behaves like an integrable system. Our model systems include both collinear and T‐shaped oscillator displacement configurations, as well as a many‐oscillator system that included both classes of motions. Oscillator parameter ranges were used that approximate vibrations in C6H6⋅He and C6H6⋅Ar van der Waals complexes.

A brief review of recent developments in the theory of unimolecular reactions is presented, with emphasis on the work carried out at The University of Chicago. The subjects considered are: the development of a paradigm for the control of selectivity of a photoinduced reaction; the development of an alternative form for the classical mechanical theory of the rate of a unimolecular reaction; the beginnings of an understanding of the influence of classical mechanical chaos on the corresponding quantum-mechanical description of an unbounded system; and the possible decoupling of a part of an N-degree-of-freedom system from the rest of the system on a time scale of interest with respect to subsystem internal energy transfer and chemical reaction. The intellectual linkages between these subjects are very briefly sketched.

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.

can be related to the leading Pollicott-Ruelle resonance of open systems and to the characteristic quantities of the microscopic dynamics. In nonequilibrium steady states, the entropy production is shown to result from a time asymmetry in the dynamical randomness of the nonequilibrium fluctuations. Furthermore, the generalizations of Onsager reciprocity relations to nonlinear response can be deduced from the fluctuation theorem for the currents. Furthermore, the principle of temporal ordering in nonequilibrium steady states is formulated and its perspectives for the generation of biological information are discussed.

International audience; The time-reversal symmetry of nonequilibrium fluctuations is experimentally investigated in two out-of-equilibrium systems namely, a Brownian particle in a trap moving at constant speed and an electric circuit with an imposed mean current. The dynamical randomness of their nonequilibrium fluctuations is characterized in terms of the standard and time-reversed entropies per unit time of dynamical systems theory. We present experimental results showing that their difference equals the thermodynamic entropy production in units of Boltzmann's constant.

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.

We use a recently proved fluctuation theorem for the currents to develop the response theory of nonequilibrium phenomena. In this framework, expressions for the response coefficients of the currents at arbitrary orders in the thermodynamic forces or affinities are obtained in terms of the fluctuations of the cumulative currents and remarkable relations are obtained which are the consequences of microreversibility beyond Onsager reciprocity relations.

The thermal conductivity is calculated with the Helfand-moment method in the Lennard-Jones fluid near the triple point. The Helfand moment of thermal conductivity is here derived for molecular dynamics with periodic boundary conditions. Thermal conductivity is given by a generalized Einstein relation with this Helfand moment. We compute thermal conductivity by this new method and compare it with our own values obtained by the standard Green-Kubo method. The agreement is excellent., Comment: Submitted to the Journal of Chemical Physics

Isometric fluctuation relations are deduced for the fluctuations of the order parameter in equilibrium systems of condensed-matter physics with broken discrete or continuous symmetries. These relations are similar to their analogues obtained for non-equilibrium systems where the broken symmetry is time reversal. At equilibrium, these relations show that the ratio of the probabilities of opposite fluctuations goes exponentially with the symmetry-breaking external field and the magnitude of the fluctuations. These relations are applied to the Curie-Weiss, Heisenberg, and $XY$~models of magnetism where the continuous rotational symmetry is broken, as well as to the $q$-state Potts model and the $p$-state clock model where discrete symmetries are broken. Broken symmetries are also considered in the anisotropic Curie-Weiss model. For infinite systems, the results are calculated using large-deviation theory. The relations are also applied to mean-field models of nematic liquid crystals where the order parameter is tensorial. Moreover, their extension to quantum systems is also deduced., Comment: 34 pages, 14 figures

We report a study of the adsorption and reaction of CO on a gold nanotip in high electrostatic fields. Field ion microscopy is used to investigate the emergence of a Au-carbonyl wave that is made visible with oxygen as the imaging gas. We set up a simple kinetic model that reproduces the adsorption wave and confirms that the presence of oxygen merely serves as an imaging gas and does not lead to field-induced oxidation of CO.

International audience; We have studied oxygen interaction with Au crystals (field emitter tips) using time-resolved (atom-probe) field desorption mass spectrometry. The results demonstrate no adsorption to take place on clean Au facets under chosen conditions of pressures (p < 10(-4) mbar) and temperatures (T=300-350 K). Steady electric fields of 6 V/nm do not allow dissociating the oxygen molecule. The measured O-2(+) intensities rather reflect ionization of O-2 molecules at critical distances above the Au tip surface. Certain amounts of Au-O-2 complex ions can be found at the onset of Au field evaporation. Calculations by density functional theory (DFT) show weak oxygen end-on interaction with Au-10 clusters (Delta E=0.023 eV) and comparatively stronger interaction with Au-1/Au(100) model surfaces (Delta E=0.25 eV). No binding is found on \210\ facets. Including (positive) electric fields in the DFT calculations leads to an increase of the activation energy for oxygen dissociation thus providing an explanation for the absence of atomic oxygen ions from the field desorption mass spectra. (c) 2006 American Institute of Physics.

