All Publications

We discuss the nonequilibrium dynamics of a quantum Ising chain following a quantum quench of the transverse field and in the presence of a Gaussian time-dependent noise. We discuss the probability distribution of the work done on the system both for static and dynamic noise. While the effect of static noise is to smooth the low energy threshold of the statistic of the work, appearing for sudden quenches, a dynamical noise protocol affects also the spectral weight of such features. We also provide a detailed derivation of the kinetic equation for the Green's functions on the Keldysh contour and the time evolution of observables of physical interest, extending previously reported results [Marino and Silva, Phys. Rev. B 86, 060408 (2012)PRBMDO1098-012110.1103/ PhysRevB.86.060408], and discussing the extension of the concept of prethermalization which can be used to study noisy quantum many-body Hamiltonians driven out of equilibrium. © 2014 American Physical Society.

We study the dynamics of a quantum Ising chain after the sudden introduction of a nonintegrable long-range interaction. Via an exact mapping onto a fully connected lattice of hard-core bosons, we show that a prethermal state emerges and we investigate its features by focusing on a class of physically relevant observables. In order to gain insight into the eventual thermalization, we outline a diagrammatic approach which complements the study of the previous quasistationary state and provides the basis for a self-consistent solution of the kinetic equation. This analysis suggests that both the temporal decay towards the prethermal state and the crossover to the eventual thermal one may occur algebraically. © 2013 American Physical Society.

We study the statistics of the work done by globally changing in time with a generic protocol the mass in a free bosonic field theory with relativistic dispersion and the transverse field in the one-dimensional Ising chain both globally and locally. In the latter case we make the system start from the critical point and we describe it in the scaling limit. We provide exact formulas in all these cases for the full statistics of the work and we show that the low-energy part of the distribution of the work displays an edge singularity whose exponent does not depend on the specifics of the protocol that is chosen and may only depend on the position of the initial and final values with respect to the critical point of the system. We also show that the condensation transition found in the bosonic system for sudden quenches is robust with respect to the choice of the protocol. © 2013 American Physical Society.

We address the issue of the validity of linear response theory for a closed quantum system subject to a periodic external driving. Linear response theory (LRT) predicts energy absorption at frequencies of the external driving where the imaginary part of the appropriate response function is different from zero. Here we show that, for a fairly general nonlinear many-body system on a lattice subject to an extensive perturbation, this approximation should be expected to be valid only up to a time t* depending on the strength of the driving, beyond which the true coherent Schrödinger evolution departs from the linear response prediction and the system stops absorbing energy from the driving. We exemplify this phenomenon in detail with the example of a quantum Ising chain subject to a time-periodic modulation of the transverse field, by comparing an exact Floquet analysis with the standard results of LRT. In this context, we also show that if the perturbation is just local, the system is expected in the thermodynamic limit to keep absorbing energy, and LRT works at all times. We finally argue more generally the validity of the scenario presented for closed quantum many-body lattice systems with a bound on the energy-per-site spectrum, discussing the experimental relevance of our findings in the context of cold atoms in optical lattices and ultra-fast spectroscopy experiments. © 2013 IOP Publishing Ltd and SISSA Medialab srl.

Motivated by experiments on splitting one-dimensional quasicondensates, we study the statistics of the work done by a quantum quench in a bosonic system. We discuss the general features of the probability distribution of the work and focus on its behavior at the lowest energy threshold, which develops an edge singularity. A formal connection between this probability distribution and the critical Casimir effect in thin classical films shows that certain features of the edge singularity are universal as the postquench gap tends to zero. Our results are quantitatively illustrated by an exact calculation for noninteracting bosonic systems. The effects of finite system size, dimensionality, and nonzero initial temperature are discussed in detail. © 2013 American Physical Society.

We study the large deviation statistics of the intensive work done by globally changing a control parameter in a thermally isolated quantum many-body system. We show that, upon approaching a critical point, large deviations well below the mean work display universal features related to the critical Casimir effect in the corresponding classical system. Large deviations well above the mean are, instead, of quantum nature and not captured by the quantum-to-classical correspondence. For a bosonic system we show that in this latter regime a transition from exponential to power-law statistics, analogous to the equilibrium Bose-Einstein condensation, may occur depending on the parameters of the quench and on the spatial dimensionality. © 2012 American Physical Society.

