Thermalization processes induced by quantum monitoring in multilevel systems.

We study the heat statistics of a multilevel N-dimensional quantum system monitored by a sequence of projective measurements. The late-time, asymptotic properties of the heat characteristic function are analyzed in the thermodynamic limit of a high, ideally infinite, number M of measurements (M→∞). In this context, the conditions allowing for an infinite-temperature thermalization (ITT), induced by the repeated monitoring of the quantum system, are discussed. We show that ITT is identified by the fixed point of a symmetric random matrix that models the stochastic process originated by the sequence of measurements. Such fixed point is independent on the nonequilibrium evolution of the system and its initial state. Exceptions to ITT, which we refer to as partial thermalization, take place when the observable of the intermediate measurements is commuting (or quasicommuting) with the Hamiltonian of the quantum system or when the time interval between measurements is smaller or comparable with the system energy scale (quantum Zeno regime). Results on the limit of infinite-dimensional Hilbert spaces (N→∞), describing continuous systems with a discrete spectrum, are also presented. We show that the order of the limits M→∞ and N→∞ matters: When N is fixed and M diverges, then ITT occurs. In the opposite case, the system becomes classical, so that the measurements are no longer effective in changing the state of the system. A nontrivial result is obtained fixing M/N^{2} where instead partial ITT occurs. Finally, an example of partial thermalization applicable to rotating two-dimensional gases is presented.

Complete analysis of ensemble inequivalence in the Blume-Emery-Griffiths model.

We study inequivalence of canonical and microcanonical ensembles in the mean-field Blume-Emery-Griffiths model. This generalizes previous results obtained for the Blume-Capel model. The phase diagram strongly depends on the value of the biquadratic exchange interaction K, the additional feature present in the Blume-Emery-Griffiths model. At small values of K, as for the Blume-Capel model, lines of first- and second-order phase transitions between a ferromagnetic and a paramagnetic phase are present, separated by a tricritical point whose location is different in the two ensembles. At higher values of K the phase diagram changes substantially, with the appearance of a triple point in the canonical ensemble, which does not find any correspondence in the microcanonical ensemble. Moreover, one of the first-order lines that starts from the triple point ends in a critical point, whose position in the phase diagram is different in the two ensembles. This line separates two paramagnetic phases characterized by a different value of the quadrupole moment. These features were not previously studied for other models and substantially enrich the landscape of ensemble inequivalence, identifying new aspects that had been discussed in a classification of phase transitions based on singularity theory. Finally, we discuss ergodicity breaking, which is highlighted by the presence of gaps in the accessible values of magnetization at low energies: it also displays new interesting patterns that are not present in the Blume-Capel model.

Violent relaxation in two-dimensional flows with varying interaction range.

Understanding the relaxation of a system towards equilibrium is a long-standing problem in statistical mechanics. Here we address the role of long-range interactions in this process by considering a class of two-dimensional flows where the interaction between fluid particles varies with the distance as ∼r(α-2) for α>0. We find that changing α with a prescribed initial state leads to different flow patterns: for small α, a coarsening process leads to the formation of a sharp interface between two regions of homogenized α-vorticity; for large α, the flow is attracted to a stable dipolar structure through a filamentation process. Assuming that the energy E and the enstrophy Z are injected at a typical scale smaller than the domain scale L, we argue that convergence towards the equilibrium state is expected when the parameter (2π/L)(α)E/Z tends to one, while convergence towards a dipolar state occurs systematically when this parameter tends to zero. This suggests that weak long-range interacting systems are more prone to relax towards an equilibrium state than strong long-range interacting systems.

Dynamics of localized modes in a composite multiferroic chain.

In a coupled ferroelectric-ferromagnetic system, i.e., a composite multiferroic, the propagation of magnetic or ferroelectric excitations across the whole structure is a key issue for applications. Of special interest is the dynamics of localized magnetic or ferroelectric modes (LM) across the ferroelectric-ferromagnetic interface, particularly when the LM's carrier frequency is in the band of the ferroelectric and in the band gap of the ferromagnet. For a proper choice of the system's parameters, we find that there is a threshold amplitude above which the interface becomes transparent and an in-band ferroelectric LM penetrates the ferromagnetic array. Below that threshold, the LM is fully reflected. Slightly below this transmission threshold, the addition of noise may lead to energy transmission, provided that the noise level is neither too low nor too high, an effect that resembles stochastic resonance. These findings represent an important step towards the application of ferroelectric and/or ferromagnetic LM-based logic.

Vlasov equation for long-range interactions on a lattice.

