The Experts below are selected from a list of 5007 Experts worldwide ranked by ideXlab platform
Juan Rivera-letelier - One of the best experts on this subject based on the ideXlab platform.
-
Sensitive Dependence of Geometric Gibbs States at Positive Temperature
Communications in Mathematical Physics, 2019Co-Authors: Daniel Coronel, Juan Rivera-letelierAbstract:We give the first example of a smooth family of real and complex maps having Sensitive Dependence of geometric Gibbs states at positive temperature. This family consists of quadratic-like maps that are non-uniformly hyperbolic in a strong sense. We show that for a dense set of maps in the family the geometric Gibbs states do not converge at positive temperature. These are the first examples of non-convergence at positive temperature in statistical mechanics or the thermodynamic formalism, and answers a question of van Enter and Ruszel. We also show that this phenomenon is robust: There is an open set of analytic 2-parameter families of quadratic-like maps that exhibit Sensitive Dependence of geometric Gibbs states at positive temperature.
-
Sensitive Dependence of geometric Gibbs measures at positive temperature
Communications in Mathematical Physics, 2019Co-Authors: Daniel Coronel, Juan Rivera-letelierAbstract:We give the first example of a smooth family of real and complex maps having Sensitive Dependence of geometric Gibbs states at positive temperature. This family consists of quadratic-like maps that are non-uniformly hyperbolic in a strong sense. We show that for a dense set of maps in the family the geometric Gibbs states do not converge at positive temperature. These are the first examples of non-convergence at positive temperature in statistical mechanics or the thermodynamic formalism, and answers a question of van Enter and Ruszel. We also show that this phenomenon is robust: There is an open set of analytic 2-parameter families of quadratic-like maps that exhibit Sensitive Dependence of geometric Gibbs states at positive temperature.
-
Sensitive Dependence of geometric Gibbs states
arXiv: Dynamical Systems, 2017Co-Authors: Daniel Coronel, Juan Rivera-letelierAbstract:For quadratic-like maps, we show a phenomenon of Sensitive Dependence of geometric Gibbs states: There are analytic families of quadratic-like maps for which an arbitrarily small perturbation of the parameter can have a definite effect on the low-temperature geometric Gibbs states. Furthermore, this phenomenon is robust: There is an open set of analytic 2-parameter families of quadratic-like maps that exhibit Sensitive Dependence of geometric Gibbs states. We introduce a geometric version of the Peierls condition for contour models ensuring that the low-temperature Gibbs states are concentrated near the critical orbit.
-
Sensitive Dependence of Gibbs Measures at Low Temperatures
Journal of Statistical Physics, 2015Co-Authors: Daniel Coronel, Juan Rivera-letelierAbstract:The Gibbs measures of an interaction can behave chaotically as the temperature drops to zero. We observe that for some classical lattice systems there are interactions exhibiting a related phenomenon of Sensitive Dependence of Gibbs measures: An arbitrarily small perturbation of the interaction can produce significant changes in the low-temperature behavior of its Gibbs measures. For some one-dimensional XY models we exhibit Sensitive Dependence of Gibbs measures for a (nearest-neighbor) interaction given by a smooth function, and for perturbations that are small in the smooth category. We also exhibit Sensitive Dependence of Gibbs measures for an interaction on a classical lattice system with finite-state space. This interaction decreases exponentially as a function of the distance between sites; it is given by a Lipschitz continuous potential in the configuration space. The perturbations are small in the Lipschitz topology. As a by-product we solve some problems stated by Chazottes and Hochman.
-
Sensitive Dependence of Gibbs measures
arXiv: Mathematical Physics, 2014Co-Authors: Daniel Coronel, Juan Rivera-letelierAbstract:Gibbs measures can behave chaotically as the temperature drops to zero. We observe that for some classical lattice systems there is a related phenomenon of Sensitive Dependence of Gibbs measures: An arbitrarily small perturbation of the interaction can produce significant fluctuations of low-temperature Gibbs measures. For the XY model we exhibit the Sensitive Dependence of Gibbs measures for a (nearest-neighbor) interaction given by a smooth function, and for perturbations that are small in the smooth category. We also exhibit the Sensitive Dependence of Gibbs measures for classical lattice systems with finite-state space. The interaction decreases exponentially as a function of the distance between sites; it is given by a Lipschitz continuous potential in the configuration space. The perturbations are small in the Lipschitz topology. As a by-product we obtain for the first time the chaotic temperature Dependence in dimension 2 for a finite-state space model, and solve some problems stated by Chazottes and Hochman.
