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We prove that a recently derived correlation equality between conserved charges and their associated conserved currents for quantum systems far from equilibrium [O.A. Castro-Alvaredo et al., Phys. Rev. X \textbf{6}, 041065 (2016)], is valid under more general conditions than assumed so far. Similar correlation identities, which in generalized Gibbs ensembles give rise to a current symmetry somewhat reminiscent of the Onsager relations, turn out to hold also in the absence of translation invariance, for lattice models, and in any space dimension, and to imply a symmetry of the non-equilibrium linear response functions., 6 pages, major revision with extension to non-translation invariant setting

Time-dependent Lindblad master equations have important applications in areas ranging from quantum thermodynamics to dissipative quantum computing. In this paper we outline a general method for writing down exact solutions of time-dependent Lindblad equations whose superoperators form closed algebras. We focus on the particular case of a single qubit and study the exact solution generated by both coherent and incoherent mechanisms. We also show that if the time-dependence is periodic, the problem may be recast in terms of Floquet theory. As an application, we give an exact solution for a two-levels quantum heat engine operating in a finite-time., Comment: 15 pages, 12 figures

International audience; We consider the open isotropic spin-1/2 Heisenberg quantum spin chain with a finite number N of sites coupled at the ends to a dissipative environment that favors polarization of the boundary spins in different directions. We review the matrix product ansatz (MPA) that yields the exact reduced density matrix of the Heisenberg chain. We develop the matrix algebra coming from the MPA in more detail than in previous work. We hence obtain exact results for the nonequilibrium partition function, about the impact of quantum fluctuations on the targeted boundary states, and for current–magnetization correlations in the steady state. The boundary states turn out to be pure to the order o(N−2). We show that the local magnetization and the local current perpendicular to the plane spanned by the boundary polarizations exhibit long-range correlations while the local magnetization correlations with the local in-plane currents are strongly suppressed.

The operation of autonomous finite-time quantum heat engines rely on the existence of a stable limit cycle in which the dynamics becomes periodic. The two main questions that naturally arise are therefore whether such a limit cycle will eventually be reached and, once it has, what is the state of the system within the limit cycle. In this paper we show that the application of Floquet's theory to Lindblad dynamics offers clear answers to both questions. By moving to a generalized rotating frame, we show that it is possible to identify a single object, the Floquet Liouvillian, which encompasses all operating properties of the engine. First, its spectrum dictates the convergence to a limit cycle. And second, the state within the limit cycle is precisely its zero eigenstate, therefore reducing the problem to that of determining the steady-state of a time-independent master equation. To illustrate the usefulness of this theory, we apply it to a harmonic oscillator subject to a time-periodic work protocol and time-periodic dissipation, an open-system generalization of the Ermakov-Lewis theory. The use of this theory to implement a finite-time Carnot engine subject to continuous frequency modulations is also discussed.

We study the dynamics of entanglement between two spins which is created by the coupling to a common thermal reservoir. The reservoir is a spin-$\frac{1}{2}$ Ising transverse field chain thermally excited, the two defect spins couple to two spins of the chain which can be at a macroscopic distance. In the weak-coupling and low-temperature limit the spin chain is mapped onto a bath of linearly interacting oscillators using the Holstein-Primakoff transformation. We analyse the time evolution of the density matrix of the two defect spins for transient times and deduce the entanglement which is generated by the common reservoir. We discuss several scenarios for different initial states of the two spins and for varying distances., Comment: 16 pages, 5 figures

