Person: Relaño Pérez, Armando
Universidad Complutense de Madrid
Faculty / Institute
Estructura de la Materia, Física Térmica y Electrónica
Now showing 1 - 10 of 60
PublicationAdiabatic invariants for the regular region of the Dicke model(IOP Publishing Ltd, 2017-04-07) Bastarrachea Magnani A.; R, M. A.; Relaño Pérez, Armando; Lerma Hernández, S.; López del Carpio, B.; Chávez Carlos, J.; Hirsch, J. G.Adiabatic invariants for the non-integrable Dicke model are introduced. They are shown to provide approximate second integrals of motion in the energy region where the system exhibits a regular dynamics. This low-energy region, present for any set of values of the Hamiltonian parameters is described both with a semiclassical and a full quantum analysis in a broad region of the parameter space. Peres lattices in this region exhibit that many observables vary smoothly with energy, along distinct lines which beg for a formal description. It is demonstrated 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 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 these regimes, far beyond the energies where a quadratic approximation around the minimal energy configuration can be used. PublicationConstant of Motion Identifying Excited-State Quantum Phases(American Physical Society, 2021-09-24) Corps, Angel L.; Relaño Pérez, ArmandoWe propose that a broad class of excited-state quantum phase transitions (ESQPTs) gives rise to two different excited-state quantum phases. These phases are identified by means of an operator (C) over cap, which is a constant of motion in only one of them. Hence, the ESQPT critical energy splits the spectrum into one phase where the equilibrium expectation values of physical observables crucially depend on this constant of motion and another phase where the energy is the only relevant thermodynamic magnitude. The trademark feature of this operator is that it has two different eigenvalues +/- 1, and, therefore, it acts as a discrete symmetry in the first of these two phases. This scenario is observed in systems with and without an additional discrete symmetry; in the first case, (C) over cap explains the change from degenerate doublets to nondegenerate eigenlevels upon crossing the critical line. We present stringent numerical evidence in the Rabi and Dicke models, suggesting that this result is exact in the thermodynamic limit, with finite-size corrections that decrease as a power law. PublicationExcited-state phase transition and onset of chaos in quantum optical models(American Physical Society, 2011-04-15) Pérez Fernández, P.; Relaño Pérez, Armando; Arias, J. M.; Cejnar, P.; Dukelsky, J.; García Ramos, J. E.We study the critical behavior of excited states and its relation to order and chaos in the Jaynes-Cummings and Dicke models of quantum optics. We show that both models exhibit a chain of excited-state quantum phase transitions demarcating the upper edge of the superradiant phase. For the Dicke model, the signatures of criticality in excited states are blurred by the onset of quantum chaos. We show that the emergence of quantum chaos is caused by the precursors of the excited-state quantum phase transition. PublicationChaos in hadrons(IOP PUBLISHING LTD, 2012) Muñoz, Laura; Fernández Ramírez, César; Relaño Pérez, Armando; Retamosa Granado, JoaquínIn the last decade quantum chaos has become a well established discipline with outreach to different fields, from condensed-matter to nuclear physics. The most important signature of quantum chaos is the statistical analysis of the energy spectrum, which distinguishes between systems with integrable and chaotic classical analogues. In recent years, spectral statistical techniques inherited from quantum chaos have been applied successfully to the baryon spectrum revealing its likely chaotic behaviour even at the lowest energies. However, the theoretical spectra present a behaviour closer to the statistics of integrable systems which makes theory and experiment statistically incompatible. The usual statement of missing resonances in the experimental spectrum when compared to the theoretical ones cannot account for the discrepancies. In this communication we report an improved analysis of the baryon spectrum, taking into account the low statistics and the error bars associated with each resonance. Our findings give a major support to the previous conclusions. Besides, analogue analyses are performed in the experimental meson spectrum, with comparison to theoretical models. PublicationChaos and 1/f noise in nuclear spectra(World Scientific Publishing Company, 2005-03) Gómez, J. M. G.; Faleiro, E.; Molina, R. A.; Muñoz, L.; Relaño Pérez, Armando; Covello, AldoMany complex systems in nature and in