相关论文: Quantum Dynamics and Random Matrix Theory
A non-relativistic quantum mechanical theory is proposed that describes the universe as a continuum of worlds whose mutual interference gives rise to quantum phenomena. A logical framework is introduced to properly deal with propositions…
Using the random matrix description of open quantum chaotic systems we calculate in closed form the universal autocorrelation function and the probability distribution of the total photodissociation cross section in the regime of quantum…
Comparing probability distributions is a core challenge across the natural, social, and computational sciences. Existing methods, such as Maximum Mean Discrepancy (MMD), struggle in high-dimensional and non-compact domains. Here we…
In this article we derive a useful expectation identity using the language of quantum statistical mechanics, where density matrices represent the state of knowledge about the system. This identity allows to establish relations between…
We investigate the survivor distributions of a spatially extended model of competitive dynamics in different geometries. The model consists of a deterministic dynamical system of individual agents at specified nodes, which might or might…
Bohmian mechanics represents the universe as a set of paths with a probability measure defined on it. The way in which a mathematical model of this kind can explain the observed phenomena of the universe is examined in general. It is shown…
We introduce a new mathematical framework for the probabilistic description of an experiment upon a system of any type in terms of initial information representing this system. Based on the notions of an information state, an information…
Quantum particles in a potential are described by classical statistical probabilities. We formulate a basic time evolution law for the probability distribution of classical position and momentum such that all known quantum phenomena follow,…
This paper aims at presenting a few models of quantum dynamics whose description involves the analysis of random unitary matrices for which dynamical localization has been proven to hold. Some models come from physical approximations…
For a general quantum theory that is describable by a path integral formalism, we construct a mathematical model of the universe as a sample point of an accumulative stochastic process. The model give predictions that are nearly identical…
The mathematical formalism of Quantum Mechanics is derived or "reconstructed" from more basic considerations of probability theory and information geometry. The starting point is the recognition that probabilities are central to QM: the…
A theoretical scheme, based on a probabilistic generalization of the Hamilton's principle, is elaborated to obtain an unified description of more general dynamical behaviors determined both from a lagrangian function and by mechanisms not…
We construct and explore a family of states for quantum systems in contact with two or more heath reservoirs. The reservoirs are described by equilibrium distributions. The interaction of each reservoir with the bulk of the system is…
Quantum experiments yield random data. We show that the most efficient way to store this empirical information by a finite number of bits is by means of the vector of square roots of observed relative frequencies. This vector has the unique…
In this paper, we introduce a new model of selection behavior under risk that describes an essential cognitive process for comparing values of objects and making a selection decision. This model is constructed by the quantum-like approach…
Previous results indicate that while chaos can lead to substantial entropy production, thereby maximizing dynamical entanglement, this still falls short of maximality. Random Matrix Theory (RMT) modeling of composite quantum systems,…
The dynamical likelihood method for analysis of high energy collider events is reformulated. The method is to reconstruct the elementary parton state from observed quantities. The basic assumption is that each of final state partons…
We present a random matrix model suitable for the quantum mechanical description of a particle confined to move inside a two-dimensional domain. Here, the ensemble average corresponds to an average over domain shapes. Although this approach…
Kolmogorov's setting for probability theory is given an original generalization to account for probabilities arising from Quantum Mechanics. The sample space has a central role in this presentation and random variables, i.e., observables,…
Quantum mechanics is derived from the principle that the universe contain as much variety as possible, in the sense of maximizing the distinctiveness of each subsystem. The quantum state of a microscopic system is defined to correspond to…