We consider space-time correlations in driven diffusive systems which undergo a fluctuation into a regime with an atypically large current or dynamical activity. For a single conserved mass we show that the spatio-temporal density correlations in one space dimension are given by conformally invariant field theories with central charge $c=1$, corresponding to a ballistic universality class with dynamical exponent $z=1$. We derive a phase diagram for atypical behaviour that besides the conformally invariant regime exhibits a regime of phase separation for atypically low current or activity. On the phase transition line, corresponding to typical behaviour, the dynamics belongs to the Kardar-Parisi-Zhang universality class with dynamical exponent $z=3/2$, except for a diffusive point with $z=2$. We demonstrate the validity of the theory for the one-dimensional asymmetric simple exclusion process with both periodic and open boundaries by exact results for the dynamical structure in the limit of maximal current., 5 pages, 2 figures. Revision with typo in Eq. (1) corrected and some cosmetic changes

We present a general construction of matrix product states for stationary density matrices of one-dimensional quantum spin systems kept out of equilibrium through boundary Lindblad dynamics. As an application we review the isotropic Heisenberg quantum spin chain which is closely related to the generator of the simple symmetric exclusion process. Exact and heuristic results as well as numerical evidence suggest a local quantum equilibrium and long-range correlations reminiscent of similar large-scale properties in classical stochastic interacting particle systems that can be understood in terms of fluctuating hydrodynamics.

The statistics of the heat exchanged between two quantum XX spin chains prepared at different temperatures is studied within the assumption of weak coupling. This provides simple formulas for the average heat and its corresponding characteristic function, from which the probability distribu- tion may be computed numerically. These formulas are valid for arbitrary sizes and therefore allow us to analyze the role of the thermodynamic limit in this non-equilibrium setting. It is found that all thermodynamic quantities are extremely sensitive to the quantum phase transition of the XX chain.

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We investigate the conditions for reactivity enhancement of a catalytic cracking process in porous crystalline solids using the concept of molecular traffic control (MTC). Using dynamic Monte Carlo simulations we obtain a quantitative description of the MTC effect for a bimodal network of intersecting size-selective channels over a wide range of grain parameters, diffusivities and reaction constants, and external operating conditions. The results are compared with those obtained on a similar network but with only one type of channels, called the reference system. We find significant reactivity enhancement in the MTC system with respect to the reference system. This effect is observed to increase with the grain size, and also with longer segments between lattice intersections. We find that in certain regions of the microscopic reaction rate the reactivity enhancement is up to 68%.

In this paper we present the results obtained concerning the relaxation behaviour of a non equilibrium Ising quantum chain. In particular, we have focues our attention into the transverse magnetization. The out-of-equilibriumness is generated by setting up an initial thermal inhomogeneity. We present two different initial conditions: a completely factorized state, where all the spins are thermalized independently and second a system-bath case, where half of the chain called the system is thermalized at a temperature Ts and the remaining half is at a temperature Tb. In both cases, the magnetization profiles are calculated either analytically or numerically and show a scaling behaviour. It is also found that in the two-temperature case the magnetization relaxes in quantized steps in the strong transverse field region.

We consider the unitary time evolution of a one-dimensional cloud of hard-core bosons loaded on a harmonic trap potential which is slowly released in time with a general ramp $g(t)$. After the identification of a typical length scale $\ell(t)$, related to the time ramp, we focus our attention on the dynamics of the density profile within a first order time-dependent perturbation scheme. In the special case of a linear ramp, we compare the first order predictions to the exact solution obtained through Ermakov-Lewis dynamical invariants. We also obtain an exact analytical solution for a cloud released from a harmonic trap with an amplitude that varies as the inverse of time. In such situation, the typical size of the cloud grows with a power law governed by an exponent that depends continuously on the initial trap frequency. At high enough initial trap amplitude, the exponent acquires an imaginary part that leads to the emergence of a log-periodic modulation of the cloud expansion., 22 pages, 12 figures

The surface magnetization of the quantum XY chain in a transverse field is found for arbitrary nearest neighbour interactions in closed form. This allows to derive the bulk phase diagram in a simple way. The magnetic surface behaviour and the bulk correlation length are found exactly., 5 pages, to be published in J. Phys. A

