arXiv subjects

A. Relaño

Publications and source records attributed to A. Relaño.

12 recordsLinked to original sources

arXiv2025

Spectral-statistics properties of the experimental and theoretical light baryon and meson spectra

We compare the statistical fluctuation properties of the baryon and meson experimental mass spectra with those obtained from theoretical models (quark models and lattice QCD). We find that for the experimental spectra the statistical properties are close to those predicted by Random Matrix Theory for chaotic systems, while for the theoretical ones they are in general closer to those predicted for integrable systems and safely incompatible with those of chaotic systems. We stress the importance of the agreement of the fluctuation properties between experiment and theoretical models, as they determine the dynamical regime and the complexity of the real interactions. We emphasize the new statistical method we use, adapted for properly analyzing the fluctuation properties for very short spectral sequences.

hep-ph↗

arXiv2020

Fluctuations of work in realistic equilibrium states of quantum systems with conserved quantities

The out-of-equilibrium dynamics of quantum systems is one of the most fascinating problems in physics, with outstanding open questions on issues such as relaxation to equilibrium. An area of particular interest concerns few-body systems, where quantum and thermal fluctuations are expected to be especially relevant. In this contribution, we present numerical results demonstrating the impact of conserved quantities (or 'charges') in the outcomes of out-of-equilibrium measurements starting from realistic equilibrium states on a few-body system implementing the Dicke model.

quant-ph↗

arXiv2020

Distribution of the Ratio of Consecutive Level Spacings for Different Symmetries and Degrees of Chaos

Theoretical expressions for the distribution of the ratio of consecutive level spacings for quantum systems with transiting dynamics remain unknown. We propose a family of one-parameter distributions $P(r)\equiv P(r;β)$, where $β\in[0,+\infty)$ is a generalized Dyson index, that describes the eigenlevel statistics of a quantum system characterized by different symmetries and degrees of chaos. We show that this crossover strongly depends on the specific properties of each model, and thus the reduction of such a family to a universal formula, albeit desirable, is not possible. We use the information entropy as a criterion to suggest particular ansatzs for different transitions, with a negligible associated error in the limits corresponding to standard random ensembles.

quant-ph↗

arXiv2019

Stringent Test on Power Spectrum of Quantum Integrable and Chaotic Systems

Quantum chaotic and integrable systems are known to exhibit a characteristic $1/f$ and $1/f^{2}$ noise, respectively, in the power spectrum associated to their spectral fluctuations. A recent work [R. Riser, V. A. Osipov, and E. Kanzieper, \textit{Power Spectrum of Long Eigenlevel Sequences in Quantum Chaotic Systems}, Phys. Rev. Lett. \textbf{118}, 204101 (2017)] calls into question the approximations used to derive these results from random matrix theory. In this paper we show that such approximations do remain valid under almost any circumstances. For the integrable limit, we devise a protocol to exactly recover the original results. As a corollary, we show that the theoretical predictions for other statistics are bound for failure regarding long-range correlations, due to unavoidable spurious effects emerging from the analysis. By means of a rigorous statistical test, we also show that the corrections for the chaotic case introduced in the aforementioned paper require huge statistics to become relevant ---averages over more than $1000$ realizations are mandatory. As an application, we study a paradigmatic model for the crossover from the thermal to the many-body localized phase. We show that our protocol succeeds in describing the crossover. Furthermore, it also succeeds in proving that the Gaussian $β$-ensemble fails to account for long-range correlations between the energy levels of this paradigmatic model.

quant-ph↗

arXiv2018

Revealing missing charges with generalised quantum fluctuation relations

The non-equilibrium dynamics of quantum many-body systems is one of the most fascinating problems in physics. Open questions range from how they relax to equilibrium to how to extract useful work from them. A critical point lies in assessing whether a system has conserved quantities (or 'charges'), as these can drastically influence its dynamics. Here we propose a general protocol to reveal the existence of charges based on a set of exact relations between out-of-equilibrium fluctuations and equilibrium properties of a quantum system. We apply these generalised quantum fluctuation relations to a driven quantum simulator, demonstrating their relevance to obtain unbiased temperature estimates from non-equilibrium measurements. Our findings will help guide research on the interplay of quantum and thermal fluctuations in quantum simulation, in studying the transition from integrability to chaos and in the design of new quantum devices.

quant-ph↗

arXiv2017

From thermal to excited-state quantum phase transitions ---the Dicke model

We study the thermodynamics of the full version of the Dicke model, including all the possible values of the total angular momentum $j$, with both microcanonical and canonical ensembles. We focus on how the excited-state quantum phase transition, which only appears in the microcanonical description of the maximum angular momentum sector, $j=N/2$, change to a standard thermal phase transition when all the sectors are taken into account. We show that both the thermal and the excited-state quantum phase transitions have the same origin; in other words, that both are two faces of the same phenomenon. Despite all the logarithmic singularities which characterize the excited-state quantum phase transition are ruled out when all the $j$-sectors are considered, the critical energy (or temperature) still divides the spectrum in two regions: one in which the parity symmetry can be broken, and another in which this symmetry is always well defined.

