1,047 research outputs found
A first-order dynamical transition in the displacement distribution of a driven run-and-tumble particle
No full textWe present here a revised version of the appendices of Gradenigo and Majumdar (2019 J. Stat. Mech. 053206). Some minor corrections are introduced and a new simplified argument to obtain the critical value of rc, the control parameter for the transition, is presented. The overall scenario and the description of the transition mechanism depicted in Gradenigo and Majumdar (2019 J. Stat. Mech. 053206) remains completely untouched, the only relevant dierence being the value of rc fixed to rc = 21/3 = 1.259 92 ... rather than rc = 1.3805 .... This dierence also implies a small quantitative changes in figures 2 and 4; a new version of both figures is reported here. A couple of other typos discovered in the paper are pointed out and the correct version of the expressions are reported
Symplectic Quantization II: Dynamics of Space–Time Quantum Fluctuations and the Cosmological Constant
No full textThe symplectic quantization scheme proposed for matter scalar fields in the companion paper (Gradenigo and Livi, arXiv:2101.02125, 2021) is generalized here to the case of space-time quantum fluctuations. That is, we present a new formalism to frame the quantum gravity problem. Inspired by the stochastic quantization approach to gravity, symplectic quantization considers an explicit dependence of the metric tensor g_{mu,nu} on an additional time variable, named intrinsic time at variance with the coordinate time of relativity, from which it is different. The physical meaning of intrinsic time, which is truly a parameter and not a coordinate, is to label the sequence of g_{mu,nu} quantum fluctuations at a given point of the four-dimensional spacetime continuum. For this reason symplectic quantization necessarily incorporates a new degree of freedom, the derivative g_{mu,nu} of the metric field with respect to intrinsic time, corresponding to the conjugated momentum pi_{mu,nu}. Our proposal is to describe the quantum fluctuations of gravity by means of a symplectic dynamics generated by a generalized action functional A[g_{mu,nu}, pi_{mu,nu}] = K[g_{mu,nu}, pi_{mu,nu}] - S[g_{mu,nu}], playing formally the role of a Hamilton function, where S[g_{mu,nu}] is the standard Einstein-Hilbert action while K[g_{mu,nu}, pi_{mu,nu}] is a new term including the kinetic degrees of freedom of the field. Such an action allows us to define an ensemble for the quantum fluctuations of g_{mu,nu} analogous to the microcanonical one in statistical mechanics, with the only difference that in the present case one has conservation of the generalized action A[g_{mu,nu}, pi_{mu,nu}] and not of energy. Since the Einstein-Hilbert action S[g_{mu,nu}] plays the role of a potential term in the new pseudo-Hamiltonian formalism, it can fluctuate along the symplectic action-preserving dynamics. These fluctuations are the quantum fluctuations of g_{mu,nu}. Finally, we show how the standard path-integral approach to gravity can be obtained as an approximation of the symplectic quantization approach. By doing so we explain how the integration over the conjugated momentum field pi_{mu,nu} gives rise to a cosmological constant term in the path-integral approach
Response to “Comment on ‘Static correlations functions and domain walls in glass-forming liquids: The case of a sandwich geometry”’ [J. Chem. Phys. 144 , 227101 (2016)]
No full textFil: Gradenigo, Giacomo. Centre National de la Recherche Scientifique; FranciaFil: Trozzo, Roberto. Aix-Marseille Université; FranciaFil: Cavagna, Andrea. Istituto Sistemi Complessi; Italia. Università degli studi di Roma "La Sapienza"; ItaliaFil: Grigera, Tomas Sebastian. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física de Líquidos y Sistemas Biológicos. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física de Líquidos y Sistemas Biológicos; Argentin
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. © 2012 American Institute of Physics
Intensity pseudo-localized phase in the glassy random laser
No full textEvidence of an emergent pseudo-localized phase characterizing the low-temperature replica symmetry breaking phase of the complex disordered models for glassy light is provided in the mode-locked random laser model. A pseudo-localized phase corresponds to a state in which the intensity of light modes is neither equipartited among all modes nor really localized on few of them. Such a hybrid phase has been recently characterized in other models, such as the Discrete Non-Linear Schrödinger equation, just as a finite size effect, while in the low temperature phase of the glassy random laser it seems to be robust in the limit of large size.21 pages, 6 figure
Glassiness and lack of equipartition in random lasers: The common roots of ergodicity breaking in disordered and nonlinear systems
No full textWe present here a unifying perspective for the lack of equipartition in nonlinear ordered systems and the low-temperature phase-space fragmentation in disordered systems. We demonstrate that they are just two manifestation of the same underlying phenomenon: ergodicity breaking. Inspired by recent experiments suggesting that lasing in optically active disordered media is related to an ergodicity-breaking transition, we studied numerically a statistical mechanics model for the nonlinearly coupled light modes in a disordered medium under external pumping. Their collective behavior appears to be akin to that displayed around the ergodicity-breaking transition in glasses, as we show measuring the glass order parameter of the replicasymmetry-breaking theory. Most remarkably, we also find that at the same critical point a breakdown of energy equipartition among light modes occurs, the typical signature of ergodicity breaking in nonlinear systems as the celebrated Fermi-Pasta-Ulam model. The crucial ingredient of our system that allows us to find equipartition breakdown together with replica symmetry breaking is that the amplitudes of light modes are locally unbounded, i.e., they are only subject to a global constraint. The physics of random lasers appears thus as a unique test-bed to develop under a unifying perspective the study of ergodicity breaking in statistical disordered systems and nonlinear ordered ones
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 base used to represent
the chain state, provided it is random.Comment: 8 pages, 5 figure
Universality class of the mode-locked glassy random laser
No full textBy means of enhanced Monte Carlo numerical simulations parallelized on GPU's
we study the critical properties of the spin-glass-like model for the
mode-locked glassy random laser, a -spin model with complex spins with a
global spherical constraint and quenched random interactions. Using two
different boundary conditions for the mode frequencies we identify the critical
points and the critical indices of the random lasing phase transition using ,
with finite size scaling techniques. The outcome of the scaling analysis is
that the mode-locked random laser is in a mean-field universality class, though
different from the mean-field class of the Random Energy Model and the glassy
random laser in the narrow band approximation, that is, the fully connected
version of the present model. The low temperature (high pumping) phase is
finally characterized by means of the overlap distribution and evidence for the
onset of replica symmetry breaking in the lasing regime is provided.Comment: 17 pages, 11 figure
Structure factors in granular experiments with homogeneous fluidization
No full textVelocity and density structure factors are measured over a hydrodynamic range of scales in a horizontal quasi-2D fluidized granular experiment, with packing fractions [10, 40]. The fluidization is realized by vertically vibrating a rough plate, on top of which particles perform a Brownian-like horizontal motion in addition to inelastic collisions. On one hand, the density structure factor is equal to that of elastic hard spheres, except in the limit of large length-scales, as it occurs in the presence of an effective interaction. On the other hand, the velocity field shows a more complex structure which is a genuine expression of a non-equilibrium steady state and which can be compared to a recent fluctuating hydrodynamic theory with non-equilibrium noise. The temporal decay of velocity modes autocorrelations is compatible with linear hydrodynamic equations with rates dictated by viscous momentum diffusion, corrected by a typical interaction time with the thermostat. Equal-time velocity structure factors display a peculiar shape with a plateau at large length-scales and another one at small scales, marking two different temperatures: the bath temperature T b, depending on shaking parameters, and the granular temperature T g T b, which is affected by collisions. The two ranges of scales are separated by a correlation length which grows with , after proper rescaling with the mean free path. © 2012 American Institute of Physics
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