arXiv subjects

Pablo R. Zangara

Publications and source records attributed to Pablo R. Zangara.

27 records · Page 2Linked to original sources

arXiv2015

Role of energy uncertainties in ergodicity breaking induced by competing interactions and disorder. A dynamical assessment through the Loschmidt echo

A local excitation in a quantum many-particle system evolves deterministically. A time-reversal procedure, involving the invertion of the signs of every energy and interaction, should produce an excitation revival: the Loschmidt echo (LE). If somewhat imperfect, only a fraction of the excitation will refocus. We use such a procedure to show how non-inverted weak disorder and interactions, when assisted by the natural reversible dynamics, fully degrade the LE. These perturbations enhance diffusion and evenly distribute the excitation throughout the system. Such a dynamical paradigm, called ergodicity, breaks down when either the disorder or the interactions are too strong. These extreme regimes give rise to the well known Anderson localization and Mott insulating phases, where quantum diffusion becomes restricted. Accordingly, regardless of the kinetic energy terms, the excitation remains mainly localized and out-of-equilibrium, and the system behaves non-ergodically. The LE constitutes a fair dynamical witness for the whole phase diagram since it evidences a surprising topography in which ergodic and non-ergodic phases interpenetrate each other. Furthermore, we provide an estimation for the critical lines separating the ergodic and non-ergodic phases around the Mott and Anderson transitions. The energy uncertainties introduced by disorder and interaction shift these thresholds towards stronger perturbations. Remarkably, the estimations of the critical lines are in good agreement with the phase diagram derived from the LE dynamics.

cond-mat.stat-mech↗

arXiv2015

Proliferation of effective interactions: decoherence-induced equilibration in a closed many-body system

We address the question on how weak perturbations, that are quite ineffective in small many-body systems, can lead to decoherence and hence to irreversibility when they proliferate as the system size increases. This question is at the heart of solid state NMR. There, an initially local polarization spreads all over due to spin-spin interactions that conserve the total spin projection, leading to an equilibration of the polarization. In principle, this quantum dynamics can be reversed by changing the sign of the Hamiltonian. However, the reversal is usually perturbed by non reversible interactions that act as a decoherence source. The fraction of the local excitation recovered defines the Loschmidt echo (LE), here evaluated in a series of closed $N$ spin systems with all-to-all interactions. The most remarkable regime of the LE decay occurs when the perturbation induces proliferated effective interactions. We show that if this perturbation exceeds some lower bound, the decay is ruled by an effective Fermi golden rule (FGR). Such a lower bound shrinks as $ N $ increases, becoming the leading mechanism for LE decay in the thermodynamic limit. Once the polarization stayed equilibrated longer than the FGR time, it remains equilibrated in spite of the reversal procedure.

quant-ph↗

arXiv2014

On the long-time asymptotics of quantum dynamical semigroups

We consider semigroups $\{α_t: \; t\geq 0\}$ of normal, unital, completely positive maps $α_t$ on a von Neumann algebra ${\mathcal M}$. The (predual) semigroup $ν_t (ρ):= ρ\circ α_t$ on normal states $ρ$ of $\mathcal M$ leaves invariant the face ${\mathcal F}_p:= \{ρ: \; ρ(p)=1\}$ supported by the projection $p\in {\mathcal M}$, if and only if $α_t(p)\geq p$ (i.e., $p$ is sub-harmonic). We complete the arguments showing that the sub-harmonic projections form a complete lattice. We then consider $r_o$, the smallest projection which is larger than each support of a minimal invariant face; then $r_o$ is subharmonic. In finite dimensional cases $\sup α_t(r_o)={\bf 1}$ and $r_o$ is also the smallest projection $p$ for which $α_t(p)\to {\bf 1}$. If $\{ν_t: \; t\geq 0\}$ admits a faithful family of normal stationary states then $r_o={\bf 1}$ is useless; if not, it helps to reduce the problem of the asymptotic behaviour of the semigroup for large times.