We report a study of the rotational dynamics in double-walled nanotubes using molecular dynamics simulations and a simple analytical model reproducing very well the observations. We show that the dynamic friction is linear in the angular velocity for a wide range of values. The molecular dynamics simulations show that for large enough systems the relaxation time takes a constant value depending only on the interlayer spacing and temperature. Moreover, the friction force increases linearly with contact area, and the relaxation time decreases with the temperature with a power law of exponent $-1.53 \pm 0.04$., Comment: submitted to PRL

Transport by normal diffusion can be decomposed into hydrodynamic modes which relax exponentially toward the equilibrium state. In chaotic systems with two degrees of freedom, the fine scale structures of these modes are singular and fractal, characterized by a Hausdorff dimension given in terms of Ruelle’s topological pressure. For long-wavelength modes, the Hausdorff dimension is related to the diffusion coefficient and the Lyapunov exponent. In the infinite-wavelength limit, the hydrodynamic modes lead to the nonequilibrium steady states, which also present a singular character. This singular character is a consequence of the mixing property of the dynamics. These results are illustrated with several systems such as the hard-disk and Yukawa-potential Lorentz gases.

We study the transport of cold fermionic atoms trapped in optical lattices in the presence of artificial Abelian or non-Abelian gauge potentials. Such external potentials can be created in optical lattices in which atom tunneling is laser assisted and described by commutative or non-commutative tunneling operators. We show that the Hall-like transverse conductivity of such systems is quantized by relating the transverse conductivity to topological invariants known as Chern numbers. We show that this quantization is robust in non-Abelian potentials. The different integer values of this conductivity are explicitly computed for a specific non-Abelian system which leads to a fractal phase diagram., Comment: 6 pages, 2 figures

A short wavelength ( λ = 0.7 A ) neutron scattering experiment has been performed on the II–VI compounds HgS, HgSe and Zn x Hg 1− x Te. Liquid HgS can be viewed as a distortion fo the blende structure; we show that this distortion decreases gradually with temperature. For Zn x Hg 1− x Te, we show that the transition between the six coordinated HgTe liquid and the four coordinated ZnTe Liquid is not continuous, the intermediate phase being a deformed cinnabar one.

Diblock copolymers of polymethacrylic acid sodium salt, forming the hair, and styrene derivatives have been studied in aqueous solutions by SANS and SAXS. The influence of both the chemical nature and the length of the hydrophobic bloxk on the size and shape of micelles have been investigated. The micellar core size is in agreement with the theoretical evaluation for copolymers with a short hydrophobic sequence. In contrast, in case of larger hydrophobic blocks, the measured size is incompatible with a star-like model. Various hypotheses are presented for the latter.

A fluctuation theorem is proved for the macroscopic currents of a system in a nonequilibrium steady state, by using Schnakenberg network theory. The theorem can be applied, in particular, in reaction systems where the affinities or thermodynamic forces are defined globally in terms of the cycles of the graph associated with the stochastic process describing the time evolution., new version : 16 pages, 1 figure, to be published in Journal of Statistical Physics

The fluctuation theorems for the currents and the dissipated work are considered for molecular motors which are driven out of equilibrium by chemical reactions. Because of the molecular fluctuations, these nonequilibrium processes are described by stochastic models based on a master equation. Analytical expressions are derived for the fluctuation theorems, allowing us to obtain predictions on the work dissipated in the motor as well as on its rotation near and far from thermodynamic equilibrium. We show that the fluctuation theorems provide a method to determine the affinity or thermodynamic force driving the motor. This affinity is given in terms of the free enthalpy of the chemical reactions. The theorems are applied to the F1 rotary motor which turns out to be a stiff system typically functioning in the nonlinear regime of nonequilibrium thermodynamics. We show that this nonlinearity confers a robustness to the functioning of the molecular motor.

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.

This paper contains a discussion of dynamical randomness among the different methods of simulation of a fluid and its characterization by the concept of Kolmogorov-Sinai entropy per unit time. Moreover, a renormalization-group method is presented in order to construct the hydrodynamic and reactive modes of relaxation in chaotic models. The renormalization-group construction allows us to obtain the dispersion relation of these modes, i.e. their damping rate versus the wavenumber. Besides, these modes are characterized by a fractal dimension given in terms of a diffusion coefficient and a Lyapunov exponent.

