Browsing by Author "Zueco, David"

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    Synchronization in a semiclassical Kuramoto model
    (2016-02-08) Hermoso de Mendoza, Ignacio; Pachón, Leonardo Augusto; Gómez-Gardeñes, Jesús; Zueco, David
    Synchronization is a ubiquitous phenomenon occurring in sociai, biological, and technological systems when the internal rythms of their constituents are adapted to be in unison as a result of their coupling. This natural tendency towards dynamical consensus has spurred a large body of theoretical and experimental research in recent decades. The Kuramoto model constitutes the most studied and paradigmatic framework in which to study synchronization. In particular, it shows how synchronization appears as a phase transition from a dynamically disordered state at some critical value for the coupling strength between the interacting units. The critical properties of the synchronization transition of this model have been widely studied and many variants of its formulations have been considered to address different physical realizations. However, the Kuramoto model has been studied only within the domain of classical dynamics,-thus neglecting its applications for the study of quantum synchronization phenomena. Based on a system-bath approach and within the Feynman path-integral formalism, we derive equations for the Kuramoto model by taking into account the first quantum fluctuations We also analyze its critical properties, the main result being the derivation of the value for the synchronization onset. This critical coupling increases its value as quantumness increases, as a consequence of the possibility of 8 tunneling that quantum fluctuations provide.
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    The Quantum Kuramoto Model
    (2013-07-17) Hermoso de Mendoza, Ignacio; Pachón, Leonardo Augusto; Gómez-Gardeñes, Jesús; Zueco, David
    Synchronization is an ubiquitous phenomenon occurring in social, biological and technological systems when the internal rhythms of a large number of units evolve coupled. This natural tendency towards dynamical consensus has spurred a large body of theoretical and experimental research during the last decades. The Kuramoto model constitutes the most studied and paradigmatic framework to study synchronization. In particular, it shows how synchronization shows up as a phase transition from a dynamically disordered state at some critical value for the coupling strength between the interacting units. The critical properties of the synchronization transition of this model have been widely studied and many variants of its formulations has been considered to address different physical realizations. However, the Kuramoto model has been only studied within the domain of classical dynamics, thus neglecting its applications for the study of quantum synchronization phenomena. Here we provide with the quantization of the Kuramoto model. Based on a system-bath approach and within the Feynman path-integral formalism, we derive the equations for the Kuramoto model by taking into account the first quantum fluctuations. We also analyze its critical properties being the main result the derivation of the value for the synchronization onset. This critical coupling turns up to increase its value as quantumness increases, as a consequence of the possibility of tunneling that quantum fluctuations provide.
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    Uncertainty Principle Consequences at Thermal Equilibrium
    (2013-05-02) Pachón, Leonardo Augusto; Triana, Johan F.; Zueco, David; Brumer, Paul
    Contrary to the conventional wisdom that deviations from standard thermodynamics originate from the strong coupling to the bath, it is shown that these deviations are intimately linked to the power spectrum of the thermal bath. Specifically, it is shown that the lower bound of the dispersion of the total energy of the system, imposed by the uncertainty principle, is dominated by the bath power spectrum and therefore, quantum mechanics inhibits the system thermal-equilibriun-state from being described by the canonical Boltzrhann's distribution. This is in sharp contrast to the classical case, for which the thermal equilibrium distribution of a system interacting via central forces with pairwise-self-interacting environment, irrespective of the interaction strength, is shown to be eractly characterized by the canonical Boltzmann distribution. As a consequence of this analysis we define an effective coupling to the environment that depends on all energy scales in the system and reservoir interaction. Sample computations in regimes predicted by this effective coupling are demonstrated. For example, for the case of strong effective coupling, deviations from standard thermodynamics are present and, for the case of weak effective coupling, quantum features such as stationary entanglement are possible at high temperatures.