On the Specific Heat of Fermi–Pasta–Ulam Systems and Their Glassy Behavior

The specific heat of Fermi–Pasta–Ulam systems has until now been estimated through the energy fluctuations of a suitable subsystem, and opposite answers were apparently provided concerning its possible vanishing for vanishing temperatures. In the present paper a more realistic numerical implementation of the specific heat measurement is discussed, which mimics the interaction of the FPU system with a calorimeter. It is found that there exists a freezing critical temperature below which the relaxation times to equilibrium between FPU system and calorimeter become relevant, so that the system presents aging and hysteresis features very similar to those familiar in glasses and spin glasses. In particular, in the framework of such a point of view involving finite long times, the specific heat appears to vanish for vanishing temperatures.     

Fermi–Pasta–Ulam recurrence and modulation instability

We give a qualitative conceptual explanation of the Fermi–Pasta–Ulam (FPU) like recurrence in the onedimensional focusing nonlinear Schrodinger equation (NLSE). The recurrence can be considered as a result of the nonlinear development of the modulation instability. All known exact localized solitary wave solutions describing propagation on the background of the modulationally unstable condensate show the recurrence to the condensate state after its interaction with solitons. The condensate state locally recovers its original form with the same amplitude but a different phase after soliton leave its initial region. Based on the integrability of the NLSE, we demonstrate that the FPU recurrence takes place not only for condensate, but also for a more general solution in the form of the cnoidal wave. This solution is periodic in space and can be represented as a solitonic lattice. That lattice reduces to isolated soliton solution in the limit of large distance between solitons. The lattice transforms into the condensate in the opposite limit of dense soliton packing. The cnoidal wave is also modulationally unstable due to soliton overlapping. The recurrence happens at the nonlinear stage of the modulation instability. Due to generic nature of the underlying mathematical model, the proposed concept can be applied across disciplines and nonlinear systems, ranging from optical communications to hydrodynamics.     

Time-Scales to Equipartition in the Fermi–Pasta–Ulam Problem: Finite-Size Effects and Thermodynamic Limit

We investigate numerically the common α+β and the pure β FPU models, as well as some higher order generalizations. We consider initial conditions in which only low-frequency normal modes are excited, and perform a very accurate systematic study of the equilibrium time as a function of the number N of particles, the specific energy ε, and the parameters α and β. While at any fixed N the equilibrium time is found to be a stretched exponential in 1/ε, in the thermodynamic limit, i.e. for N→∞ at fixed ε, we observe a crossover to a power law. Concerning the (usually disregarded) dependence of T _eq on α and β, we find it is nontrivial, and propose and test a general law. A central role is played by the comparison of the FPU models with the Toda model.     

Instability and noise-induced thermalization of Fermi–Pasta–Ulam recurrence in the nonlinear Schrödinger equation

We investigate the spontaneous growth of noise that accompanies the nonlinear evolution of seeded modulation instability into Fermi–Pasta–Ulam recurrence. Results from the Floquet linear stability analysis of periodic solutions of the three-wave truncation are compared with full numerical solutions of the nonlinear Schrödinger equation. The predicted initial stage of noise growth is in a good agreement with simulations, and is expected to provide further insight into the subsequent dynamics of the field evolution after recurrence breakup.     

Boson bound states in the β-Fermi–Pasta–Ulam model

The bound states of four bosons in the quantum β-Fermi–Pasta–Ulam model are investigated and some interesting results are presented using the number conserving approximation combined with the number state method. We find that the relative magnitude of anharmonic coefficient has a significant effect on forming localized energy in the model, and the wave number plays an important role in forming different bound states. The signature of the quantum breather is also set up by the square of the amplitudes of the corresponding eigenvectors in real space.     

Behaviors of thermalization for the Fermi–Pasta–Ulam–Tsingou system with small number of particles

We study the behaviors of thermalization in Fermi–Pasta–Ulam–Tsingou(FPUT) system with small number of particles using periodic boundary conditions. The total energy has initially equidistributed among some of the lowest frequency modes. The thermalization time t_(eq) depending on system's energy density ε scales as t_(eq) ∝ε~(-4) only within a certain range of nonlinearity. In this range of nonlinearity, energies can interchange between the initial excited modes and other modes continuously with time until reaching the thermalized state. With a further decreasing nonlinearity, a steeper growth than ε~(-4) will appear. In the very weakly nonlinear regime, energies on low frequency modes are found to be frozen on large time scales. Redistribution of mode energies happens through the resonances of high frequency modes.     

