Related papers: Jensen-Shannon Divergence and Non-linear Quantum D…
This is a review paper concerned with the global consistency of the quantum dynamics of non-commutative systems. Our point of departure is the theory of constrained systems, since it provides a unified description of the classical and…
A previous derivation of the single-particle Schr\"odinger equation from statistical assumptions is generalized to an arbitrary number $N$ of particles moving in three-dimensional space. Spin and gauge fields are also taken into account. It…
We provide a complete derivation of hydrodynamic equations for nonrelativistic systems based on quantum field theories of spinless Schr\"odeinger fields, assuming that an initial density operator takes a special form of the local Gibbs…
Using a generalized energy-conserving transition probability, it is shown how nonadiabatic calculations, within the Wigner-Heisenberg representation of quantum mechanics, can be reliably extended to far longer times than those allowed by a…
Starting from the Schr\"odinger-equation of a composite system, we derive unified dynamics of a classical harmonic system coupled to an arbitrary quantized system. The classical subsystem is described by random phase-space coordinates…
The master equation describing non-equilibrium one-dimensional problems like diffusion limited reactions or critical dynamics of classical spin systems can be written as a Schr\"odinger equation in which the wave function is the probability…
We propose the construction of equations of motion based on symmetries in quantum-mechanical systems, using Heisenberg's uncertainty principle as a minimal foundation. From canonical operators, two spaces of conjugate operators are…
We have developed a method for complementing an arbitrary classical dynamical system to a quantum system using the Lorenz and R\"ossler systems as examples. The Schr\"odinger equation for the corresponding quantum statistical ensemble is…
The theory of a complex scalar interacting with a pure Chern-Simons gauge field is quantized canonically. Dynamical and nondynamical variables are separated in a gauge-independent way. In the physical subspace of the full Hilbert space,…
In this paper, the classical Schr\"odinger equation, which allows the study of classical dynamics in terms of wave functions, is analyzed theoretically and numerically. First, departing from classical (Newtonian) mechanics, and assuming an…
Classical nonlinear theories are highly successful in describing far-from-equilibrium dynamics of magnets, encompassing phenomena such as parametric resonance, ultrafast switching, and even chaos. However, at ultrashort length and time…
Nonlinear quantum dynamics is often invoked in models trying to bridge the gap between the quantum micro-world and the classical macro-world. Such endeavors, however, encounter challenges at the nexus with relativity. In 1989 Nicolas Gisin…
The importance of the quantum Fisher information metric is testified by the number of applications that this has in very different fields, ranging from hypothesis testing to metrology, passing through thermodynamics. Still, from the rich…
Shannon entropy and Fisher information functionals are known to quantify certain information-theoretic properties of continuous probability distributions of various origins. We carry out a systematic study of these functionals, while…
In this chapter, a statistical measure of complexity and the Fisher-Shannon information product are introduced and their properties are discussed. These measures are based on the interplay between the Shannon information, or a function of…
Dyson--Schwinger equations are an established, powerful non-perturbative tool for QCD. In the Hamiltonian formulation of a quantum field theory they can be used to perform variational calculations with non-Gaussian wave functionals. By…
Informational dependence between statistical or quantum subsystems can be described with Fisher matrix or Fubini-Study metric obtained from variations of the sample/configuration space coordinates. Using these non-covariant objects as…
The Fisher-Shannon information and a statistical measure of complexity are calculated in the position and momentum spaces for the wave functions of the quantum isotropic harmonic oscillator. We show that these magnitudes are independent of…
In the present paper, a discrete differential calculus is introduced and used to describe dynamical systems over arbitrary graphs. The discretization of space and time allows the derivation of Heisenberg-like uncertainty inequalities and of…
We discuss new approach to mathematical foundations of quantum theory, which is completely independent of Hilbert spaces and measure spaces. New kinematics is defined by non-linear geometry of spaces of integrals on abstract non-commutative…