arXiv subjects

Stefano Lepri

Publications and source records attributed to Stefano Lepri.

At least 73 records · Page 4Linked to original sources

arXiv2007

Resonant activation in bistable semiconductor lasers

We theoretically investigate the possibility of observing resonant activation in the hopping dynamics of two-mode semiconductor lasers. We present a series of simulations of a rate-equations model under random and periodic modulation of the bias current. In both cases, for an optimal choice of the modulation time-scale, the hopping times between the stable lasing modes attain a minimum. The simulation data are understood by means of an effective one-dimensional Langevin equation with multiplicative fluctuations. Our conclusions apply to both Edge Emitting and Vertical Cavity Lasers, thus opening the way to several experimental tests in such optical systems.

physics.optics↗

arXiv2007

Statistical regimes of random laser fluctuations

Statistical fluctuations of the light emitted from amplifying random media are studied theoretically and numerically. The characteristic scales of the diffusive motion of light lead to Gaussian or power-law (Levy) distributed fluctuations depending on external control parameters. In the Levy regime, the output pulse is highly irregular leading to huge deviations from a mean--field description. Monte Carlo simulations of a simplified model which includes the population of the medium, demonstrate the two statistical regimes and provide a comparison with dynamical rate equations. Different statistics of the fluctuations helps to explain recent experimental observations reported in the literature.

physics.optics↗

arXiv2006

Anomalous kinetics and transport from 1D self--consistent mode--coupling theory

We study the dynamics of long-wavelength fluctuations in one-dimensional (1D) many-particle systems as described by self-consistent mode-coupling theory. The corresponding nonlinear integro-differential equations for the relevant correlators are solved analytically and checked numerically. In particular, we find that the memory functions exhibit a power-law decay accompanied by relatively fast oscillations. Furthermore, the scaling behaviour and, correspondingly, the universality class depends on the order of the leading nonlinear term. In the cubic case, both viscosity and thermal conductivity diverge in the thermodynamic limit. In the quartic case, a faster decay of the memory functions leads to a finite viscosity, while thermal conductivity exhibits an even faster divergence. Finally, our analysis puts on a more firm basis the previously conjectured connection between anomalous heat conductivity and anomalous diffusion.

cond-mat.stat-mech↗

arXiv2005

The one-dimensional Lennard-Jones system: collective fluctuations and breakdown of hydrodynamics

The dynamical correlations of a model consisting of particles constrained on the line and interacting with a nearest--neighbour Lennard--Jones potential are computed by molecular--dynamics simulations. A drastic qualitative change of the spectral shape, from a phonon--like to a diffusive form, is observed upon reducing the particle density even ad moderate temperatures. The latter scenario is due to the spontaneus fragmentation of the crystal--like structure into an ensemble of "clusters" colliding among themselves. In both cases, the spectral linewidths do not follow the usual q^2 behaviour for small wavenumbers q, thus signalling a breakdown of linearized hydrodynamics. This anomaly is traced back by the presence of correlations due to the reduced dimensionality.

cond-mat.stat-mech↗

arXiv2005

A simulation study of energy transport in the Hamiltonian XY-model

The transport properties of the planar rotator model on a square lattice are analyzed by means of microcanonical and non--equilibrium simulations. Well below the Kosterlitz--Thouless--Berezinskii transition temperature, both approaches consistently indicate that the energy current autocorrelation displays a long--time tail decaying as t^{-1}. This yields a thermal conductivity coefficient which diverges logarithmically with the lattice size. Conversely, conductivity is found to be finite in the high--temperature disordered phase. Simulations close to the transition temperature are insted limited by slow convergence that is presumably due to the slow kinetics of vortex pairs.

cond-mat.stat-mech↗

arXiv2005

Stretched--exponential relaxation in arrays of coupled rotators

We consider the non--equilibrium dynamics of a chain of classical rotators coupled at its edges to an external reservoir at zero temperature. We find that the energy is released in a strongly discontinuous fashion, with sudden jumps alternated with long stretches during which dissipation is extremely weak. The jumps mark the disappearance of strongly localized structures, akin to the rotobreather solutions of the Hamiltonian model, which act as insulating boundaries of a hot central core. As a result of this complex kinetics, the ensemble--averaged energy follows a stretched exponential law until a residual pseudo--stationary state is attained, where the hot core has reduced to a single localized object. We give a statistical description of the relaxation pathway and connect it to the properties of return periods of rare events in correlated time series. This approach sheds some light into the microscopic mechanism underlying the slow dynamics of the system. Finally, we show that the stretched exponential law remains unaltered in the presence of isotopic disorder.