The Fermi–Pasta–Ulam Problem and Its Underlying Integrable Dynamics: An Approach Through Lyapunov Exponents

FPU models, in dimension one, are perturbations either of the linear model or of the Toda model; perturbations of the linear model include the usual \(\beta \)-model, perturbations of Toda include the usual \(\alpha +\beta \) model. In this paper we explore and compare two families, or hierarchies, of FPU models, closer and closer to either the linear or the Toda model, by computing numerically, for each model, the maximal Lyapunov exponent \(\chi \). More precisely, we consider statistically typical trajectories and study the asymptotics of \(\chi \) for large N (the number of particles) and small \(\varepsilon \) (the specific energy E / N), and find, for all models, asymptotic power laws \(\chi \simeq C\varepsilon ^a\), C and a depending on the model. The asymptotics turns out to be, in general, rather slow, and producing accurate results requires a great computational effort. We also revisit and extend the analytic computation of \(\chi \) introduced by Casetti, Livi and Pettini, originally formulated for the \(\beta \)-model. With great evidence the theory extends successfully to all models of the linear hierarchy, but not to models close to Toda.     

Conduction centers in a Ta2O5−δ Fermi glass

We compare our photoemission spectra with the calculated energy spectra of oxygen vacancies in Ta oxide to identify the defects responsible for the formation of a band in the gap of a Ta oxide-based memristor. We have previously explained transitions between high and low resistance states in a memristor conducting channel under bias reversal by accumulation and depletion of oxygen in the channel. Oxidation leads to a higher resistance due to sparser conduction centers for the electrons to hop between. Here, we show that they are likely due to neutral oxygen vacancies located at ‘in-plane’ sites of the Ta–O polyhedra.     

Investigation of bright and dark solitons in α,β-Fermi Pasta Ulam lattice

We consider the Hamiltonian ofα,β-Fermi Pasta Ulam lattice and explore the Hamilton-Jacobi formalism to obtain the discrete equation of motion.By using the continuum limit approximations and incorporating some normalized parameters,the extended Korteweg-de Vries equation is obtained,with solutions that elucidate on the Fermi Pasta Ulam paradox.We further derive the nonlinear Schrodinger amplitude equation from the extended Korteweg-de Vries equation,by exploring the reductive perturbative technique.The dispersion and nonlinear coefficients of this amplitude equation are functions of theαandβparameters,with theβparameter playing a crucial role in the modulational instability analysis of the system.Forβgreater than or equal to zero,no modulational instability is observed and only dark solitons are identified in the lattice.However forβless than zero,bright solitons are traced in the lattice for some large values of the wavenumber.Results of numerical simulations of both the Korteweg-de Vries and nonlinear Schr¨odinger amplitude equations with periodic boundary conditions clearly show that the bright solitons conserve their amplitude and shape after collisions.     

Anomalous Heat Conduction in One-Dimensional Dimerized Lattices

The process of heat conduction in one-dimensional dimerized systems is studied by means of numerical simulation. Taking into account the difference between the strong bond and the weak one of the systems, our calculation indicates that heat conduction in the lattice is anomalous. For the typical parameter related to a real physical system, the divergent exponent is shown to be in agreement with that predicted by the mode-coupling theory. Moreover, our study shows that the homogeneous chain is the best thermal conductor.     

Numerical Simulation of the Non-Fourier Heat Conduction in a Solid-State Laser Medium

A hyperbolic model of non-Fourier heat conduction with non-uniform heat source is used to simulate the transient heat transfer in a high-pulse-pumped solid-state laser medium. The temperature fields are numerically analysed using the finite difference method combined with the TDMA algorithm for different pump power densities, pulse durations, thermal relaxation time and cooling intensities, respectively. The calculated results are compared with those predicted by the parabolic heat conduction model based on the Fourier law. The results indicate that the non-Fourier heat conduction phenomenon in laser media should be considered when the pump power density exceeds 104 W/m^2 or under low pulse duration. In addition, the conditions of non-Fourier effects and their influencing factors are analysed.     

The effects of cubic potentials on discrete breathers in a mixed Klein－Gordon /Fermi－Pasta－Ulam chain

Nonlinearity has a crucial impact on the symmetry properties of dynamical systems. This paper studies a one-dimensional mixed Klein--Gordon/Fermi--Pasta--Ulam diatomic chain using the expanded rotating plane-wave approximation and numerical calculations to determine the effect of cubic potentials on the symmetry properties of discrete breathers in this system. The results will be very useful to researchers in the field of numerical calculations on discrete breathers.     

On Bose–Einstein condensates in the Thomas–Fermi regime

We study a multi-group version of the mean-field or Curie–Weiss spin model. For this model, we show how, analogously to the classical (single-group) model, the three temperature regimes are defined. Then we use the method of moments to determine for each regime how the vector of the group magnetisations behaves asymptotically. Some possible applications to social or political sciences are discussed.

     

A Harmonic Solution for the Hyperbolic Heat Conduction Equation and Its Relationship to the Guyer–Krumhansl Equation

A particular solution of the hyperbolic heat-conduction equation was constructed using the method of operators. The evolution of a harmonic solution is studied, which simulates the propagation of electric signals in long wire transmission lines. The structures of the solutions of the telegraph equation and of the Guyer–Krumhansl equation are compared. The influence of the phonon heat-transfer mechanism in the environment is considered from the point of view of heat conductivity. The fulfillment of the maximum principle for the obtained solutions is considered. The frequency dependences of heat conductivity in the telegraph equation and in an equation of the Guyer–Krumhansl type are studied and compared with each other. The influence of the Knudsen number on heat conductivity in the model of thin films is studied.     