Recent work on the connections between dynamical systems theory and nonequilibrium statistical mechanics is reviewed with emphasis on results which are compatible with Liouville’s theorem. Starting from a general discussion of time-reversal symmetry in the Newtonian scheme, it is shown that the Liouvillian eigenstates associated with the Pollicott-Ruelle resonances spontaneously break the time-reversal symmetry. We explain that such a feature is compatible with the time reversibility of Newton’s equations because of a selection of trajectories which are not time-reversal symmetric. The Pollicott-Ruelle resonances and their associated eigenstates can be constructed not only for decay processes but also for transport processes such as diffusion or viscosity, as well as for reaction-diffusion processes. The Pollicott-Ruelle resonances thus describe the relaxation toward the thermodynamic equilibrium. The entropy production of hese relaxation processes can be calculated and shown to take the value expected from nonequilibrium thermodynamics. In nonequilibrium steady states, an identity is obtained which shows that the entropy production directly characterizes the breaking of time-reversal symmetry by nonequilibrium boundary conditions. The extension to quantum systems is also discussed.

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.

We study the transport property of diffusion in a finite translationally invariant quantum subsystem described by a tight-binding Hamiltonian with a single energy band and interacting with its environment by a coupling in terms of correlation functions which are delta-correlated in space and time. For weak coupling, the time evolution of the subsystem density matrix is ruled by a quantum master equation of Lindblad type. Thanks to the invariance under spatial translations, we can apply the Bloch theorem to the subsystem density matrix and exactly diagonalize the time evolution superoperator to obtain the complete spectrum of its eigenvalues, which fully describe the relaxation to equilibrium. Above a critical coupling which is inversely proportional to the size of the subsystem, the spectrum at given wavenumber contains an isolated eigenvalue describing diffusion. The other eigenvalues rule the decay of the populations and quantum coherences with decay rates which are proportional to the intensity of the environmental noise. On the other hand, an analytical expression is obtained for the dispersion relation of diffusion. The diffusion coefficient is proportional to the square of the width of the energy band and inversely proportional to the intensity of the environmental noise because diffusion results from the perturbation of quantum tunneling by the environmental fluctuations in this model. Diffusion disappears below the critical coupling., Comment: Submitted to J. Stat. Phys

A fluctuation theorem is derived for stochastic nonequilibrium reactions ruled by the chemical master equation. The theorem is expressed in terms of the generating and large-deviation functions characterizing the fluctuations of a quantity which measures the loss of detailed balance out of thermodynamic equilibrium. The relationship to entropy production is established and discussed. The fluctuation theorem is verified in the Schlogl model of far-from-equilibrium bistability.

Spontaneous emission of an atom in contact with the modified radiation field of a Photonic band gap (PBG) material is known to present a typically non-Markovian behavior. In addition, the presence of a gap of forbidden frequencies in the photonic density of states (DOS), produces residual population of the excited level, and population inversion when the atomic system is driven by an external laser field. It's our aim to study those effects using non-Markovian Stochastic Schroedinger equations (NMSSE). This formalism permit us to describe the evolution of the atom in terms of a wave function, |ψ t ( z )], which due to the presence of the radiation field depends on a stochastic variable z t . Having a singularity at the origin, the models of field correlation function usually found in literature, are not suitable to generate the corresponding z t . We have proposed a new correlation function that do not have this problem, and reproduces all the important physical phenomena of the system under study. The results obtained with NMSSE are compared with those of the master equation, since the ensemble average of stochastic trajectories gives the reduced density matrix of the system, ρ s . In addition, we propose a new non-Markovian master equation derived from the stochastic formalism, which in contrast to the current models of master equation preserves positivity for the problem under study.

A new perturbative quantum master equation is presented for the dissipative dynamics of a subsystem inside a nanosystem with a constant and finite total energy. The degrees of freedom besides those of the subsystem play the role of the environment. Our equation rules the time evolution of the distribution functions of the subsystem populations and coherences over the energy of the environment. Thanks to these distribution functions, we can take into account the effects of the conservation of the total energy. This equation is more general than the standard perturbative equations used for describing a subsystem interacting with an environment (such as the Redfield or Cohen-Tannoudji equations) because these latter equations can be deduced from it in the limit of an infinitely large environment. We numerically apply this equation to the spin-GORM model for the interaction of a two-level subsystem with an environment described by random matrices. We compare our equation with the exact von Neumann equation of the total system and show its superiority compared to the Redfield equation (in the Markovian and non-Markovian cases).

