1,721,021 research outputs found
A study of the Fermi-Pasta-Ulam problem in dimension two
No full textContinuing the previous work on the same subject, we study here different two-dimensional Fermi–Pasta–Ulam (FPU)-like models, namely, planar models with a triangular cell, molecular-type potential and different boundary conditions, and perform on them both traditional FPU-like numerical experiments, i.e., experiments in which energy is initially concentrated on a small subset of normal modes, and other experiments, in which we test the time scale for the decay of a large fluctuation when all modes are excited almost to the same extent. For each experiment, we observe the behavior of the different two-dimensional systems and also make an accurate comparison with the behavior of a one-dimensional model with an identical potential. We assume the thermodynamic point of view and try to understand the behavior of the system for large n (the number of degrees of freedom) at fixed specific energy ε = E/n. As a result, it turns out that: (i) The difference between dimension one and two, if n is large, is substantial. In particular (making reference to FPU-like initial conditions) the “one-dimensional scenario,” in which the dynamics is dominated for a long time scale by a weakly chaotic metastable situation, in dimension two is absent; moreover in dimension two, for large n, the time scale for energy sharing among normal modes is drastically shorter than in dimension one. (ii) The boundary conditions in dimension two play a relevant role. Indeed, models with fixed or open boundary conditions give fast equipartition, on a rather short time scale of order ε−1, while a periodic model gives longer equilibrium times (although much shorter than in dimension one)
How non-equilibrium correlations in active matter reveal the topological crossover in glasses
No full textAs shown by early studies on mean-field models of the glass transition, the geometrical features of the energy landscape provide fundamental information on the crossover from high-temperature simple relaxational dynamics to low-temperature activated relaxation. In particular, the critical slowing down of dynamics typical of glass formers has been related to a crossover from a saddle-dominated energy landscape (at high temperatures) to a minima-dominated landscape (at low temperatures). We show that active particles can serve as a useful tool to gain insight into this topological crossover. Once configurations equilibrated down in the glassy phase are provided, we show how features of the landscape are revealed by switching on some activity in particle dynamics. In particular we explain here the mechanism, taking as a reference point the pure p-spin model, by which the presence of self-propulsion is expected to induce critical stationary non-equilibrium correlations in correspondence to the minima-to saddles crossover
Symplectic quantization I: dynamics of quantum fluctuations in a relativistic field theory
No full textWe propose here a new symplectic quantization scheme, where quantum fluctuations of a scalar field theory stem from two main assumptions: relativistic invariance and equiprobability of the field configurations with identical value of the action. In this approach the fictitious time of stochastic quantization becomes a genuine additional time variable, with respect to the coordinate time of relativity. This intrinsic time is associated to a symplectic evolution in the action space, which allows one to investigate not only asymptotic, i.e. equilibrium, properties of the theory, but also its non-equilibrium transient evolution. In this paper, which is the first one in a series of two, we introduce a formalism which will be applied to general relativity in its companion work (Gradenigo, Symplectic quantization II: dynamics of space-time quantum fluctuations and the cosmological constant, 2021)
Entropy production in non-equilibrium fluctuating hydrodynamics
No full textFluctuating entropy production is studied for a set of linearly coupled complex fields. The general result is applied to non-equilibrium fluctuating hydrodynamic equations for coarse-grained fields (density, temperature, and velocity), in the framework of model granular fluids. We find that the average entropy production, obtained from the microscopic stochastic description, can be expressed in terms of macroscopic quantities, in analogy with linear non-equilibrium thermodynamics. We consider the specific cases of driven granular fluids with two different kinds of thermostat and the homogeneous cooling regime. In all cases, the average entropy production turns out to be the product of a thermodynamic force and a current: the former depends on the specific energy injection mechanism, the latter takes always the form of a static correlation between fluctuations of density and temperature time-derivative. Both vanish in the elastic limit. The behavior of the entropy production is studied at different length scales and the qualitative differences arising for the different granular models are discussed
Confinement as a tool to probe amorphous order
No full textWe study the effect of confinement on glassy liquids using Random First Order Transition theory as framework. We show that the characteristic length-scale above which confinement effects become negligible is related to the point-to-set length-scale introduced to measure the spatial extent of amorphous order in super-cooled liquids. By confining below this characteristic size, the system becomes a glass. Eventually, for very small sizes, the effect of the boundary is so strong that any collective glassy behavior is wiped out. We clarify similarities and differences between the physical behaviors induced by confinement and by pinning particles outside a spherical cavity (the protocol introduced to measure the point-to-set length). Finally, we discuss possible numerical and experimental tests of our predictions