We show that, in the continuum limit, the dynamics of Hamiltonian systems defined on a lattice with long-range couplings is well described by the Vlasov equation. This equation can be linearized around the homogeneous state, and a dispersion relation, which depends explicitly on the Fourier modes of the lattice, can be derived. This allows one to compute the stability thresholds of the homogeneous state, which turns out to depend on the mode number. When this state is unstable, the growth rates are also functions of the mode number. Explicit calculations are performed for the α-Hamiltonian mean field model with 0≤α<1, for which the mean-field mode is always found to dominate the exponential growth. The theoretical predictions are successfully compared with numerical simulations performed on a finite lattice.

Abundance of regular orbits and nonequilibrium phase transitions in the thermodynamic limit for long-range systems.

We investigate the dynamics of many-body long-range interacting systems, taking the Hamiltonian mean-field model as a case study. We show that regular trajectories, associated with invariant tori of the single-particle dynamics, prevail. The presence of such tori provides a dynamical interpretation of the emergence of long-lasting out-of-equilibrium regimes observed generically in long-range systems. This is alternative to a previous statistical mechanics approach to such phenomena which was based on a maximum entropy principle. Previously detected out-of-equilibrium phase transitions are also reinterpreted within this framework.

Time scale for magnetic reversal and the topological nonconnectivity threshold.

Anisotropic classical Heisenberg models with all-to-all spin coupling display a topological nonconnectivity threshold (TNT) for any number N of spins. Below this threshold, the energy surface is disconnected in two components with positive and negative total magnetizations, respectively, so that magnetization cannot reverse its sign and ergodicity is broken, even at finite N. Here, we solve the model in the microcanonical ensemble, using a recently developed method based on large deviation techniques, and show that a phase transition is present at an energy higher than the TNT energy. In the energy range between the TNT energy and the phase transition, magnetization changes sign stochastically and its behavior can be fully characterized by an average magnetization reversal time. The time scale for magnetic reversal can be computed analytically, using statistical mechanics. Numerical simulations confirm this calculation and further show that the magnetic reversal time diverges with a power law at the TNT threshold, with a size-dependent exponent. This exponent can be computed in the thermodynamic limit N-->(infinity), by the knowledge of entropy as a function of magnetization, and turns out to be in reasonable agreement with finite numerical simulations. We finally generalize our results to other models: Heisenberg chains with distance-dependent coupling, small 3D clusters with nearest-neighbor interactions, metastable states. We conjecture that the power-law divergence of the magnetic reversal time scale might be a universal signature of the presence of a TNT.

Breaking of ergodicity and long relaxation times in systems with long-range interactions.

The thermodynamic and dynamical properties of an Ising model with both short-range and long-range, mean-field-like, interactions are studied within the microcanonical ensemble. It is found that the relaxation time of thermodynamically unstable states diverges logarithmically with system size. This is in contrast with the case of short-range interactions where this time is finite. Moreover, at sufficiently low energies, gaps in the magnetization interval may develop to which no microscopic configuration corresponds. As a result, in local microcanonical dynamics the system cannot move across the gap, leading to breaking of ergodicity even in finite systems. These are general features of systems with long-range interactions and are expected to be valid even when the interaction is slowly decaying with distance.

First- and second-order clustering transitions for a system with infinite-range attractive interaction.

We consider a Hamiltonian system made of N classical particles moving in two dimensions, coupled via an infinite-range interaction gauged by a parameter A. This system shows a low energy phase with most of the particles trapped in a unique cluster. At higher energy it exhibits a transition towards a homogenous phase. For sufficiently strong coupling A, an intermediate phase characterized by two clusters appears. Depending on the value of A, the observed transitions can be either second or first order in the canonical ensemble. In the latter case, microcanonical results differ dramatically from canonical ones. However, a canonical analysis, extended to metastable and unstable states, is able to describe the microcanonical equilibrium phase. In particular, a microcanonical negative specific heat regime is observed in the proximity of the transition whenever it is canonically discontinuous. In this regime, microcanonically stable states are shown to correspond to saddles of the Helmholtz free energy, located inside the spinodal region.

Pattern formation and localization in the forced-damped Fermi-Pasta-Ulam 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.

Transport properties of the diluted Lorentz slab.

We study the behavior of a point particle incident on a slab of a randomly diluted triangular array of circular scatterers. Various scattering properties, such as the reflection and transmission probabilities and the scattering time are studied as a function of thickness and dilution. We show that a diffusion model satisfactorily describes the mentioned scattering properties. We also show how some of these quantities can be evaluated exactly and their agreement with numerical experiments. Our results exhibit the dependence of these scattering data on the mean free path. This dependence again shows excellent agreement with the predictions of a Brownian motion model.

