Related papers: The relativistic Hopfield model with correlated pa…
Lattice growth models where uncorrelated random deposition competes with some aggregation dynamics that generates correlations are studied with rates of the correlated component decreasing as a power law. These models have anomalous…
A mechanism describing state reduction dynamics in relativistic quantum field theory is outlined. The mechanism involves nonlinear stochastic modifications to the standard description of unitary state evolution and the introduction of a…
Onsager's regression hypothesis connects the temporal relaxation of close-to-equilibrium systems with their dynamical correlation functions at thermal equilibrium. While the hypothesis is provably correct in classical systems, it is known…
Using a result of Behrend concerning sets without arithmetic progressions, we construct some examples of dynamical systems with slow time of multiple recurrence. Our theorem is a quatitative analog of Furstenberg's Correspondence Principle.
A completely Lorentz-invariant Bohmian model has been proposed recently for the case of a system of non-interacting spinless particles, obeying Klein-Gordon equations. It is based on a multi-temporal formalism and on the idea of treating…
The violent relaxation and the metastable states of the Hamiltonian Mean-Field model, a paradigmatic system of long-range interactions, is studied using a Hamiltonian formalism. Rigorous results are derived algebraically for the time…
The interplay of disorder and strong correlations in quantum many-body systems remains an open question. That is despite much progress made in recent years with ultracold atoms in optical lattices to better understand phenomena such as…
Human social interactions are typically recorded as time-specific dyadic interactions, and represented as evolving (temporal) networks, where links are activated/deactivated over time. However, individuals can interact in groups of more…
We extend the coupled-cluster method to correlated quantum dynamics of both closed and open systems at finite temperatures using the thermo-field formalism. The approach expresses the time-dependent density matrix in an exponential ansatz…
How to understand the set of correlations admissible in nature is one outstanding open problem in the core of the foundations of quantum theory. Here we take a complementary viewpoint to the device-independent approach, and explore the…
We analyze the effects of thermal conduction in a relativistic fluid just after its departure from spherical symmetry, on a time scale of the order of relaxation time. Using first order perturbation theory, it is shown that, as in spherical…
We review some of the properties of higher-dimensional superstatistical stochastic models. As an example, we analyse the stochastic properties of a superstatistical model of 3-dimensional Lagrangian turbulence, and compare with experimental…
Systems of interacting random replicators are studied using generating functional techniques. While replica analyses of such models are limited to systems with symmetric couplings, dynamical approaches as presented here allow specifically…
The space-time features of the relativistic dynamics are analyzed in the framework of the time dependent propagator theory. The adiabatic hypothesis is substituted by the disturbative adiabatic hypothesis, resulting with the corresponding…
The out-of-time-order correlator (OTOC), recently analyzed in several physical contexts, is studied for low-dimensional chaotic systems through semiclassical expansions and numerical simulations. The semiclassical expansion for the OTOC…
The standard Hopfield model for associative neural networks accounts for biological Hebbian learning and acts as the harmonic oscillator for pattern recognition, however its maximal storage capacity is $\alpha \sim 0.14$, far from the…
Topological Data Analysis (TDA) can be used to detect and characterize holes in an image, such as zero-dimensional holes (connected components) or one-dimensional holes (loops). However, there is currently no widely accepted statistical…
The time elapsed model describes the firing activity of an homogeneous assembly of neurons thanks to the distribution of times elapsed since the last discharge. It gives a mathematical description of the probability density of neurons…
We extend random matrix theory to consider randomly interacting spin systems with spatial locality. We develop several methods by which arbitrary correlators may be systematically evaluated in a limit where the local Hilbert space dimension…
A method for calculating the short-range order part of the free energy of order-disorder systems is proposed. The method is based on the apllication of the cumulant expansion to the exact configurational entropy. Second-order correlation…