Daniel Coronel - One of the best experts on this subject based on the ideXlab platform.
-
Sensitive Dependence of Geometric Gibbs States at Positive Temperature
Communications in Mathematical Physics, 2019Co-Authors: Daniel Coronel, Juan Rivera-letelierAbstract:We give the first example of a smooth family of real and complex maps having Sensitive Dependence of geometric Gibbs states at positive temperature. This family consists of quadratic-like maps that are non-uniformly hyperbolic in a strong sense. We show that for a dense set of maps in the family the geometric Gibbs states do not converge at positive temperature. These are the first examples of non-convergence at positive temperature in statistical mechanics or the thermodynamic formalism, and answers a question of van Enter and Ruszel. We also show that this phenomenon is robust: There is an open set of analytic 2-parameter families of quadratic-like maps that exhibit Sensitive Dependence of geometric Gibbs states at positive temperature.
-
Sensitive Dependence of geometric Gibbs measures at positive temperature
Communications in Mathematical Physics, 2019Co-Authors: Daniel Coronel, Juan Rivera-letelierAbstract:We give the first example of a smooth family of real and complex maps having Sensitive Dependence of geometric Gibbs states at positive temperature. This family consists of quadratic-like maps that are non-uniformly hyperbolic in a strong sense. We show that for a dense set of maps in the family the geometric Gibbs states do not converge at positive temperature. These are the first examples of non-convergence at positive temperature in statistical mechanics or the thermodynamic formalism, and answers a question of van Enter and Ruszel. We also show that this phenomenon is robust: There is an open set of analytic 2-parameter families of quadratic-like maps that exhibit Sensitive Dependence of geometric Gibbs states at positive temperature.
-
Sensitive Dependence of geometric Gibbs states
arXiv: Dynamical Systems, 2017Co-Authors: Daniel Coronel, Juan Rivera-letelierAbstract:For quadratic-like maps, we show a phenomenon of Sensitive Dependence of geometric Gibbs states: There are analytic families of quadratic-like maps for which an arbitrarily small perturbation of the parameter can have a definite effect on the low-temperature geometric Gibbs states. Furthermore, this phenomenon is robust: There is an open set of analytic 2-parameter families of quadratic-like maps that exhibit Sensitive Dependence of geometric Gibbs states. We introduce a geometric version of the Peierls condition for contour models ensuring that the low-temperature Gibbs states are concentrated near the critical orbit.
-
Sensitive Dependence of Gibbs Measures at Low Temperatures
Journal of Statistical Physics, 2015Co-Authors: Daniel Coronel, Juan Rivera-letelierAbstract:The Gibbs measures of an interaction can behave chaotically as the temperature drops to zero. We observe that for some classical lattice systems there are interactions exhibiting a related phenomenon of Sensitive Dependence of Gibbs measures: An arbitrarily small perturbation of the interaction can produce significant changes in the low-temperature behavior of its Gibbs measures. For some one-dimensional XY models we exhibit Sensitive Dependence of Gibbs measures for a (nearest-neighbor) interaction given by a smooth function, and for perturbations that are small in the smooth category. We also exhibit Sensitive Dependence of Gibbs measures for an interaction on a classical lattice system with finite-state space. This interaction decreases exponentially as a function of the distance between sites; it is given by a Lipschitz continuous potential in the configuration space. The perturbations are small in the Lipschitz topology. As a by-product we solve some problems stated by Chazottes and Hochman.
-
Sensitive Dependence of Gibbs measures
arXiv: Mathematical Physics, 2014Co-Authors: Daniel Coronel, Juan Rivera-letelierAbstract:Gibbs measures can behave chaotically as the temperature drops to zero. We observe that for some classical lattice systems there is a related phenomenon of Sensitive Dependence of Gibbs measures: An arbitrarily small perturbation of the interaction can produce significant fluctuations of low-temperature Gibbs measures. For the XY model we exhibit the Sensitive Dependence of Gibbs measures for a (nearest-neighbor) interaction given by a smooth function, and for perturbations that are small in the smooth category. We also exhibit the Sensitive Dependence of Gibbs measures for classical lattice systems with finite-state space. The interaction decreases exponentially as a function of the distance between sites; it is given by a Lipschitz continuous potential in the configuration space. The perturbations are small in the Lipschitz topology. As a by-product we obtain for the first time the chaotic temperature Dependence in dimension 2 for a finite-state space model, and solve some problems stated by Chazottes and Hochman.