We consider cooperative processes (quantum spin chains and random walks) in one-dimensional fluctuating random and aperiodic environments characterized by fluctuating exponents omega>0. At the critical point the random and aperiodic systems scale essentially anisotropically in a similar fashion: length (L) and time (t) scales are related as t ~ log^{1/omega}. Also some critical exponents, characterizing the singularities of average quantities, are found to be universal functions of omega, whereas some others do depend on details of the distribution of the disorder. In the off-critical region there is an important difference between the two types of environments: in aperiodic systems there are no extra (Griffiths)-singularities., 13 pages RevTeX, 10 eps-figures included

The effect of point defects on persistent currents in mesoscopic systems is studied in a simple tight-binding model. Using an analogy with the treatment of the critical quantum Ising chain with defects, conformal invariance techniques are employed to relate the persitent current amplitude to the Hamiltonian spectrum jsut above the Fermi energy. From this, the dependence of the current on the magnetic flux is found exactly for a ring with one or two point defects. The effect of an aperiodic modulation of the ring, generated through a binary substitution sequence, on the persistent current is also studied. The flux-dependence of the current is found to vary remarkably between the Fibonacci and the Thue-Morse sequences., Comment: 18 pages, Latex with epsf, including 5 figures

We consider the defect production of a quantum system, initially prepared in a current-carrying non-equilibrium state, during its unitary driving through a quantum critical point. At low values of the initial current, the quantum Kibble-Zurek scaling for the production of defects is recovered. However, at large values of the initial current, i.e., very far from an initial equilibrium situation, a universal scaling of the defect production is obtained which shows an algebraic dependence with respect to the initial current value. These scaling predictions are demonstrated by the exactly solvable Ising quantum chain where the current-carrying state is selected through the imposition of a Dzyaloshinskii-Moriya interaction term., Comment: 13 pages, 3 figures. v2: Minor changes. This is an author-created, un-copyedited version of an article published in JSTAT. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at http://dx.doi.org/10.1088/1742-5468/2016/03/033204

Conformal invariance has been a spectacularly successful tool in advancing our understanding of the two-dimensional phase transitions found in classical systems at equilibrium. This volume sharpens our picture of the applications of conformal invariance, introducing non-local observables such as loops and interfaces before explaining how they arise in specific physical contexts. It then shows how to use conformal invariance to determine their properties. Moving on to cover key conceptual developments in conformal invariance, the book devotes much of its space to stochastic Loewner evolution (SLE), detailing SLE’s conceptual foundations as well as extensive numerical tests. The chapters then elucidate SLE’s use in geometric phase transitions such as percolation or polymer systems, paying particular attention to surface effects. As clear and accessible as it is authoritative, this publication is as suitable for non-specialist readers and graduate students alike.

An easily readable introduction to the main concepts and techniques of conformal invariance is provided. Starting from the global scale-invariance at a critical point, it is argued, through the local conformal Ward identities, that under mild conditions an extension to a local form of scale-invariance, namely conformally invariance, is in general possible. In two space dimensions, the particular role of the infinite-dimensional Lie algebra of conformal transformations is outlined and the main concepts, namely those of a primary scaling operator, the conformal energy-momentum tensor, the Virasoro algebra and the central charge and the main facts of their unitary and/or minimal representations will be presented. Some simple applications for the explicit calculation of two-point functions will be given. The free boson will be used as a paradigmatic illustration and we shall close with an outline of surface critical phenomena and their description in terms of boundary conformal field-theory.

We describe the coherent quantum evolution of a quantum many-body system with a time-dependent power-law confining potential. The amplitude of the inhomogeneous potential is driven in time along a nonlinear ramp which crosses a critical point. Using Kibble-Zurek-like scaling arguments we derive general scaling laws for the density of excitations and energy excess generated during the nonlinear sweep of the confining potential. It is shown that, with respect to the sweeping rate, the densities follow algebraic laws with exponents that depend on the space-time properties of the potential and on the scaling dimensions of the densities. We support our scaling predictions with both analytical and numerical results on the Ising quantum chain with an inhomogeneous transverse field varying in time.

