1,720,964 research outputs found
Dynamic correlations, fluctuation-dissipation relations, and effective temperatures after a quantum quench of the transverse field Ising chain
No full textFluctuation-dissipation relations, i.e., the relation between two-time correlation and linear response functions, were successfully used to search for signs of equilibration and to identify effective temperatures in the non-equilibrium behavior of a number of macroscopic classical and quantum systems in contact with thermal baths. Among the most relevant cases in which the effective temperatures thus defined were shown to have a thermodynamic meaning one finds the stationary dynamics of driven super-cooled liquids and vortex glasses, and the relaxation of glasses. Whether and under which conditions an effective thermal behavior can be found in quantum isolated many-body systems after a global quench is a question of current interest. We propose to study the possible emergence of thermal behavior long after the quench by studying fluctuation-dissipation relations in which (possibly time- or frequency-dependent) parameters replace the equilibrium temperature. If thermalization within the Gibbs ensemble eventually occurs these parameters should be constant and equal for all pairs of observables in 'partial' or 'mutual' equilibrium. We analyze these relations in the paradigmatic quantum system, i.e., the quantum Ising chain, in the stationary regime after a quench of the transverse field. The lack of thermalization to a Gibbs ensemble becomes apparent within this approach
On the relation between kinetically constrained models of glass dynamics and the random first-order transition theory
No full textIn this paper we revisit and extend the mapping between two apparently different classes of models. The first class contains the prototypical models described-at the mean-field level-by the random first-order transition (RFOT) theory of the glass transition, called either the 'random XORSAT problem' (in the information theory community) or the 'diluted p-spin model' (in the spin glass community), undergoing a single spin-flip Glauber dynamics. The models in the second class are kinetically constrained models (KCM): their Hamiltonian is that of independent spins in a constant magnetic field, hence their thermodynamics is completely trivial, but the dynamics is such that only groups of spins can flip together, thus implementing a kinetic constraint that induces a non-trivial dynamical behavior. A mapping between some representatives of these two classes has been known for a long time. Here we formally prove this mapping at the level of the master equation, and we apply it to the particular case of Bethe lattice models. This allows us to show that an RFOT model can be mapped exactly into a KCM. However, the natural order parameter for the RFOT model, namely the spin overlap, is mapped into a very complicated non-local function in the KCM. Therefore, if one were to study the KCM without knowing the mapping onto the RFOT model, one would guess that its physics is quite different from the RFOT one. Our results instead suggest that these two apparently different descriptions of the glass transition are, at least in some cases, closely related
Fluctuation-dissipation relations and critical quenches in the transverse field Ising chain
No full textDynamic correlation and response functions of classical and quantum systems in thermal equilibrium are connected by fluctuation-dissipation theorems, which allow an alternative definition of their (unique) temperature. Motivated by this fundamental property, we revisit the issue of thermalization of closed many-body quantum systems long after a sudden quench, focusing on the nonequilibrium dynamics of the Ising chain in a critical transverse field. We show the emergence of distinct observable-dependent effective temperatures, which rule out Gibbs thermalization in a strict sense but might still have a thermodynamic meaning
Leggett's bound for amorphous solids
No full textWe investigate the constraints on the superfluid fraction of an amorphous solid following from an upper bound derived by Leggett. To accomplish this, we use as input density profiles generated for amorphous solids in a variety of different manners including by investigating Gaussian fluctuations around classical results. These rough estimates suggest that, at least at the level of the upper bound, there is not much difference in terms of superfluidity between a glass and a crystal characterized by the same Lindemann ratio. Moreover, we perform path integral Monte Carlo simulations of distinguishable helium-4 rapidly quenched from the liquid phase to very low temperature, at the density of the freezing transition. We find that the system crystallizes very quickly, without any sign of intermediate glassiness. Overall our results suggest that the experimental observations of large superfluid fractions in helium-4 particles after a rapid quench correspond to samples evolving far from equilibrium, instead of being in a stable glass phase. Other scenarios and comparisons to other results on the super-glass phase are also discussed
Electrostatic solution of massless quenches in Luttinger liquids
No full textThe study of non-equilibrium dynamics of many-body systems after a quantum quench received a considerable boost and a deep theoretical understanding from the path integral formulation in imaginary time. However, the celebrated problem of a quench in the Luttinger parameter of a one dimensional quantum critical system (massless quench) has so far only been solved in the real-time Heisenberg picture. In order to bridge this theoretical gap and to understand on the same ground massive and massless quenches, we study the problem of a gaussian field characterized by a coupling parameter K within a strip and a different one K-0 in the remaining two semi-infinite planes. We give a fully analytical solution using the electrostatic analogy with the problem of a dielectric material within a strip surrounded by an infinite medium of different dielectric constant, and exploiting the method of charge images. After analytic continuation, this solution allows us to obtain all the correlation functions after the quench within a path integral approach in imaginary time, thus recovering and generalizing the results in real time. Furthermore, this imaginary-time approach establishes a remarkable connection between the quench and the famous problem of the conductivity of a Tomonaga-Luttinger liquid coupled to two semi-infinite leads: the two are in fact related by a rotation of the spacetime coordinates
The quantum adiabatic algorithm applied to random optimization problems: The quantum spin glass perspective
No full textAmong various algorithms designed to exploit the specific properties of quantum computers with respect to classical ones, the quantum adiabatic algorithm is a versatile proposition to find the minimal value of an arbitrary cost function (ground state energy). Random optimization problems provide a natural testbed to compare its efficiency with that of classical algorithms. These problems correspond to mean field spin glasses that have been extensively studied in the classical case. This paper reviews recent analytical works that extended these studies to incorporate the effect of quantum fluctuations, and presents also some original results in this direction. (c) 2012 Elsevier B.V. All rights reserved
Solvable Model of Quantum Random Optimization Problems
No full textWe study the quantum version of a simplified model of optimization problems, where quantum fluctuations are introduced by a transverse field acting on the qubits. We find a complex low-energy spectrum of the quantum Hamiltonian, characterized by an abrupt condensation transition and a continuum of level crossings as a function of the transverse field. We expect this complex structure to have deep consequences on the behavior of quantum algorithms attempting to find solutions to these problems
Quantum Biroli-Mézard model: Glass transition and superfluidity in a quantum lattice glass model
No full textWe study the quantum version of a lattice model whose classical counterpart captures the physics of structural glasses. We discuss the role of quantum fluctuations in such systems and in particular their interplay with the amorphous order developed in the glass phase. We show that quantum fluctuations might facilitate the formation of the glass at low enough temperature. We also show that the glass transition becomes a first-order transition between a superfluid and an insulating glass at very low temperature, and is therefore accompanied by phase coexistence between superfluid and glassy regions
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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