Relaxation dynamics of two coherently coupled one-dimensional bosonic gases

In this work we consider the non-equilibrium dynamics of two tunnel coupled bosonic gases which are created from the coherent splitting of a one-dimensional gas. The consequences of the tunneling both in the non-stationary regime as well as at large time are investigated and compared with equilibrium results. In particular, within a semiclassical approximation, we compute correlation functions for the relative phase which are experimentally measurable and we observe a transient regime displaying oscillations as a function of the distance. The steady regime is very well approximated by a thermal state with a temperature independent of the tunneling strength.Comment: 12 pages, 4 figure

Finite temperature crossovers in periodic disordered systems

We consider the static properties of periodic structures in weak random disorder. We apply a functional renormalization group approach (FRG) and a Gaussian variational method (GVM) to study their displacement correlations. We focus in particular on the effects of temperature and we compute explicitly the crossover length scales separating different regimes in the displacement correlation function. To do so using the FRG we introduce a functional form that approximate very accurately the flow of the disorder correlator at all scales. We compare the FRG and GVM results and find excellent agreement. We show that the FRG predicts in addition the existence of a third length scale associated with the screening of the disorder by thermal fluctuations and discuss a protocol to observe it.Comment: 10 page

Leggett's bound for amorphous solids

We investigate the constraints on the superfluid fraction of an amorphous solid following from an upper bound derived by Leggett. In order 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 lower 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 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.Comment: 11 pages, 5 figure

A solvable model of quantum random optimization problems

We 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.Comment: 4 pages, 3 figures, accepted versio

Non-equilibrium dynamics of coupled Luttinger liquids

In this work we consider the dynamics of two tunnel coupled chains after a quench in the tunneling strength is performed and the two systems are let evolve independently. We describe the form of the initial state comparing with previous results concerning the dynamics after the splitting of a one-dimensional gas of bosons into two phase coherent systems. We compute different correlation functions, among which those that are relevant for interference measurements, and discuss the emergence of effective temperatures also in connection with previous works.Comment: 8 page

Fluctuation-dissipation relations and critical quenches in the transverse field Ising chain

Dynamic 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, focussing on the non-equilibrium 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.Comment: 5 pages, 3 figure

Microcanonical windows on quantum operators

We discuss a construction of a microcanonical projection WOW of a quantum operator O, its spectrum, and the retrieval of canonical many-time correlations from it.Comment: 18 pages, 4 figure

The Quantum Adiabatic Algorithm applied to random optimization problems: the quantum spin glass perspective

Among 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.Comment: 151 pages, 21 figure