1,721,259 research outputs found
Spike train distances and neuronal coding
Full text linkDaffertshofer, A. [Promotor]Livi, R. [Promotor]Kreuz, T. [Copromotor
Symplectic quantization I: dynamics of quantum fluctuations in a relativistic field theory
No full textWe propose here a new symplectic quantization scheme, where quantum fluctuations of a scalar field theory stem from two main assumptions: relativistic invariance and equiprobability of the field configurations with identical value of the action. In this approach the fictitious time of stochastic quantization becomes a genuine additional time variable, with respect to the coordinate time of relativity. This intrinsic time is associated to a symplectic evolution in the action space, which allows one to investigate not only asymptotic, i.e. equilibrium, properties of the theory, but also its non-equilibrium transient evolution. In this paper, which is the first one in a series of two, we introduce a formalism which will be applied to general relativity in its companion work (Gradenigo, Symplectic quantization II: dynamics of space-time quantum fluctuations and the cosmological constant, 2021)
The influence of noise on synchronous dynamics in a diluted neural network
No full textWe study the influence of noise on the dynamics of a simple model of excitatory leaky integrate - and - fire neurons in a diluted network. The stochastic process amounts to a random walk with boundaries acting on the external current, whose average value plays the role of a control parameter identifying different dynamical phases. Above a given threshold value one observes a gaussian statistics of synchronous firing events, that changes to an asymmetric long-tail distribution below threshold. For uncorrelated noise the distribution below threshold exhibits an exponential tail for large rare events, while for strongly correlated noise the long-tail turns to a power-law. This interesting dynamical scenario is shown to persist also when short-term plasticity is introduced in the model. Synchronous firing events change to population bursts and the model with plasticity is shown to reproduce quantitatively what observed in in vitro experiments. We also discuss the persistence of this scenario in the thermodynamic limit. © 2013 The Authors. Published by Elsevier Ltd. All rights reserved
Broken ergodicity and single-particle statistical properties
No full textWe investigate violations of ergodicity in a chain of anharmonically coupled oscillators (Fermi-Pasta-Ulam model). We show that the statistical properties of the autocorrelation function of a single oscillator reveal a sharp transition at the value of the control parameter, the energy density, εc = 1.14 ± 0.01. The phase of broken ergodicity (ε < εc) reveals Poincaré recurrences on observable time scales
On the quantization of the three-particle Toda lattice
No full textThe authors compare the Einstein-Brillouin-Keller quantization procedure and the canonical quantization of a three-particle Toda chain with periodic boundary conditions. In particular, the transition from very low energies, at which the system may be approximated by harmonic oscillators, to intermediate energies is investigated. This is the regime of a general integrable nonlinear system, for which they find a Poissonian statistics for the energy levels. In the limit of very high energies they exploit the fact that the system may be described essentially by a triangular billiard and thus can derive some exact results
The Fermi-Pasta-Ulam Problem: Scaling Laws vs. Initial Conditions
No full textNumerical evidence on the relevance of the initial conditions to the Fermi-Pasta-Ulam problem is reported, supported by analytic estimates. In particular, we analyze the special, crucial role played by the phases of the low frequency normal modes initially excited, their energy being the same. The results found are the following. When the phases of the initially excited modes are randomly chosen, the parameter ruling the first stage of the transfer of energy to higher frequency modes turns out to be the energy per degree of freedom (or specific energy) of the system, i.e. an intensive parameter. On the other hand, if the initial phases are “coherently” selected (e.g. they are all equal or equispaced on the unit circle), then the energy cascade is ruled by the total energy of the system, i.e. an extensive parameter. Finally, when a few modes are initially excited, in which case specifying the randomness or coherence of the phases becomes meaningless, the relevant parameter turns out to be again the specific energy (this is the case of the original Fermi-Pasta-Ulam experiment)
Discrete breathers and negative-temperature states
Full text linkWe explore the statistical behaviour of the discrete nonlinear Schrödinger equation as a test bed for the observation of negative-temperature (i.e. above infinite temperature) states in Bose–Einstein condensates in optical lattices and arrays of optical waveguides. By monitoring the microcanonical temperature, we show that there exists a parameter region where the system evolves towards a state characterized by a finite density of discrete breathers and a negative temperature. Such a state persists over very long (astronomical) times since the convergence to equilibrium becomes increasingly slower as a consequence of a coarsening process. We also discuss two possible mechanisms for the generation of negative-temperature states in experimental setups, namely, the introduction of boundary dissipations and the free expansion of wavepackets initially in equilibrium at a positive temperature
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