Inequivalence of ensembles in a system with long-range interactions.

We study the global phase diagram of the infinite-range Blume-Emery-Griffiths model both in the canonical and in the microcanonical ensembles. The canonical phase diagram shows first-order and continuous transition lines separated by a tricritical point. We find that below the tricritical point, when the canonical transition is first order, the phase diagrams of the two ensembles disagree. In this region the microcanonical ensemble exhibits energy ranges with negative specific heat and temperature jumps at transition energies. These results can be extended to weakly decaying nonintegrable interactions.

One-dimensional toy model of globular clusters.

We introduce a one-dimensional toy model of globular clusters. The model is a version of the well-known gravitational sheets system, where we also take into account mass and energy loss by evaporation of stars at the boundaries. Numerical integration by the "exact" event-driven dynamics is performed, for initial uniform density and Gaussian random velocities. Two distinct quasistationary asymptotic regimes are attained, depending on the initial energy of the system. We guess the forms of the density and velocity profiles that fit numerical data extremely well and allow us to perform an independent calculation of the self-consistent gravitational potential. Some power laws for the asymptotic number of stars and for the collision times are suggested.

Finite times to equipartition in the thermodynamic limit.

We study the time scale T to equipartition in a 1D lattice of N masses coupled by quartic nonlinear (hard) springs (the Fermi-Pasta-Ulam beta model). We take the initial energy to be either in a single mode gamma or in a package of low-frequency modes centered at gamma and of width deltagamma, with both gamma and deltagamma proportional to N. These initial conditions both give, for finite energy densities E/N, a scaling in the thermodynamic limit (large N), of a finite time to equipartition which is inversely proportional to the central mode frequency times a power of the energy density (E/N). A theory of the scaling with (E/N) is presented and compared to the numerical results in the range 0.03

A twist opening model for DNA.

The real mechanisms of several biological processes involving DNA are not yet understood. We discuss here some aspects of the initiation of transcription, in particular the formation of the open complex and the activation mechanism associated to enhancer binding proteins. Transcription activation seems to be governed by underlying dynamical mechanisms related to several distortions of the double chain structure: a dynamical approach on a mesoscopic description level could then allow a deeper understanding of this complex process. Starting from the Peyrard Bishop (PB) model, that considers only the hydrogen bond stretching of each base pair, we describe here an extended DNA model, proposed in [1], that allows a rather good representation of the double helix geometry and of its structural features by the introduction of angular variables related to the twist angle. Using a generalized multiple scale expansion for the case of vectorial lattices derived elsewhere [2], we derive analytically small amplitude approximate solutions of the model which are movable and spatially localized: we present here the results of this calculation and show how the special shape of the solutions is in good agreement with what can be expected for coupled angular radial distortions in the real molecule.

Analysis of genomic patchiness of Haemophilus influenzae and Saccharomyces cerevisiae chromosomes.

We have analysed some aspects of the primary structure of the chromosome of the prokaryote Haemophilus influenzae and of the eukaryote Saccharomyces cerevisiae that share the same G + C content. In particular, we have investigated genomic patchiness over the gene size level (10 Kb) and that patchiness due to long homogenous tracts. Long polypurine and polypyrmidine tracts that are largely over-represented in S. cerevisiae chromosomes and under-represented in H. influenzae, are responsible for a large fraction of long correlation signals. Generating mechanisms of long homogenous tracts are DNA replication slippage and duplication events that appear to be linked processes driving chromosome primary structure evolution.

High statistics block entropy measures of DNA sequences.

We have used an improved block-entropy measure in order to gain some further insights into the short-range correlations present in whole chromosomes of S. cerevisiae, viruses and organelles and very large genomic regions of E. coli. Although DNA sequences are largely inhomogeneous and word frequencies are unevenly distributed, the comparison of entire chromosomes and large genomic regions show a "bulk" composition homogeneity. This property suggests that biases in selection, directional mutational pressure and recombination processes act in homogenizing the base composition of the DNA molecules within a genome but their mode of action, relative impact and direction may vary in different organisms. The most interesting results appear to be the differences between the SW (C,G/A,T) and RY (A,G/C,T) two-letter alphabet entropies. Deviations from randomness in E. coli and S. cerevisiae sequences particularly concern SW dinucleotide frequencies and RY tetranucleotide frequencies.