We report the study of a fluid of hard-disk particles in a contracting cavity. Under supersonic contraction speed, a shock wave converges to the center of the cavity where it implodes, creating a central peak in temperature. The dynamics of the fluid is studied by solving the Euler and Navier-Stokes equations, as well as by molecular dynamics simulations and the Enskog direct simulation Monte Carlo method. The value of the maximum temperature reached at the center of the cavity is systematically investigated with the different methods which give consistent results. Moreover, we develop a scaling theory for the maximum temperature based on the self-similar solutions of Euler's equations and mean-free-path considerations. This scaling theory provides a comprehensive scheme for the interpretation of the numerical results. In addition, the effects of the imploding shock wave on an passively driven isomerization reaction A B are also studied.

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.

We report the study of a model of a two-level system interacting in a non-diagonal way with a complex environment described by Gaussian orthogonal random matrices (GORM). The effect of the interaction on the total spectrum and its consequences on the dynamics of the two-level system are analyzed. We show the existence of a critical value of the interaction, depending on the mean level spacing of the environment, above which the dynamics is self-averaging and closely obey a master equation for the time evolution of the observables of the two-level system. Analytic results are also obtained in the strong coupling regimes. We finally study the equilibrium values of the two-level system population and show under which condition it thermalizes to the environment temperature., 45 pages, 49 figures

A perturbative quantum master equation is derived for a system interacting with its environment, which is more general than the ones derived before. Our master equation takes into account the effect of the energy exchanges between the system and the environment and the conservation of energy in a finite total system. This master quantum describes relaxation mechanisms in isolated nanoscopic quantum systems. In its most general form, this equation is non-Markovian and a Markovian version of it rules the long-time relaxation. We show that our equation reduces to the Redfield equation in the limit where the energy of the system does not affect the density of state of its environment. This master equation and the Redfield one are applied to a spin-environment model defined in terms of random matrices and compared with the solutions of the exact von Neumann equation. The comparison proves the necessity to allow energy exchange between the subsystem and the environment in order to correctly describe the relaxation in isolated nanoscopic total system., 39 pages, 10 figures

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 apply the escape-rate formalism to compute the shear viscosity in terms of the chaotic properties of the underlying microscopic dynamics. A first passage problem is set up for the escape of the Helfand moment associated with viscosity out of an interval delimited by absorbing boundaries. At the microscopic level of description, the absorbing boundaries generate a fractal repeller. The fractal dimensions of this repeller are directly related to the shear viscosity and the Lyapunov exponent, which allows us to compute its values. We apply this method to the Bunimovich-Spohn minimal model of viscosity which is composed of two hard disks in elastic collision on a torus. These values are in excellent agreement with the values obtained by other methods such as the Green-Kubo and Einstein-Helfand formulas., Comment: 16 pages, 16 figures (accepted in Phys. Rev. E; October 2003)

We report a study of viscosity by the method of Helfand moment in systems with periodic boundary conditions. We propose a new definition of Helfand moment which takes into account the minimum image convention used in molecular dynamics with periodic boundary conditions. Our Helfand-moment method is equivalent to the method based on the Green-Kubo formula and is not affected by ambiguities due to the periodic boundary conditions. Moreover, in hard-ball systems, our method is equivalent to the one developed by B. J. Alder, D. M. Gass, and T. E. Wainwright [{\it J. Chem. Phys.} {\bf 53}, 3813 (1970)]. We apply and verify our method in a fluid composed of $N\geq 2$ hard disks in elastic collisions. We show that the viscosity coefficients already take values in good agreement with Enskog's theory for N=2 hard disks in a hexagonal geometry., Comment: 30 pages, 32 figures, accepted in August 2003 (Phys.Rev. E)

For a piecewise linear version of the periodic map with anomalous diffusion, the evolution of statistical averages of a class of observables with respect to piecewise constant initial densities is investigated and generalized eigenfunctions of the Frobenius-Perron operator are explicitly derived. The evolution of the averages is controlled by real eigenvalues as well as continuous spectra terminating at the unit circle. Appropriate scaling limits are shown to give a normal diffusion if the reduced map is in the stationary regime with normal fluctuations, a L\'evy flight if the reduced map is in the stationary regime with L\'evy-type fluctuations and a transport of ballistic type if the reduced map is in the non-stationary regime., Comment: submitted to Physica D (CHAOTRAN conference proceedings)