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Register a new userNon equilibrium dynamics of isolated disordered systems: the classical Hamiltonian p-spin model
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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.
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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.
We study a quantum spin-1/2 chain that is dual to the canonical problem of non-equilibrium Kawasaki dynamics of a classical Ising chain coupled to a thermal bath. The Hamiltonian is obtained for the general disordered case with non-uniform Ising couplings. The quantum spin chain (dubbed Ising-Kawasaki) is stoquastic, and depends on the Ising couplings normalized by the baths temperature. We give its exact ground states. Proceeding with uniform couplings, we study the one- and two-magnon excitations. Solutions for the latter are derived via a Bethe Ansatz scheme. In the antiferromagnetic regime, the two-magnon branch states show intricate behavior, especially regarding their hybridization with the continuum. We find that that the gapless chain hosts multiple dynamics at low energy as seen through the presence of multiple dynamical critical exponents. Finally, we analyze the full energy level spacing distribution as a function of the Ising coupling. We conclude that the system is non-integrable for generic parameters, or equivalently, that the corresponding non-equilibrium classical dynamics are ergodic.
We review generalized Fluctuation-Dissipation Relations which are valid under general conditions even in ``non-standard systems, e.g. out of equilibrium and/or without a Hamiltonian structure. The response functions can be expressed in terms of suitable correlation functions computed in the unperperturbed dynamics. In these relations, typically one has nontrivial contributions due to the form of the stationary probability distribution; such terms take into account the interaction among the relevant degrees of freedom in the system. We illustrate the general formalism with some examples in non-standard cases, including driven granular media, systems with a multiscale structure, active matter and systems showing anomalous diffusion.
Equilibrium is a rather ideal situation, the exception rather than the rule in Nature. Whenever the external or internal parameters of a physical system are varied its subsequent relaxation to equilibrium may be either impossible or take very long times. From the point of view of fundamental physics no generic principle such as the ones of thermodynamics allows us to fully understand their behaviour. The alternative is to treat each case separately. It is illusionary to attempt to give, at least at this stage, a complete description of all non-equilibrium situations. Still, one can try to identify and characterise some concrete but still general features of a class of out of equilibrium problems - yet to be identified - and search for a unified description of these. In this report I briefly describe the behaviour and theory of a set of non-equilibrium systems and I try to highlight common features and some general laws that have emerged in recent years.
We propose a simple procedure by which the interaction parameters of the classical spin Hamiltonian can be determined from the knowledge of four-point correlation functions and specific heat. The proposal is demonstrated by using the correlation and specific heat data generated by Monte Carlo method on one- and two-dimensional Ising-like models, and on the two-dimensional Heisenberg model with Dzyaloshinkii-Moriya interaction. A recipe for applying our scheme to experimental images of magnetization such as those made by magnetic force microscopy is outlined.
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