cond-mat.other↗

arXiv2004

Studies of thermal conductivity in Fermi-Pasta-Ulam like lattices

The pioneering computer simulations of the energy relaxation mechanisms performed by Fermi, Pasta and Ulam can be considered as the first attempt of understanding energy relaxation and thus heat conduction in lattices of nonlinear oscillators. In this paper we describe the most recent achievements about the divergence of heat conductivity with the system size in 1d and 2d FPU-like lattices. The anomalous behavior is particularly evident at low energies, where it is enhanced by the quasi-harmonic character of the lattice dynamics. Remakably, anomalies persist also in the strongly chaotic region where long--time tails develop in the current autocorrelation function. A modal analysis of the 1d case is also presented in order to gain further insight about the role played by boundary conditions.

cond-mat.stat-mech↗

arXiv2004

Nonlinear supratransmission and bistability in the Fermi-Pasta-Ulam model

The recently discovered phenomenon of nonlinear supratransmission consists in a sudden increase of the amplitude of a transmitted wave triggered by the excitation of nonlinear localized modes of the medium. We examine this process for the Fermi-Pasta-Ulam chain, sinusoidally driven at one edge and damped at the other. The supratransmission regime occurs for driving frequencies above the upper band-edge and originates from direct moving discrete breather creation. We derive approximate analytical estimates of the supratransmission threshold, which are in excellent agreement with numerics. When analysing the long-time behavior, we discover that, below the supratransmission threshold, a conducting stationary state coexists with the insulating one. We explain the bistable nature of the energy flux in terms of the excitation of quasi-harmonic extended waves. This leads to the analytical calculation of a lower-transmission threshold which is also in reasonable agreement with numerical experiments.

cond-mat.stat-mech↗

arXiv2003

On the universality of anomalous one-dimensional heat conductivity

In one and two dimensions, transport coefficients may diverge in the thermodynamic limit due to long--time correlation of the corresponding currents. The effective asymptotic behaviour is addressed with reference to the problem of heat transport in 1d crystals, modeled by chains of classical nonlinear oscillators. Extensive accurate equilibrium and nonequilibrium numerical simulations confirm that the finite-size thermal conductivity diverges with the system size $L$ as $κ\propto L^α$. However, the exponent $α$ deviates systematically from the theoretical prediction $α=1/3$ proposed in a recent paper [O. Narayan, S. Ramaswamy, Phys. Rev. Lett. {\bf 89}, 200601 (2002)].

cond-mat.stat-mech↗

arXiv2003

Thermal denaturation of an helicoidal DNA model

We study the static and dynamical properties of DNA in the vicinity of its melting transition, i.e. the separation of the two strands upon heating. The investigation is based on a simple mechanical model which includes the helicoidal geometry of the molecule and allows an exact numerical evaluation of its thermodynamical properties. Dynamical simulations of long-enough molecular segments allow the study of the structure factors and of the properties of the denaturated regions. Simulations of finite chains display the hallmarks of a first order transition for sufficiently long-ranged stacking forces although a study of the model's ``universality class'' strongly suggests the presence of an ``underlying'' continuous transition.

cond-mat.stat-mech↗

arXiv2003

Clustering and ensembles inequivalence in the phi-4 and phi-6 mean-field Hamiltonian models

We investigate a model of globally coupled conservative oscillators. Two different algebraic potentials are considered that display in the canonical ensemble either a second ($ϕ^{4}$) or both a second and a first order phase transition separated by tricritical points ($ϕ^{6}$). The stability of highly clustered states appearing in the low temperature/energy region is studied both analytically and numerically for the $ϕ^{4}$-model. Moreover, long-lived out-of-equilibrium states appear close to the second order phase transition when starting with "water-bag" initial conditions, in analogy with what has been found for the Hamiltonian Mean Field (HMF) model. The microcanonical simulations of the $ϕ^{6}$-model show strong hysteretic effects and metastability near the first-order phase transition and a narrow region of negative specific heat.