R. Vilela Mendes - One of the best experts on this subject based on the ideXlab platform.
-
Quantum Sensitive Dependence
Physics Letters A, 2002Co-Authors: Vladimir I. Man’ko, R. Vilela MendesAbstract:Abstract Wave functions of bounded quantum systems with time-independent potentials, being almost periodic functions, cannot have time asymptotics as in classical chaos. However, bounded quantum systems with time-dependent interactions, as used in quantum control, may have continuous spectrum and the rate of growth of observables is an issue of both theoretical and practical concern. Rates of growth in quantum mechanics are discussed by constructing quantities with the same physical meaning as those involved in the classical Lyapunov exponent. A generalized notion of quantum Sensitive Dependence is introduced and the mathematical structure of the operator matrix elements that correspond to different types of growth is characterized.
-
Structure-generating mechanisms in agent-based models
Physica A-statistical Mechanics and Its Applications, 2001Co-Authors: R. Vilela MendesAbstract:The emergence of dynamical structures in multi-agent systems is analysed. Three different mechanisms are identified, namely: (1) Sensitive-Dependence (in the agent dynamics) and convex coupling, (2) Sensitive-Dependence and extremal dynamics and (3) interaction through a collectively generated field. The dynamical origin of the emergent structures is traced back either to a modification, by interaction, of the Lyapunov spectrum or to multistable dynamics.
-
Structure-generating mechanisms in agent-based models
arXiv: Adaptation and Self-Organizing Systems, 2000Co-Authors: R. Vilela MendesAbstract:The emergence of dynamical structures in multi-agent systems is analysed. Three different mechanisms are identified, namely: (1) Sensitive-Dependence and convex coupling, (2) Sensitive-Dependence and extremal dynamics and (3) interaction through a collectively generated field. The dynamical origin of the emergent structures is traced back either to a modification, by interaction, of the Lyapunov spectrum or to multistable dynamics.
-
Sensitive Dependence in quantum systems : Some examples and results
Physics Letters A, 1992Co-Authors: R. Vilela MendesAbstract:Abstract Considering the time evolution of perturbations of the wave function along directions of δ' type we obtain the notions of quantum Sensitive Dependence and quantum characteristic exponent, resembling the corresponding classical quantities. These notions are proposed as a tool to characterize quantum chaos. From the study of some examples we conclude that the problems of quantum Sensitive Dependence and the delocalization of the wave functions are independent questions. The numerical reversibility of classically chaotic quantum systems is discussed in the quantum Sensitive Dependence context.
-
Sensitive Dependence and entropy for quantum systems
Journal of Physics A: Mathematical and General, 1991Co-Authors: R. Vilela MendesAbstract:An attempt is made to carry to quantum mechanics the notion of Sensitive Dependence to initial conditions. A few simple examples and properties are described. For the entropy of quantum evolution a quantity is proposed, in the spirit of the Brin-Katok definition which characterizes orbit complexity rather than the state reduction nature of the quantum measurement process.
Wei Zheng - One of the best experts on this subject based on the ideXlab platform.
-
estimation of amplitude and phase of a weak signal by using the property of Sensitive Dependence on initial conditions of a nonlinear oscillator
Signal Processing, 2002Co-Authors: Guanyu Wang, Wei ZhengAbstract:A new method is presented to determine the amplitude and phase of a weak signal by using a fundamental property of a nonlinear dynamical system, namely, the Sensitive Dependence on initial conditions (SDIC), given that some a priori knowledge about the signal order of magnitude is available. The corresponding bifurcation process for the Duffing oscillator is discussed in detail, and the Floquet exponents are employed to represent SDIC quantitatively. To show the efficiency of the present method, simulation results for the reconstruction are given and compared with those obtained by the maximum likelihood (ML) method. The robustness of the present method against variations of some experimental conditions is addressed.
Reinhold Blümel - One of the best experts on this subject based on the ideXlab platform.
-
Sensitivity and chaos in quantum systems
Nuclear Physics A, 1994Co-Authors: Reinhold BlümelAbstract:Abstract Sensitive Dependence and chaos can occur in quantum mechanics. This is demonstrated by constructing a quantum mapping with a positive Liapunov exponent.