We study the coherent dynamics of a quantum many-body system subject to a time-periodic driving. We argue that in many cases, destructive interference in time makes most of the quantum averages time periodic, after an initial transient. We discuss in detail the case of a quantum Ising chain periodically driven across the critical point, finding that, as a result of quantum coherence, the system never reaches an infinite temperature state. Floquet resonance effects are moreover observed in the frequency dependence of the various observables, which display a sequence of well-defined peaks or dips. Extensions to nonintegrable systems are discussed. © 2012 American Physical Society.

We study the unitary relaxation dynamics of disordered spin chains following a sudden quench of the Hamiltonian. We give analytical arguments, corroborated by specific numerical examples, to show that the existence of a stationary state depends crucially on the spectral and localization properties of the final Hamiltonian, and not on the initial state. We test these ideas on integrable one-dimensional models of the Ising or XY class, but argue more generally on their validity for more complex (nonintegrable) models. © 2012 American Physical Society.

We study the dynamics of thermalization resulting from a time-dependent noise in a quantum Ising chain subject to a sudden quench of the transverse magnetic field. For weak noise the dynamics shows a prethermalized state at intermediate time scales, eventually drifting towards an asymptotic infinite temperature steady state characterized by diffusive behavior. By computing analytically the density of kinks, as well as the transverse and longitudinal magnetic field correlators, we characterize these two regimes, their observability, and their signatures in the various physical quantities. © 2012 American Physical Society.

We study the emission of quasiparticles in the scaling limit of the 1D quantum Ising chain at the critical point perturbed by a time-dependent local transverse field. We compute exactly and for a generic time dependence the average value of the transverse magnetization, its correlation functions, as well as the statistics of both the inclusive and exclusive work. We show that, except for a cyclic perturbation, the probability distribution of the work at low energies is a power law whose exponent is universal, i.e., does not depend on the specific time-dependent protocol, but only on the final value attained by the perturbation. © 2012 American Physical Society.

This Colloquium gives an overview of recent theoretical and experimental progress in the area of nonequilibrium dynamics of isolated quantum systems. There is particularly a focus on quantum quenches: the temporal evolution following a sudden or slow change of the coupling constants of the system Hamiltonian. Several aspects of the slow dynamics in driven systems are discussed and the universality of such dynamics in gapless systems with specific focus on dynamics near continuous quantum phase transitions is emphasized. Recent progress on understanding thermalization in closed systems through the eigenstate thermalization hypothesis is also reviewed and relaxation in integrable systems is discussed. Finally key experiments probing quantum dynamics in cold atom systems are overviewed and put into the context of our current theoretical understanding. © 2011 American Physical Society.

We investigate the out-of-equilibrium dynamics of the one-dimensional quantum Ising model after a sudden quench in the transverse magnetic field. While for a translationally invariant system the statistical description of the asymptotic order parameter correlations after the quench can be performed in terms of the generalized Gibbs ensemble, we show that a breaking of translational invariance, e.g. by perturbing the boundary conditions, disrupts its validity. This effect, which of course vanishes in the thermodynamic limit, is shown to be very important in the presence of disorder. © 2011 IOP Publishing Ltd.

We conjecture that thermalization following a quantum quench in a strongly correlated quantum system is closely connected to many-body delocalization in the space of quasi-particles. This scenario is tested in the anisotropic Heisenberg spin chain with different types of integrability-breaking terms. We first quantify the deviations from integrability by analyzing the level spacing statistics and the inverse participation ratio of the system's eigenstates. We then focus on thermalization, by studying the dynamics after a sudden quench of the anisotropy parameter. Our numerical simulations clearly support the conjecture, as long as the integrability-breaking term acts homogeneously on the quasiparticle space, in such a way as to induce ergodicity over all the relevant Hilbert space. © 2011 American Physical Society.