human society exhibit time fluctuations characterized by a power spectrum S(f) which is a power function of the frequency f . Examples with this behavior are the Sun spot activity, the human heartbeat, the DNA sequence, or Bach’s First Brandenburg Concert. In this work, we show that the energy spectrum fluctuations of quantum systems can be formally considered as a discrete time series, with energy playing the role of time. Because of this analogy, the fluctuations of quantum energy spectra can be studied using traditional methods of time series, like calculating the Fourier transform and studying the power spectrum. We present the results for paradigmatic quantum chaotic systems like atomic nuclei (by means of large scale shell-model calculations) and the predictions of random matrix theory. We have found a surprising general property of quantum systems: The energy spectra of chaotic quantum systems are characterized by 1= f noise, while regular quantum systems exhibit 1= f^2 noise. Some other interesting applications of this time series analogy are a test of the existence of quantum chaos remnants in the nuclear masses, and the study of the order to chaos transition in semiclassical systems. In this case, it is found that the energy level spectrum exhibits 1= f^α noise with the exponent changing smoothly from α = 2 in regular systems to α= 1 in chaotic systems. PublicationOrigin of the 1/f(alpha) spectral noise in chaotic and regular quantum systems(Amer Physical Soc, 2018-10-19) Pachón, Leonardo A.; Relaño Pérez, Armando; Peropadre, Borja; Aspuru-Guzik, AlánBased on the connection between the spectral form factor and the probability to return, the origin of the energy level fluctuation 1/f(alpha) 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 nonlinear system. An immediate prediction of the connection established here is that in the presence of decoherence, the spectral exponent a takes the same value, alpha = 2, for both fully chaotic and fully integrable systems. PublicationQuantum phase transitions and spontaneous symmetry-breaking in Dicke Model(American Institute of Physics (AIP), 2013) Puebla, Ricardo; Relaño Pérez, Armando; Retamosa Granado, JoaquínA method to find the Excited-States Quantum Phase Transitions (ESQPT's) from parity-symmetry in the Dicke model is studied and presented. This method allows us to stablish a critical energy where ESQPT's take places, and divides the whole energy spectrum in two regions with different properties. PublicationThermalization in the two-body random ensemble(IOP Publishing, 2008-10-01) Kota, V. K. B.; Relaño Pérez, Armando; Retamosa Granado, Joaquín; Vyas, MananUsing 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 especially 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, such as 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 originating 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 quasicomplete 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. PublicationDecoherence induced by an interacting spin environment in the transition from integrability to chaos(American Physical Society, 2007-10) Relaño Pérez, Armando; Dukelsky, J.; Molina, R. A.We investigate the decoherence properties of a central system composed of two spins 1/2 in contact with a spin bath. The dynamical regime of the bath ranges from a fully integrable limit to complete chaoticity. We show that the dynamical regime of the bath determines the efficiency of the decoherence process. For perturbative regimes, the integrable limit provides stronger decoherence, while in the strong coupling regime the chaotic limit becomes more efficient. We also show that the decoherence time behaves in a similar way. On the contrary, the rate of decay of magnitudes like linear entropy or fidelity does not depend on the dynamical regime of the bath. We interpret the latter results as due to a comparable complexity of the Hamiltonian for both the integrable and the fully chaotic limits. PublicationConnection between decoherence and excited state quantum phase transitions(American Institute of Physics (AIP), 2010) Pérez Fernández, P.; Relaño Pérez, Armando; Arias, J. M.; Dukelsky, J.; García Ramos, J. E.; Caballero, J. A.; Alonso, C. E.; Andrés, M. V.; García Ramos, J. E.; Pérez Bernal, F.In this work we explore the relationship between an excited state quantum phase transition (ESQPT) and the phenomenon of quantum decoherence. For this purpose, we study how the decoherence is affected by the presence of a continuous ESQPT in the environment. This one is modeled as a two level boson system described by a Lipkin Hamiltonian. We will show that the decoherence of the system is maximal when the environment undergoes a continuous ESQPT.