quant-ph↗

arXiv2016

Adiabatic invariants for the regular region of the Dicke model

Adiabatic invariants are introduced and shown to provide an approximate second integral of motion for the non-integrable Dicke model, in the energy region where the system exhibits a regular dynamics. This low-energy region is always present and has been described both in a semiclassical and a full quantum analysis. Its Peres lattices exhibit that many observables vary smoothly with energy, along lines which beg for a formal description. It is shown how the adiabatic invariants provide a rationale to their presence in many cases. They are built employing the Born-Oppenheimer approximation, valid when a fast system is coupled to a much slower one. As the Dicke model has a one bosonic and one fermionic degree of freedom, two versions of the approximation are used, depending on which one is the faster. In both cases a noticeably accord with exact numerical results is obtained. The employment of the adiabatic invariants provides a simple and clear theoretical framework to study the physical phenomenology associated to this energy regime, far beyond the energies where the quadratic approximation can be employed.

quant-ph↗

arXiv2016

Approximated integrability of the Dicke model

A very approximate second integral of motion of the Dicke model is identified within a broad region above the ground state, and for a wide range of values of the external parameters. This second integral, obtained from a Born Oppenheimer approximation, classifies the whole regular part of the spectrum in bands labelled by its corresponding eigenvalues. Results obtained from this approximation are compared with exact numerical diagonalization for finite systems in the superradiant phase, obtaining a remarkable accord. The region of validity of our approach in the parameter space, which includes the resonant case, is unveiled. The energy range of validity goes from the ground state up to a certain upper energy where chaos sets in, and extends far beyond the range of applicability of a simple harmonic approximation around the minimal energy configuration. The upper energy validity limit increases for larger values of the coupling constant and the ratio between the level splitting and the frequency of the field. These results show that the Dicke model behaves like a two-degree of freedom integrable model for a wide range of energies and values of the external parameters.

quant-ph↗

arXiv2016

Entropy, chaos and excited-state quantum phase transitions in the Dicke model

We study non-equilibrium processes in an isolated quantum system ---the Dicke model--- focusing on the role played by the transition from integrability to chaos and the presence of excited-state quantum phase transitions. We show that both diagonal and entanglement entropies are abruptly increased by the onset of chaos. Also, this increase ends in both cases just after the system crosses the critical energy of the excited-state quantum phase transition. The link between entropy production, the development of chaos and the excited-state quantum phase transition is more clear for the entanglement entropy. On the contrary, the heat dissipated by the process is affected neither by the onset of chaos, nor by the excited-state quantum phase transition.

quant-ph↗

arXiv2013

High resolution simulations of the head-on collision of white dwarfs

The direct impact of white dwarfs has been suggested as a plausible channel for type Ia supernovae. In spite of their (a priori) rareness, in highly populated globular clusters and in galactic centers, where the amount of white dwarfs is considerable, the rate of violent collisions between two of them might be non-negligible. Even more, there are indications that binary white dwarf systems orbited by a third stellar-mass body have an important chance to induce a clean head-on collision. Therefore, this scenario represents a source of contamination for the supernova light-curves sample that it is used as standard candles in cosmology, and it deserves further investigation. Some groups have conducted numerical simulations of this scenario, but their results show several differences. In this paper we address some of the possible sources of these differences, presenting the results of high resolution hydrodynamical simulations jointly with a detailed nuclear post-processing of the nuclear abundances, to check the viability of white dwarf collisions to produce significant amounts of 56Ni. To that purpose, we use a 2D-axial symmetric smoothed particle hydrodynamic code to obtain a resolution considerably higher than in previous studies. In this work, we also study how the initial mass and nuclear composition affect the results. The gravitational wave emission is also calculated, as this is a unique signature of this kind of events. All calculated models produce a significant amount of 56Ni, ranging from 0.1 Msun to 1.1 Msun, compatible not only with normal-Branch type Ia supernova but also with the subluminous and super-Chandrasekhar subset. Nevertheless, the distribution mass-function of white dwarfs favors collisions among 0.6-0.7 Msun objects, leading to subluminous events.

astro-ph.SR↗

arXiv2011

Thermalization in the Two-Body Random Ensemble

Using the ergodicity principle for the expectation values of several types of observables, we investigate the thermalization process in isolated fermionic systems. These are described by the two-body random ensemble, which is a paradigmatic model to study quantum chaos and specially the dynamical transition from integrability to chaos. By means of exact diagonalizations we analyze the relevance of the eigenstate thermalization hypothesis as well as the influence of other factors, like the energy and structure of the initial state, or the dimension of the Hilbert space. We also obtain analytical expressions linking the degree of thermalization for a given observable with the so-called number of principal components for transition strengths originated at a given energy, with the dimensions of the whole Hilbert space and microcanonical energy shell, and with the correlations generated by the observable. As the strength of the residual interaction is increased an order-to-chaos transition takes place, and we show that the onset of Wigner spectral fluctuations, which is the standard signature of chaos, is not sufficient to guarantee thermalization in finite systems. When all the signatures of chaos are fulfilled, including the quasi complete delocalization of eigenfunctions, the eigenstate thermalization hypothesis is the mechanism responsible for the thermalization of certain types of observables, such as (linear combinations of) occupancies and strength function operators. Our results also suggest that fully chaotic systems will thermalize relative to most observables in the thermodynamic limit.

cond-mat.stat-mech↗

arXiv2004

Theoretical derivation of 1/f noise in quantum chaos

It was recently conjectured that 1/f noise is a fundamental characteristic of spectral fluctuations in chaotic quantum systems. This conjecture is based on the behavior of the power spectrum of the excitation energy fluctuations, which is different for chaotic and integrable systems. Using random matrix theory we derive theoretical expressions that explain the power spectrum behavior at all frequencies. These expressions reproduce to a good approximation the power laws of type 1/f (1/f^2) characteristics of chaotic (integrable) systems, observed in almost the whole frequency domain. Although we use random matrix theory to derive these results, they are also valid for semiclassical systems.

nlin.CD↗