cond-mat.stat-mech↗

arXiv2003

Thermal conduction in classical low-dimensional lattices

Deriving macroscopic phenomenological laws of irreversible thermodynamics from simple microscopic models is one of the tasks of non-equilibrium statistical mechanics. We consider stationary energy transport in crystals with reference to simple mathematical models consisting of coupled oscillators on a lattice. The role of lattice dimensionality on the breakdown of the Fourier's law is discussed and some universal quantitative aspects are emphasized: the divergence of the finite-size thermal conductivity is characterized by universal laws in one and two dimensions. Equilibrium and non-equilibrium molecular dynamics methods are presented along with a critical survey of previous numerical results. Analytical results for the non-equilibrium dynamics can be obtained in the harmonic chain where the role of disorder and localization can be also understood. The traditional kinetic approach, based on the Boltzmann-Peierls equation is also briefly sketched with reference to one-dimensional chains. Simple toy models can be defined in which the conductivity is finite. Anomalous transport in integrable nonlinear systems is briefly discussed. Finally, possible future research themes are outlined.

cond-mat.stat-mech↗

arXiv2002

Excitation of travelling multibreathers in anharmonic chains

We study the dynamics of the "externally" forced and damped Fermi-Pasta-Ulam (FPU) 1D lattice. The forcing has the spatial symmetry of the Fourier mode with wavenumber p and oscillates sinusoidally in time with the frequency omega. When omega is in the phonon band, the p-mode becomes modulationally unstable above a critical forcing, which we determine analytically in terms of the parameters of the system. For omega above the phonon band, the instability of the p-mode leads to the formation of a travelling multibreather, that, in the low-amplitude limit could be described in terms of soliton solutions of a suitable driven-damped nonlinear Schroedinger (NLS) equation. Similar mechanisms of instability could show up in easy-axis magnetic structures, that are governed by such NLS equations.

nlin.PS↗

arXiv2001

Pattern formation and localization in the forced-damped FPU lattice

We study spatial pattern formation and energy localization in the dynamics of an anharmonic chain with quadratic and quartic intersite potential subject to an optical, sinusoidally oscillating field and a weak damping. The zone-boundary mode is stable and locked to the driving field below a critical forcing that we determine analytically using an approximate model which describes mode interactions. Above such a forcing, a standing modulated wave forms for driving frequencies below the band-edge, while a ``multibreather'' state develops at higher frequencies. Of the former, we give an explicit approximate analytical expression which compares well with numerical data. At higher forcing space-time chaotic patterns are observed.

nlin.PS↗

arXiv2000

Memory Effects and Heat Transport in One-dimensional Insulators

We study the dynamical correlation functions and heat conduction for the simplest model of quasi one-dimensional (1d) dielectric crystal i.e. a chain of classical particles coupled by quadratic and cubic intersite potential. Even in the weakly nonlinear regime, numerical simulation on long enough chains reveal sizeable deviations from the perturbative results in the form of a slower decay of correlations in equilibrium. Their origin can be traced back to the subtle nonlinear effects described by mode-coupling theories. Measures of thermal conductivity with nonequilibrium molecular-dynamics method confirm the relevance of such effects for low-dimensional lattices even at very low temperatures.

cond-mat.stat-mech↗

arXiv1999

On modulational instability and energy localization in anharmonic lattices at finite energy density

The localization of vibrational energy, induced by the modulational instability of the Brillouin-zone-boundary mode in a chain of classical anharmonic oscillators with finite initial energy density, is studied within a continuum theory. We describe the initial localization stage as a gas of envelope solitons and explain their merging, eventually leading to a single localized object containing a macroscopic fraction of the total energy of the lattice. The initial-energy-density dependences of all characteristic time scales of the soliton formation and merging are described analytically. Spatial power spectra are computed and used for the quantitative explanation of the numerical results.

cond-mat↗

arXiv1998

Relaxation of classical many-body hamiltonians in one dimension

The relaxation of Fourier modes of hamiltonian chains close to equilibrium is studied in the framework of a simple mode-coupling theory. Explicit estimates of the dependence of relevant time scales on the energy density (or temperature) and on the wavenumber of the initial excitation are given. They are in agreement with previous numerical findings on the approach to equilibrium and turn out to be also useful in the qualitative interpretation of them. The theory is compared with molecular dynamics results in the case of the quartic Fermi-Pasta-Ulam potential.

cond-mat.stat-mech↗

arXiv1998

Mean field theory of critical coupled map lattices

We study the single-site approximation of the Perron-Frobenius equation for a coupled map lattice exhibiting a phase transition at a critical value g_c of the coupling constant. We found that the critical exponents are the same as in the usual mean-field theory of equilibrium statistical mechanics. Remarkably, the value of g_c is within six percent of the one previously obtained by numerical simulations with asynchronous updating.

cond-mat↗