arXiv subjects

Armando Relaño

Publications and source records attributed to Armando Relaño.

29 records · Page 2Linked to original sources

arXiv2021

Long-range level correlations in quantum systems with finite Hilbert space dimension

We study the spectral statistics of quantum systems with finite Hilbert spaces. We derive a theorem showing that eigenlevels in such systems cannot be globally uncorrelated, even in the case of fully integrable dynamics, as a consequence of the unfolding procedure. We provide an analytic expression for the power spectrum of the $δ_n$ statistic for a model of intermediate statistics with level repulsion but independent spacings, and we show both numerically and analytically that the result is spoiled by the unfolding procedure. Then, we provide a simple model to account for this phenomenon, and test it by means of numerics on the disordered XXZ chain, the paradigmatic model of many-body localization, and the rational Gaudin-Richardson model, a prototypical model for quantum integrability.

cond-mat.stat-mech↗

arXiv2020

Thouless Energy Challenges Thermalization on the Ergodic Side of the Many-Body Localization Transition

We study the ergodic side of the many-body localization transition in its standard model, the disordered Heisenberg quantum spin chain. We show that the Thouless energy, extracted from long-range spectral statistics and the power-spectrum of the full momentum distribution fluctuations, is not large enough to guarantee thermalization. We find that both estimates coincide and behave non-monotonically, exhibiting a strong peak at an intermediate value of the disorder. Furthermore, we show that non-thermalizing initial conditions occur well within the ergodic phase with larger probability than expected. Finally, we propose a mechanism, driven by the Thouless energy and the presence of anomalous events, for the transition to the localized phase.

cond-mat.stat-mech↗

arXiv2020

Decoherence framework for Wigner's friend experiments

The decoherence interpretation of quantum measurements is applied to Wigner's friend experiments. A framework in which all the experimental outcomes arise from unitary evolutions is proposed. Within it, a measurement is not completed until an uncontrolled environment monitorizes the state composed by the system, the apparatus and the observer. The (apparent) wave-function collapse and the corresponding randomness result from tracing out this environment; it is thus the ultimate responsible for the emergence of definite outcomes. Two main effects arise from this fact. First, external interference measurements, trademark of Wigner's friend experiments, modify the memory records of the internal observers; this framework provides a univocal protocol to calculate all these changes. Second, it can be used to build a consistent scenario for the recenly proposed extended versions of the Wigner's friend experiment. Regarding [D. Frauchiger and R. Renner, {\em Quantum theory cannot consistently describe the use of itself}, Nat. Comm. {\bf 9}, 3711 (2018)], this framework shows that the agents' claims become consistent if the changes in their memories are properly taken into account. Furthermore, the particular setup discussed in [C. Brukner, {\em A no-go theorem for observer-indepdendent facts}, Entropy {\bf 20}, 350 (2018)] cannot be tested against the decoherence framework, because it does not give rise to well-defined outcomes according to this formalism. A variation of this setup, devised to fill this gap, makes it possible to assign joint truth values to the observations made by all the agents. This framework also narrows down the requisites for such experiments, making them virtually impossible to apply to conscious (human) beings. Notwithstanding, it also opens the door to future relizations on quantum machines.

quant-ph↗

arXiv2020

Anomalous Thermalization in Quantum Collective Models

We show that apparently thermalized states still store relevant amounts of information about their past, information that can be tracked by experiments involving nonequilibrium processes. We provide a condition for the microcanonical quantum Crookś theorem, and we test it by means of numerical experiments. In the Lipkin-Meshkov-Glick model, two different procedures leading to the same equilibrium states give rise to different statistics of work in nonequilibrium processes. In the Dicke model, two different trajectories for the same nonequilibrium protocol produce different statistics of work. Microcanonical averages provide the correct results for the expectation values of physical observables in all the cases; the microcanonical quantum Crookś theorem fails in some of them. We conclude that testing quantum fluctuation theorems is mandatory to verify if a system is properly thermalized.

quant-ph↗

arXiv2018

Decoherence allows quantum theory to describe the use of itself

We show that the quantum description of measurement based on decoherence fixes the bug in quantum theory discussed in [D. Frauchiger and R. Renner, {\em Quantum theory cannot consistently describe the use of itself}, Nat. Comm. {\bf 9}, 3711 (2018)]. Assuming that the outcome of a measurement is determined by environment-induced superselection rules, we prove that different agents acting on a particular system always reach the same conclusions about its actual state.

