arXiv subjects

Nicolas Nessi

Publications and source records attributed to Nicolas Nessi.

12 recordsLinked to original sources

arXiv2025

Dynamical typicality in classical lattice systems

Considering deterministic classical lattice systems with continuous variables, we show that, if the initial conditions are sampled according to a probability distribution in which the dynamical variables are statistically independent, the dynamical trajectory of any macroscopic observable is approximately the same for the vast majority of the states in the sample. Our proof relies on general concentration of measure results which provide tight bounds for the deviation from typical behavior in the case of large system sizes. The only condition that we assume for the dynamics is that the influence of a local perturbation in the initial state decays sufficiently fast with distance at any finite time. Our results are relevant, in particular, to classical Hamiltonian systems on a lattice. We apply our general results to a system of coupled rotors with long-range interactions, and report dynamical simulations which verify our findings.

cond-mat.stat-mech↗

arXiv2025

Similarities and differences of typicality in quantum and classical systems

Typicality is a well-established and very general property of quantum many-body systems, referring to the phenomenon that the expectation values of any given observable are practically indistinguishable for the overwhelming majority of all pure states (normalized vectors) in a sufficiently high-dimensional Hilbert (sub-)space. Here, we provide very simple and general arguments that analogous typicality properties of pure states (phase space points) in classical many-body systems are still expected to hold true for macroscopic observables, but not any more for microscopic (few-body) observables.

cond-mat.stat-mech↗

arXiv2024

Typicality from concentration of measure in models with binary state variables

We study the emergence of typicality in classical systems with a large number of binary state variables. We show analytically that for sufficiently large subsets of the complete state space, state functions which can be associated with macroscopic observables, such as density or energy, are sharply concentrated around a typical value, i.e., the vast majority of microscopic states show the same macroscopic behavior. From this static typicality result we obtain the dynamical counterpart, which states that if two initial conditions are drawn from a sufficiently large subset of the state space, the dynamical trajectories of the macroscopic observables would be approximately the same, provided that the dynamics does not compress abruptly the size of sets of states under evolution. The ensuing dynamical typicality phenomenon is very similar to what was recently found in the context of the dynamics of isolated quantum systems. We illustrate and apply our analytical results by analyzing one-dimensional cellular automata.

cond-mat.stat-mech↗

arXiv2023

Dynamic and static properties of Quantum Hall and Harmonic Oscillator systems on the non-commutative plane

We study two quantum mechanical systems on the noncommutative plane using a representation independent approach. First, in the context of the Landau problem, we obtain an explicit expression for the gauge transformation that connects the Landau and the symmetric gauge in noncommutative space. This lead us to conclude that the usual form of the symmetric gauge $\vec{A}=\left(-\fracβ{2}\hat{Y},\fracβ{2}\hat{X}\right)$, in which the constant $β$ is interpreted as the magnetic field, is not true in noncommutative space. We also be able to establish a precise definition of $β$ as function of the magnetic field, for which the equivalence between the symmetric and Landau gauges is hold in noncommutative plane. Using the symmetric gauge we obtain results for the spectrum of the Quantum Hall system, its transverse conductivity in the presence of an electric field and other static observables. These results amend the literature on Quantum Hall Effect in noncommutative plane in which the incorrect form of the symmetric gauge, in noncommutative space, is assumed. We also study the non-equilibrium dynamics of simple observables for this system. On the other hand, we study the dynamics of the harmonic oscillator in non-commutative space and show that, in general, it exhibit quasi-periodic behavior, in striking contrast with its commutative version. The study of the dynamics reveals itself as a most powerful tool to characterize and understand the effects of non-commutativity.

hep-th↗

arXiv2020

(Non equilibrium) Thermodynamics of Integrable models: The Generalized Gibbs Ensemble description of the classical Neumann Model

We study a classical integrable (Neumann) model describing the motion of a particle on the sphere, subject to harmonic forces. We tackle the problem in the infinite dimensional limit by introducing a soft version in which the spherical constraint is imposed only on average over initial conditions. We show that the Generalized Gibbs Ensemble captures the long-time averages of the soft model. We reveal the full dynamic phase diagram with extended, quasi-condensed, coordinate-, and coordinate and momentum-condensed phases. The scaling properties of the fluctuations allow us to establish in which cases the strict and soft spherical constraints are equivalent, confirming the validity of the GGE hypothesis for the Neumann model on a large portion of the dynamic phase diagram.

cond-mat.stat-mech↗

arXiv2019

Pre-asymptotic dynamics of the infinite size Neumann (p=2 spherical) model

In this contribution we further study the classical disordered p=2 spherical model with Hamiltonian dynamics, or in integrable systems terms, the Neumann model, in the infinite size limit. We summarise the asymptotic results that some of us presented in a recent publication, and we deepen the analysis of the pre-asymptotic dynamics. We also discuss the possible description of the asymptotic steady state with a Generalised Gibbs Ensemble.

cond-mat.stat-mech↗

arXiv2018

Role of initial conditions in the dynamics of quantum glassy systems

We set the formalism to study the way in which the choice of canonical equilibrium initial conditions affect the real-time dynamics of quantum disordered models. We use a path integral formulation on a time contour with real and imaginary time branches. The factorisation of the time-integration paths usually assumed in field-theoretical studies breaks down due to the averaging over quenched randomness. We derive the set of Schwinger-Dyson dynamical equations that govern the evolution of linear response and correlation functions. The solution of these equations is not straightforward as it needs, as an input, the full imaginary-time (or Matsubara frequency) dependence of the correlation in equilibrium. We check some limiting cases (equilibrium dynamics, classical limit) and we set the stage for the analytic and numerical analysis of quenches in random quantum systems.