We study the transport properties of a one-dimensional hard-core bosonic lattice gas coupled to two particle reservoirs at different chemical potentials which generate a current flow through the system. In particular, the influence of random fluctuations of the underlying lattice on the stationary-state properties is investigated. We show analytically that the steady-state density presents a linear profile. The local steady-state current obeys the Fourier law $j=-\kappa(\tau)\nabla n $ where $\tau$ is a typical timescale of the lattice fluctuations and $\nabla n$ the density gradient imposed by the reservoirs., Comment: 9 pages, 2 figures

We analyze the coherent quantum evolution of a many-particle system after slowly sweeping a power-law confining potential. The amplitude of the confining potential is varied in time along a power-law ramp such that the many-particle system finally reaches or crosses a critical point. Under this protocol we derive general scaling laws for the density of excitations created during the non-adiabatic sweep of the confining potential. It is found that the mean excitation density follows an algebraic law as a function of the sweeping rate with an exponent that depends on the space-time properties of the potential. We confirm our scaling laws by first order adiabatic calculation and exact results on the Ising quantum chain with a varying transverse field., Comment: To appear in Phys. Rev. Lett

The Ising quantum chain with arbitrary coupling distribution {λi} leading to an anisotropic scaling is considered. The smallest gap of the chain is connected to the surface magnetization by the relation Λ1 = ms({λi})ms({λ−1i}). For some aperiodic distribution {λi}, a weak universality of the critical behaviour is found.

We study the relaxation dynamics of a quantum Ising chain initially prepared in a product of canonical states corresponding each to an equilibrium state of part of the chain at a given temperature. We focus our attention on the transverse magnetization for which a general expression is given. Explicite results are given for the completely factorized initial state, corresponding to a situation where all the spins are thermalized independently, and for the two-temperatures initial state, where part of the chain called the system is thermalized at a temperature $T_s$ and the remaining part is at a temperature $T_b$., 7 pages, submitted to EPJB

International audience

We consider the nonequilibrium time evolution of the transverse magnetization in the critical Ising and $XX$ quantum chains. For some inhomogeneously magnetized initial states we derive analytically the transverse magnetization profiles and show that they evolve into scaling forms in the long-time limit. In particular it is seen that the Ising chain exhibits some similarities with the conserved dynamics $XX$ chain. That is, after a transient regime, the total residual magnetization in the transverse direction is also conserved in the Ising case. A class of general initial states is also considered., 6 pages, 2 figures, accepted in EPJB

We study the critical behavior of Ising quantum magnets with broadly distributed random couplings (J), such that $P(\ln J) \sim |\ln J|^{-1-\alpha}$, $\alpha>1$, for large $|\ln J|$ (L\'evy flight statistics). For sufficiently broad distributions, $\alpha, Comment: 10pages, 13figures, final form

According to the Harris-Luck criterion the relevance of a fluctuating interaction at the critical point is connected to the value of the fluctuation exponent omega. Here we consider different types of relevant fluctuations in the quantum Ising chain and investigate the universality class of the models. At the critical point the random and aperiodic systems behave similarly, due to the same type of extreme broad distribution of the energy scales at low energies. The critical exponents of some averaged quantities are found to be a universal function of omega, but some others do depend on other parameters of the distribution of the couplings. In the off-critical region there is an important difference between the two systems: there are no Griffiths singularities in aperiodic models., Comment: 4 pages RevTeX, 2 eps-figures included

A new realization of the conformal algebra is studied which mimics the behaviour of a statistical system on a discrete albeit infinite lattice. The two-point function is found from the requirement that it transforms covariantly under this realization. The result is in agreement with explicit lattice calculations of the $(1+1)D$ Ising model and the $d-$dimensional spherical model. A hard core is found which is not present in the continuum. For a semi-infinite lattice, profiles are also obtained., Comment: 5 pages, plain Tex with IOP macros, no figures