Thermalization without chaos in harmonic systems
No full textRecent numerical results showed that thermalization of Fourier modes is achieved in short time-scales in the Toda model, despite its integrability and the absence of chaos. Here we provide numerical evidence that the scenario according to which chaos is irrelevant for thermalization is realized even in the simplest of all classical integrable system: the harmonic chain. We study relaxation from an atypical condition given with respect to random modes, showing that a thermal state with equilibrium properties is attained in short times. Such a result is independent from the orthonormal basis used to represent the chain state, provided it is a random basis
Field-induced superdiffusion and dynamical heterogeneity
No full textBy analyzing two Kinetically Constrained Models of supercooled liquids we show that the anomalous transport of a driven tracer observed in supercooled liquids is another facet of the phenomenon of dynamical heterogeneity. We focus on the Fredrickson-Andersen and the Bertin-Bouchaud-Lequeux models. By numerical simulations and analytical arguments we demonstrate that the violation of the Stokes-Einstein relation and the observed field-induced superdiffusion have the same physical origin: while a fraction of probes do not move, others jump repeatedly because they are close to local mobile regions. The anomalous fluctuations observed out of equilibrium in presence of a pulling force ε, σ2x(t)=⟨x2ε(t)⟩−⟨xε(t)⟩2∼t3/2, which are accompanied by the asymptotic decay αε(t)∼t−1/2 of the non-Gaussian parameter from non-trivial values to zero, are due to the splitting of the probes population in the two (mobile and immobile) groups and to dynamical correlations, a mechanism expected to happen generically in supercooled liquids
First-order condensation transition in the position distribution of a run-and-tumble particle in one dimension
No full textWe consider a single run-and-tumble particle (RTP) moving in one dimension. We assume that the velocity of the particle is drawn independently at each tumbling from a zero-mean Gaussian distribution and that the run times are exponentially distributed. We investigate the probability distribution P(X, N) of the position X of the particle after N runs, with N >> 1. We show that in the regime X ~ N^{3/4} the distribution P(X, N) has a large deviation form with a rate function characterized by a discontinuous derivative at the critical value X = X_c > 0. The same is true for X = −X_c due to the symmetry of P(X, N). We show that this singularity corresponds to a first-order condensation transition: for X > X_c a single large jump dominates the RTP trajectory. We consider the participation ratio of the single-run displacements as the order parameter of the system, showing that this quantity is discontinuous at X = X_c. Our results are supported by numerical simulations performed with a constrained Markov chain Monte Carlo algorithm
Statistical Mechanics of an Integrable System
No full textWe provide here an explicit example of Khinchin’s idea that the validity of equilibrium statistical mechanics in high dimensional systems does not depend on the details of the dynamics, as it is basically a matter of choosing the “proper” observables. This point of view is supported by extensive numerical simulation of the one-dimensional Toda chain, an integrable non-linear Hamiltonian system where all Lyapunov exponents are zero by definition. We study the relaxation to equilibrium starting from very atypical initial conditions and focusing on energy equipartion among Fourier modes, as done in the original Fermi-Pasta-Ulam-Tsingou numerical experiment. We consider other indicators of thermalization as well, e.g. Boltzmann-like probability distributions of energy and the behaviour of the specific heat as a function of temperature, which is compared to analytical predictions. We find evidence that in the general case, i.e., not in the perturbative regime where Toda and Fourier modes are close to each other, there is a fast reaching of thermal equilibrium in terms of a single temperature. We also find that equilibrium fluctuations, in particular the behaviour of specific heat as function of temperature, are in agreement with analytic predictions drawn from the ordinary Gibbs ensemble. The result has no conflict with the established validity of the Generalized Gibbs Ensemble for the Toda model, which is on the contrary characterized by an extensive number of different temperatures. Our results suggest thus that even an integrable Hamiltonian system reaches thermalization on the constant energy hypersurface, provided that the considered observables do not strongly depend on one or few of the conserved quantities. This suggests that dynamical chaos is irrelevant for thermalization in the large-N limit, where any macroscopic observable reads of as a collective variable with respect to the coordinate which diagonalize the Hamiltonian. The possibility for our results to be relevant for the problem of thermalization in generic quantum systems, i.e., non-integrable ones, is commented at the end
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