cond-mat.dis-nn↗

arXiv2017

Quenched dynamics of classical isolated systems: the spherical spin model with two-body random interactions or the Neumann integrable model

We study the Hamiltonian dynamics of the spherical spin model with fully-connected two-body interactions drawn from a Gaussian probability distribution. In the statistical physics framework, the potential energy is of the so-called $p=2$ spherical disordered kind. Most importantly for our setting, the energy conserving dynamics are equivalent to the ones of the Neumann integrable system. We take initial conditions in thermal equilibrium and we subsequently evolve the configurations with Newton dynamics dictated by a different Hamiltonian. We identify three dynamical phases depending on the parameters that characterise the initial state and the final Hamiltonian. We obtain the {\it global} dynamical observables with numerical and analytic methods and we show that, in most cases, they are out of thermal equilibrium. We note, however, that for shallow quenches from the condensed phase the dynamics are close to (though not at) thermal equilibrium. Surprisingly enough, for a particular relation between parameters the global observables comply Gibbs-Boltzmann equilibrium. We next set the analysis of the system with finite number of degrees of freedom in terms of $N$ non-linearly coupled modes. We evaluate the mode temperatures and we relate them to the frequency-dependent effective temperature measured with the fluctuation-dissipation relation in the frequency domain, similarly to what was recently proposed for quantum integrable cases. Finally, we analyse the $N-1$ integrals of motion and we use them to show that the system is out of equilibrium in all phases, even for parameters that show an apparent Gibbs-Boltzmann behaviour of global observables. We elaborate on the role played by these constants of motion in the post-quench dynamics and we briefly discuss the possible description of the asymptotic dynamics in terms of a Generalised Gibbs Ensemble.

cond-mat.stat-mech↗

arXiv2017

Non equilibrium dynamics of isolated disordered systems: the classical Hamiltonian p-spin model

We study the dynamics of a classical disordered macroscopic model completely isolated from the environment reproducing, in a classical setting, the "quantum quench" protocol. We show that, depending on the pre and post quench parameters the system approaches equilibrium, succeeding to act as a bath on itself, or remains out of equilibrium, in two different ways. In one of the latter, the system stays confined in a metastable state in which it undergoes stationary dynamics characterised by a single temperature. In the other, the system ages and its dynamics are characterised by two temperatures associated to observations made at short and long time differences (high and low frequencies). The parameter dependence of the asymptotic states is rationalised in terms of a dynamic phase diagram with one equilibrium and two out of equilibrium phases. Aspects of pre-thermalisation are observed and discussed. Similarities and differences with the dynamics of the dissipative model are also explained.

cond-mat.stat-mech↗

arXiv2015

Prethermalization and glassiness in the bosonic Hubbard model

We investigate the non-equilibrium dynamics of the bosonic Hubbard model starting from inhomogeneous superfluid or Mott insulator initial states using the truncated Wigner approximation (TWA). We find that the relaxation of the system develops in two steps for sufficiently large interaction strengths: after a fast relaxation the system gets caught in metastable prethermalized states that precede the true equilibrium state. We find that the lifetime of these prethermalized states increases by several orders of magnitude as we increase the on-site interaction strength beyond a threshold value. We show that the emergence of long-lived metastable states in the quantum dynamics is associated with an ergodic (active) to non-ergodic (inactive) dynamical phase transition in the ensemble of classical trajectories that contribute to the semiclassical limit. This dynamic phase transition, which is very similar to that found in different classical models of glasses, is closely related to the dynamic heterogeneity of the classical relaxation.

cond-mat.stat-mech↗

arXiv2015

Glass-like Behavior in a System of One Dimensional Fermions after a Quantum Quench

We investigate the non-equilibrium relaxation dynamics of a one dimensional system of interacting spinless fermions near the XXZ integrable point. We observe two qualitatively different regimes: close to integrability and for low energies the relaxation proceeds in two steps (prethermalization scenario), while for large energies and/or away from integrability the dynamics develops in a single step. When the integrability breaking parameter is below a certain finite threshold and the energy of the system is sufficiently low the lifetime of the metastable states increases abruptly by several orders of magnitude, resembling the physics of glassy systems. This is reflected in a sudden jump in the relaxation timescales. We present results for finite but large systems and for large times compared to standard numerical methods. Our approach is based on the construction of equations of motion for one- and two-particle correlation functions using projection operator techniques.

cond-mat.quant-gas↗

arXiv2011

Finite-temperature properties of one-dimensional hard-core bosons in a quasiperiodic optical lattice

We investigate the properties of impenetrable bosons confined in a one-dimensional lattice at finite temperature in the presence of an additional incommensurate periodic potential. Relying on the exact Fermi-Bose mapping, we study the effects of temperature on the one-particle density matrix and related quantities such as the momentum distribution function and the natural orbitals. We found evidence of a finite-temperature crossover related to the zero-temperature superfluid-to-Bose-glass transition that induces a delocalization of the lowest natural orbitals.

cond-mat.quant-gas↗