Related papers: Free to Harmonic Unitary Transformations in Quantu…
The ongoing discussion whether thermodynamic properties can be extracted from a (possibly approximate) quantum mechanical time evolution using time averages is fed with an instructive example. It is shown for the harmonic oscillator how the…
We have shown that quantum systems on finite-dimensional Hilbert spaces are equivalent under local transformations. Using these transformations give rise to a gauge group that connects the hamiltonian operators associated with each quantum…
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…
We address the question of unitary implementation of the dynamics for scalar fields in cosmological scenarios. Together with invariance under spatial isometries, the requirement of a unitary evolution singles out a rescaling of the scalar…
In this paper, we analyze classical and quantum physical systems from an optimal control perspective. Specifically, we explore whether their associated dynamics can correspond to an open or closed-loop feedback evolution of a control…
We address the multiplicity of solutions to the time-energy canonical commutation relation for a given Hamiltonian. Specifically, we consider a particle spatially confined in a potential free interval, where it is known that two distinct…
We define an observable-space framework of Quantum Koopman Algorithms (QKAs) for simulating the dynamics of both linear quantum and nonlinear classical systems, based on approximately closed sets of observables and efficient coherent…
Quantum systems with a non-conserved probability can be described by means of non-Hermitian Hamiltonians and non-unitary dynamics. In this paper, the case in which the degrees of freedom can be partitioned in two subsets with light and…
While it is well-known that quantum mechanics can be reformulated in terms of a path integral representation, it will be shown that such a formulation is also possible in the case of classical mechanics. From Koopman-von Neumann theory,…
It is shown that the recently proposed quantum analogue of classical energy equipartition theorem for two paradigmatic, exactly solved models (i.e., a free Brownian particle and a dissipative harmonic oscillator) also holds true for all…
We investigate the quantization of a free particle coupled linearly to a harmonic oscillator. This system, whose classical counterpart has clearly separated regular and chaotic regions, provides an ideal framework for studying the…
We general-quantize the dynamics of the quantum harmonic oscillator to obtain a covariant finite quantum dynamics in a finite quantum time. The usual central (``superselected'') time results from a self-organization. Unitarity necessarily…
Classical physics is reformulated as a constrained Hamiltonian system in the history phase space. Dynamics, i.e. the Euler-Lagrange equations, play the role of first-class constraints. This allows us to apply standard methods from the…
Consistent dynamics which couples classical and quantum degrees of freedom exists. This dynamics is linear in the hybrid state, completely positive and trace preserving. Starting from completely positive classical-quantum master equations,…
We formulate non-relativistic classical and quantum mechanics in the non-commutative two dimensional plane. The approach we use is based on the Galilei group, where the non-commutativity is seen as a central extension upon identification of…
The understanding of how classical dynamics can emerge in closed quantum systems is a problem of fundamental importance. Remarkably, while classical behavior usually arises from coupling to thermal fluctuations or random spectral noise, it…
We obtain analytic solutions to various models of dissipation of the quantum harmonic oscillator, employing a simple method in the Wigner function Fourier transform description of the system; and study as an exemplification, the driven open…
We model the dynamics of a closed quantum system brought out of mechanical equilibrium, undergoing a non-driven, spontaneous, thermodynamic transformation. In particular, we consider a quantum particle in a box with a moving and insulating…
We provide a new canonical approach for studying the quantum mechanical damped harmonic oscillator based on the doubling of degrees of freedom approach. Explicit expressions for Lagrangians of the elementary modes of the problem,…
An exact invariant is derived for $n$-degree-of-freedom Hamiltonian systems with general time-dependent potentials. The invariant is worked out in two equivalent ways. In the first approach, we define a special {\it Ansatz\/} for the…