Heat Conductivity of One-Dimensional Carbon Chain in an External Potential

The heat transport m a one-dimensional （ID） carbon nanowire （CNW） lying in an external potential with different amplitudes and periods is studied by the non-equilibrium molecular dynamics method. It is found that the thermal conductivity of CNW is always anomalous, increasing with the CNW length and obeying the power law k- N, in which a decreases with the increasing external potential amplitude. The thermal conductivity could be enhanced by the external potential with rather larger amplitudes, which means that an applied external potential could be an efficient tool to improve the heat conductivity of a real 1D material In addition, the effect of different periods of the external potential is studied, finding the external potential with an incommensurate period leads to the smaller a value.     

Current state of the investigation of superallowed Fermiβ decays

Nuclear Structure: Superallowed Fermiβ transitions; derivation of the effective vector (G′_v) and induced scalar (f _s) coupling constants from experimental data. At the present time, the crucial point in a systematic study of superallowed 0⁺-0⁺ β transitions is the evaluation of the isospin impurity correctionδ _c. In the literature,δ _c is decomposed into two parts,δ _c1 and δ_c2. Several estimates ofδ _c1 have been published, while only one is available forδ _c2. We analyze the compatibility of the different estimates ofδ _c1 with the most recent surveys of experimental data. The simplest evaluation ofδ _c1 reported some years ago by Damgaard is found to yield the most satisfactory ?t values; these provide reliable values of the effective vector coupling constantG _v [e.g.,G _v=(1.41242+0.00023)×10^?49 ergcm³]. These values are in excellent agreement with a recent valueG _v=(1.41248+0.00044)×10^?49 erg cm³ obtained by Wilkinson on the basis of a phenomenologic approach toδ _c. Conversely, the most recent and detailed parentageexpansion approaches toδ _c1 lead to?t values which increase with Z, showing pronounced slopes. This fact might be due to a relative overestimation ofδ _c1 for the lighter nuclei. Using the ?t values calculated withδ _c1 as reported by Damgaard, we evaluate the coupling constant for the induced scalar interaction following a procedure described in a previous paper. The mean of such values isf _s/f _v=(?0.17±0.80)×10^?3. In addition, we develop an alternative way of determining a limit forf _s/f _v using the phenomenological approach toδ _c suggested by Wilkinson. This new procedure yieldsf _s/f _v=(?0.16±0.87)×10^?3, a result which is in excellent agreement with that obtained using the former method; both values are consistent with a value of zero, supporting the conserved vector current theory. The better accuracy of the experimental data makes it possible to reduce by a factor of two the limit established in a previous work.     

Kinetic Processes in Fermi–Luttinger Liquids

Journal of Experimental and Theoretical Physics - In this work we discuss extensions of the pioneering analysis by Dzyaloshinskii and Larkin [Sov. Phys. JETP 38, 202 (1974)] of correlation...     

Stability of the Landau–Fermi Liquid Theory

The stability of the Landau–Fermi liquid theory is investigated. It has been shown that if the interaction function of the Fermi system is a finite function of the angle between the momenta of two particles at the Fermi surface, then the liquid can be stable. We have shown that the absolute value of the expansion coefficients of the interaction functions in Legendre polynomials are decreasing function of the coefficients indices. We solve the stability condition for one photon exchange (OPE) in an electron gas. The results show that we must use the massive boson propagator (higher order corrections to the photon propagator). Similar to previous works (Abrikosov et al. in Method of Quantum Field Theory in Statistical Physics, Pergamon, Elmsford, 1965), our result is proportional to g ². The density and temperature dependence of results is occulted in the effective mass of the system.     

Heat Conduction and Entropy Production in Anharmonic Crystals with Self-Consistent Stochastic Reservoirs

We investigate a class of anharmonic crystals in d dimensions, d≥1, coupled to both external and internal heat baths of the Ornstein-Uhlenbeck type. The external heat baths, applied at the boundaries in the 1-direction, are at specified, unequal, temperatures T _l and T _r . The temperatures of the internal baths are determined in a self-consistent way by the requirement that there be no net energy exchange with the system in the non-equilibrium stationary state (NESS). We prove the existence of such a stationary self-consistent profile of temperatures for a finite system and show that it minimizes the entropy production to leading order in (T _l ?T _r ). In the NESS the heat conductivity κ is defined as the heat flux per unit area divided by the length of the system and (T _l ?T _r ). In the limit when the temperatures of the external reservoirs go to the same temperature T, κ(T) is given by the Green-Kubo formula, evaluated in an equilibrium system coupled to reservoirs all having the temperature T. This κ(T) remains bounded as the size of the system goes to infinity. We also show that the corresponding infinite system Green-Kubo formula yields a finite result. Stronger results are obtained under the assumption that the self-consistent profile remains bounded.