We study the dynamics of the quantum Ising chain following a zero-temperature quench of the transverse field strength. Focusing on the behavior of two-point spin correlation functions, we show that the correlators of the order parameter display an effective asymptotic thermal behavior; i.e., they decay exponentially to zero with a phase coherence rate and a correlation length dictated by the equilibrium law with an effective temperature set by the energy of the initial state. On the contrary, the two-point correlation functions of the transverse magnetization or the density-of-kinks operator decay as a power law and do not exhibit thermal behavior. We argue that the different behavior is linked to the locality of the corresponding operator with respect to the quasiparticles of the model: nonlocal operators, such as the order parameter, behave thermally, while local ones do not. We study which features of the two-point correlators are a consequence of the integrability of the model by analyzing their robustness with respect to a sufficiently strong integrability-breaking term. © 2010 The American Physical Society.

We study the statistics of the work done in a zero temperature quench of the coupling constant in the Dicke model describing the interaction between an ensemble of two level systems and a single bosonic mode. When either the final or the initial coupling constants approach the critical coupling λc that separates the normal and superradiant phases of the system, the probability distribution of the work done displays singular behavior. The average work tends to diverge as the initial coupling parameter is brought closer to the critical value λc. In contrast, for quenches ending close to criticality, the distribution of work has finite moments but displays a sequence of edge singularities. This contrasting behavior is related to the difference between the processes of compression and expansion of a particle subject to a sudden change in its confining potential. We confirm this by studying in detail the time-dependent statistics of other observables, such as the quadratures of the photons and the total occupation of the bosonic modes. © 2009 The American Physical Society.

We study the dynamics of open quantum many-body systems driven across a critical point by quenching a parameter of the Hamiltonian at a certain velocity. General scaling laws are derived for the density of excitations and of energy produced during the quench as a function of the quench velocity and the bath temperature. The scaling laws and their regimes of validity are verified for the XY spin chain locally coupled to bosonic baths. A detailed derivation and analysis of the kinetic equations for the problem is presented. © 2009 The American Physical Society.

We investigate the dissipative dynamics of a quantum critical system in contact with a thermal bath, focusing on the response of the system to a sudden change of the bath temperature, in analogy to studies of aging. The specific example of the XY model in a transverse magnetic field whose spins are locally coupled to a set of bosonic baths is considered. We analyze the spin-spin correlations and block correlations and identify some universal features in the out-of-equilibrium dynamics. Two distinct regimes, characterized by different time and length scales, emerge. The initial transient dynamics is characterized by the same critical exponents as those of the equilibrium quantum phase transition and resembles the dynamics of thermal phase transitions. At long times equilibrium is reached through the propagation along the chain of a thermal front in a manner similar to the classical Glauber dynamics. © 2009 The American Physical Society.

We study the nonequilibrium dynamics of the quantum Ising model following an abrupt quench of the transverse field. We focus on the on-site autocorrelation function of the order parameter, and extract the phase-coherence time τQφ from its asymptotic behavior. We show that the initial state determines τQφ only through an effective temperature set by its energy and the final Hamiltonian. Moreover, we observe that the dependence of τQφ on the effective temperature fairly agrees with that obtained in thermal equilibrium as a function of the equilibrium temperature. © 2009 The American Physical Society.

The purpose of this work is to understand the effect of an external environment on the adiabatic dynamics of a quantum critical system. By means of scaling arguments we derive a general expression for the density of excitations produced in the quench as a function of its velocity and of the temperature of the bath. We corroborate the scaling analysis by explicitly solving the case of a one-dimensional quantum Ising model coupled to an Ohmic bath. © 2008 The American Physical Society.

We study the statistics of the work done on a quantum critical system by quenching a control parameter in the Hamiltonian. We elucidate the relation between the probability distribution of the work and the Loschmidt echo, a quantity emerging usually in the context of dephasing. Using this connection we characterize the statistics of the work done on a quantum Ising chain by quenching locally or globally the transverse field. We show that for local quenches starting at criticality the probability distribution of the work displays an interesting edge singularity. © 2008 The American Physical Society.