math-ph↗

arXiv2013

GPU accelerated Trotter-Suzuki solver for quantum spin dynamics

The resolution of dynamics in out of equilibrium quantum spin systems lies at the heart of fundamental questions among Quantum Information Processing, Statistical Mechanics and Nano-Technologies. Efficient computational simulations of interacting many-spin systems are extremely valuable tools for tackling such questions. Here, we use the Trotter-Suzuki (TS) algorithm, a well-known strategy that provides the evolution of quantum systems, to address the spin dynamics. We present a GPU implementation of a particular TS version, which has been previously implemented on single cores in CPUs. We develop a massive parallel version of this algorithm and compare the efficiency between CPU and GPU implementations. This method reduces the execution time considerably and is capable of dealing with systems of up to 27 spins (only limited by GPU memory).

physics.comp-ph↗

arXiv2013

Interaction-disorder competition in a spin system evaluated through the Loschmidt Echo

The interplay between interactions and disorder in closed quantum many-body systems is relevant for thermalization phenomenon. In this article, we address this competition in an infinite temperature spin system, by means of the Loschmidt echo (LE), which is based on a time reversal procedure. This quantity has been formerly employed to connect quantum and classical chaos, and in the present many-body scenario we use it as a dynamical witness. We assess the LE time scales as a function of disorder and interaction strengths. The strategy enables a qualitative phase diagram that shows the regions of ergodic and nonergodic behavior of the polarization under the echo dynamics.

cond-mat.stat-mech↗

arXiv2013

Fragility of superposition states evaluated by the Loschmidt Echo

We consider the degradation of the dynamics of a Gaussian wave packet in a harmonic oscillator under the presence of an environment. This last is given by a single non-degenerate two level system. We analyze how the binary degree of freedom perturbs the free evolution of the wave packet producing decoherence, which is quantified by the Loschmidt Echo. This magnitude measures the reversibility of a perturbed quantum evolution. In particular, we use it here to study the relative "fragility" of coherent superpositions (cat states) with respect to incoherent ones. This fragility or sensitivity turns to increase exponentially with the energy separation of the two components of the superposition.

quant-ph↗

arXiv2013

Time Fluctuations in Isolated Quantum Systems of Interacting Particles

Numerically, we study the time fluctuations of few-body observables after relaxation in isolated dynamical quantum systems of interacting particles. Our results suggest that they decay exponentially with system size in both regimes, integrable and chaotic. The integrable systems considered are solvable with the Bethe ansatz and have a highly nondegenerate spectrum. This is in contrast with integrable Hamiltonians mappable to noninteracting ones. We show that the coefficient of the exponential decay depends on the level of delocalization of the initial state with respect to the energy shell.

cond-mat.stat-mech↗

arXiv2012

The Loschmidt Echo as a robust decoherence quantifier for many-body systems

We employ the Loschmidt Echo, i.e. the signal recovered after the reversal of an evolution, to identify and quantify the processes contributing to decoherence. This procedure, which has been extensively used in single particle physics, is here employed in a spin ladder. The isolated chains have 1/2 spins with XY interaction and their excitations would sustain a one-body like propagation. One of them constitutes the controlled system S whose reversible dynamics is degraded by the weak coupling with the uncontrolled second chain, i.e. the environment E. The perturbative SE coupling is swept through arbitrary combinations of XY and Ising like interactions, that contain the standard Heisenberg and dipolar ones. Different time regimes are identified for the Loschmidt Echo dynamics in this perturbative configuration. In particular, the exponential decay scales as a Fermi golden rule, where the contributions of the different SE terms are individually evaluated and analyzed. Comparisons with previous analytical and numerical evaluations of decoherence based on the attenuation of specific interferences, show that the Loschmidt Echo is an advantageous decoherence quantifier at any time, regardless of the S internal dynamics.

quant-ph↗

arXiv2011

Non-Markovian decay and dynamics of decoherence in private and public environments

We study the decay process in an open system, emphasizing on the relevance of the environment's spectral structure. Non-Markovian effects are included to quantitatively analyze the degradation rate of the coherent evolution. The way in which a two level system is coupled to different environments is specifically addressed: multiple connections to a single bath (public environment)or single connections to multiple baths (private environments). We numerically evaluate the decay rate of a local excitation by using the Survival Probability and the Loschmidt Echo. These rates are compared to analytical results obtained from the standard Fermi Golden Rule (FGR) in Wide Band Approximation, and a Self-Consistent evaluation that accounts for the bath's memory in cases where an exact analytical solution is possible. We observe that the correlations appearing in a public bath introduce further deviations from the FGR as compared with a private bath.

quant-ph↗