Related papers: A new time-dependent quantum theory based on Tsall…
We find the limit distributions for a spectrum of a system of n particles governed by a k-body interaction. The hamiltonian of this system is modelled by a Gaussian random matrix. We show that the limit distribution is a q-deformed Gaussian…
We describe radiative processes in Quantum Cosmology, from the solutions of the Wheeler De Witt equation. By virtue of this constraint equation, the quantum propagation of gravity is modified by the matter interaction hamiltonian at the…
We study the Schr\"odinger equation driven by a weak Brownian forcing, and derive Gaussian fluctuations in the form of a time-inhomogeneous Ornstein-Uhlenbeck process. As a result, when evaluated at a fixed frequency, the intensity of the…
In this first of a series of four articles, it is shown how a hamiltonian quantum dynamics can be formulated based on a generalization of classical probability theory using the notion of quasi-invariant measures on the classical phase space…
Non-relativistic quantum mechanics for a free particle is shown to emerge from classical mechanics through an invariance principle under transformations that preserve the Heisenberg position-momentum inequality. These transformations are…
We study the time-evolution of a quantum particle subjected to time-dependent zero-range forces in two dimensions. After establishing a conceivable ansatz for the solution to the Schr\"{o}dinger equation, we prove that the wave packet…
We derived the expression of the normalized $q$-expectation value based on the density operator to the order $1-q$ with the physical temperature in the Tsallis nonextensive statistics of entropic parameter $q$. With the derived expression…
We construct a class of fixed-time models in which the commutations relations of a Dirac field with a bosonic field are non-trivial and depend on the choice of a given distribution ("twisting factor"). If the twisting factor is fundamental…
We show that within classical statistical mechanics without taking the thermodynamic limit, the most general Boltzmann factor for the canonical ensemble is a q-exponential function. The only assumption here is that microcanonical…
Given a bipartite quantum system in an energy eigenstate, the dynamical description for one component can be derived via entanglement using the other component as a clock. This is the essence of the Page and Wootters mechanism. Moreover, if…
The tomographic invertable map of the Wigner function onto the positive probability distribution function is studied. Alternatives to the Schr\"odinger evolution equation and to the energy level equation written for the positive probability…
The classical and quantum evolution of a generic probability distribution is analyzed. To that end, a formalism based on the decomposition of the distribution in terms of its statistical moments is used, which makes explicit the differences…
Understanding the real-time evolution of many-electron quantum systems is essential for studying dynamical properties in condensed matter, quantum chemistry, and complex materials, yet it poses a significant theoretical and computational…
We describe a time evolution algorithm for quantum spin chains whose Hamiltonians are composed of an infinite uniform left and right bulk part, and an arbitrary finite region in between. The left and right bulk parts are allowed to be…
The Boltzmann distribution of an ideal gas is determined by the Hamiltonian function generating single particle dynamics. Systems with higher complexity often exhibit topological constraints, which are independent of the Hamiltonian and may…
I extend the three-dimensional q-deformed Euclidean space by a time element and discuss the algebraic structure of this quantum space together with its differential calculi. Using the star-product formalism, I will give basic operations of…
It is shown how the time-dependent Schr\"{o}dinger equation may be simply derived from the dynamical postulate of Feynman's path integral formulation of quantum mechanics and the Hamilton-Jacobi equation of classical mechanics.…
We analyze the quantum dynamics of the fractional-time Jaynes-Cummings model using a recent unitary framework for the fractional-time Schr\"odinger equation. We examine how the fractional derivative order $\alpha$ influences non-classical…
Using standard results from statistics, we show that for Gaussian quantum systems the distribution of a time measurement at a fixed position can be directly inferred from the distribution of a position measurement at a fixed time as given…
Using the simplest but fundamental example, the problem of the infinite potential well, this paper makes an ideological attempt (supported by rigorous mathematical proofs) to approach the issue of…