quant-ph↗

arXiv2017

Origin of the $1/f^α$-Spectral-Noise in Chaotic and Regular Quantum Systems

Based on the connection between the spectral form factor and the probability to return, the origin of the $1/f^α$-noise in fully chaotic and fully integrable systems is traced to the quantum interference between invariant manifolds of the classical dynamics and the dimensionality of those invariant manifolds. This connection and the order-to-chaos transition are analyzed in terms of the statistics of Floquet's quasienergies of a classically chaotic driving non-linear system. An immediate prediction of the connection established here is that in the presence of decoherence, the spectral exponent $α$ takes the same value, $α=2$, for both, fully chaotic and fully integrable systems.

quant-ph↗

arXiv2015

Irreversible processes without energy dissipation in an isolated Lipkin-Meshkov-Glick model

For a certain class of isolated quantum systems, we report the existence of irreversible processes in which the energy is not dissipated. After a closed cycle in which the initial energy distribution is fully recovered, the expectation value of a symmetry-breaking observable changes from a value different from zero in the initial state, to zero in the final state. This entails the unavoidable loss of a certain amount of information, and constitutes a source of irreversibility. We show that the von Neumann entropy of time-averaged equilibrium states increases in the same magnitude as a consequence of the process. We support this result by means of numerical calculations in an experimentally feasible system, the Lipkin-Meshkov-Glick model.

quant-ph↗

arXiv2014

Quantum phase transitions of atom-molecule Bose mixtures in a double-well potential

The ground state and spectral properties of Bose gases in double-well potentials are studied in two different scenarios: i) an interacting atomic Bose gas, and ii) a mixture of an atomic gas interacting with diatomic molecules. A ground state second-order quantum phase transition (QPT) is observed in both scenarios. For large attractive values of the atom-atom interaction, the ground-state is degenerate. For repulsive and small attractive interaction, the ground-state is not degenerate and is well approximated by a boson coherent state. Both systems depict an excited state quantum phase transition (ESQPT). For the mixed atom-molecule system the critical point of the ESQPT displays a discontinuity in the first derivative of the density of states.

quant-ph↗

arXiv2013

Non-thermal quantum phase transitions

We report a kind of quantum phase transition which takes place in isolated quantum systems with non-thermal equilibrium states and an extra symmetry that commutes with the Hamiltonian for any values of the system parameters. A critical energy separates two different phases, one in which the symmetry is broken. This critical behavior is ruled out as soon as the system is put in contact with a thermal bath. The critical point is crossed when a sufficent amount of work is performed on the system, keeping it isolated from the environment. Different phases are identified by means of an order parameter, which is only different from zero in the symmetry-breaking phase. The behavior of the system near the critical point is determined by a set of critical exponents. We illustrate this phenomenon by means of numerical calculations in three different two-level systems.

quant-ph↗

arXiv2012

Excited-state phase transition leading to symmetry-breaking steady states in the Dicke model

We study the phase diagram of the Dicke model in terms of the excitation energy and the radiation-matter coupling constant $λ$. Below a certain critical value $λ_c$ of the coupling constant $λ$ all the energy levels have a well-defined parity. For $λ> λ_c$ the energy spectrum exhibits two different phases separated by a critical energy $E_c$ that proves to be independent of $λ$. In the upper phase, the energy levels have also a well defined parity, but below $E_c$ the energy levels are doubly degenerated. We show that the long-time behavior of appropriate parity-breaking observables distinguishes between the different phases of the energy spectrum of the Dicke model. Steady states reached from symmetry-breaking initial conditions restore the symmetry only if their expected energies are above the critical. This fact makes it possible to experimentally explore the complete phase diagram of the excitation spectrum of the Dicke model.

quant-ph↗

arXiv2012

Quantum quenches in disordered systems: Approach to thermal equilibrium without a typical relaxation time

We study spectral properties and the dynamics after a quench of one-dimensional spinless fermions with short-range interactions and long-range random hopping. We show that a sufficiently fast decay of the hopping term promotes localization effects at finite temperature, which prevents thermalization even if the classical motion is chaotic. For slower decays, we find that thermalization does occur. However, within this model, the latter regime falls in an unexpected universality class, namely, observables exhibit a power-law (as opposed to an exponential) approach to their thermal expectation values.

cond-mat.dis-nn↗