Related papers: A new time-dependent quantum theory based on Tsall…
We review the random matrix description of electron transport through open quantum dots, subject to time-dependent perturbations. All characteristics of the current linear in the bias can be expressed in terms of the scattering matrix,…
In this paper, we present the results of our investigation relating particle dynamics and non-commutativity of space-time by using Dirac's constraint analysis. In this study, we re-parameterise the time $t=t(\tau)$ along with $x=x(\tau)$…
A principle is proposed according to which the dynamics of a quantum particle in a one-dimensional configuration space (OCS) is determined by a variational problem for two functionals: one is based on the mean value of the Hamilton…
We study the covariance property of quadratic time-frequency distributions with respect to the action of the extended symplectic group. We show how covariance is related, and in fact in competition, with the possibility of damping the…
A variety of dynamics in nature and society can be approximately treated as a driven and damped parametric oscillator. An intensive investigation of this time-dependent model from an algebraic point of view provides a consistent method to…
At non-zero temperature classical systems exhibit statistical fluctuations of thermodynamic quantities arising from the variation of the system's initial conditions and its interaction with the environment. The fluctuating work, for…
We prove a global well-posedness result for defocusing nonlinear Schrodinger equations with time dependent potential. We then focus on time dependent harmonic potentials. This aspect is motivated by Physics (Bose--Einstein condensation),…
Quantum mechanics is challenging even for advanced undergraduate and graduate students. In the Schr\"odinger representation, the wave function evolves in time according to the time dependent Schr\"odinger equation. The time dependence of…
We present a rigorous study of quantum diffusion of a relativistic particle subjected to a time-dependent random potential with $\delta$ correlation in time. We find that in the asymptotic time limit the particle wave packet spreads…
In this article we study the nature of time in Mechanics. The fundamental principle, according to which a mechanical system evolves governed by a second order differential equation, implies the existence of an absolute time-duration in the…
This article generalizes the conditional probability interpretation of time in which time evolution is realized through entanglement between a clock and a system of interest. This formalism is based upon conditioning a solution to the…
The time-dependent variational principle using generalized Gaussian trial functions yields a finite dimensional approximation to the full quantum dynamics and is used in many disciplines. It is shown how these 'semi-quantum' dynamics may be…
The propagation of a localized wave packet in the conical space-time created by a pointlike massive source in 2+1 dimensional gravity is analyzed. The scattering amplitude is determined and shown to be finite along the classical scattering…
We reformulate the time-independent Schr\"odinger equation as a Maurer-Cartan equation on the superspace of eigensystems of the former equation. We then twist the differential so that its cohomology becomes the space of solutions with a set…
In this paper we introduce an alternative approach to studying the evolution of a quantum harmonic oscillator subject to an arbitrary time dependent force. With the purpose of finding the evolution operator, certain unitary transformations…
We study large time behavior of quantum walks (QWs) with self-dependent (nonlinear) coin. In particular, we show scattering and derive the reproducing formula for inverse scattering in the weak nonlinear regime. The proof is based on…
In the covariant canonical approach to classical physics, each point in phase space represents an entire classical trajectory. Initial data at a fixed time serve as coordinates for this ``timeless'' phase space, and time evolution can be…
How would the world appear to us if its ontology was that of classical mechanics but every agent faced a restriction on how much they could come to know about the classical state? We show that in most respects, it would appear to us as…
The purpose of the present paper is to discuss the time dependent Schr\"odinger equation on a metric graph with time-dependent edge lengths, and the proper way to pose the problem so that the corresponding time evolution is unitary. We show…
Our work explore the time evolution of entanglement, local quantum uncertainty, and correlated coherence, within a system modeled by two double quantum dots. The dynamics is represented using a time-fractional Schr\"odinger equation, which…