Related papers: Quantitative Hypocoercivity and Lifting of Classic…
We provide the first quantitative result of convergence to equilibrium in the context of the spatially homogeneous Boltzmann-Fermi-Dirac equation associated to hard potentials interactions under angular cut-off assumption, providing an…
Within the framework of loop quantum cosmology, there exists a semi-classical regime where spacetime may be approximated in terms of a continuous manifold, but where the standard Friedmann equations of classical Einstein gravity receive…
We explore the relaxation dynamics of quantum many-body systems that undergo purely dissipative dynamics through non-classical jump operators that can establish quantum coherence. Our goal is to shed light on the differences in the…
We present a unified study of some aspects of quantum bicrossproduct algebras of inhomogeneous Lie algebras, like Poincare, Galilei and Euclidean in N dimensions. The action associated to the bicrossproduct structure allows to obtain a…
It is well known that the statistics of closed classical systems evolves according to the Liouville theorem. Here we study the dynamics of the marginal statistics of classical systems coupled to external degrees of freedom, by developing a…
The presence of higher index saddles on a multidimensional potential energy surface is usually assumed to be of little significance in chemical reaction dynamics. Such a viewpoint requires careful reconsideration, thanks to elegant…
Quantum open systems are described in the Markovian limit by master equations in Lindblad form. I argue that common ``quantum jumps'' techniques, which solve the master equation by unraveling its evolution into stochastic trajectories in…
We investigate the relaxation dynamics of a Rydberg gas in regimes where coherent processes and dissipation compete. In the strongly dissipative limit, the dynamics is known to be governed by an effective classical rate equation and to…
Following a minisuperspace approach to the dynamics of a spherically symmetric shell, a reduced Lagrangian for the radial degree of freedom is derived directly from the Einstein-Hilbert action. The key feature of this new Lagrangian is its…
A direct comparison of quantum and classical dynamical systems can be accomplished through the use of distribution functions. This is useful for both fundamental investigations such as the nature of the quantum-classical transition as well…
We study dynamics of quantum open systems, paying special attention to those aspects of their evolution which are relevant to the transition from quantum to classical. We begin with a discussion of the conditional dynamics of simple…
This review investigates the landscapes of prevalent hybrid quantum-classical optimization algorithms in many rapidly developing quantum technologies, where the objective function is either computed by a natural quantum system or a quantum…
Quantum and classical systems evolving under the same formal Hamiltonian $H$ may dramatically differ after the Ehrenfest timescale $t_E \sim \log(\hbar^{-1})$, even as $\hbar \to 0$. Coupling the system to a Markovian environment results in…
We consider two interacting systems when one is treated classically while the other system remains quantum. Consistent dynamics of this coupling has been shown to exist, and explored in the context of treating space-time classically. Here,…
Classical dynamics is formulated as a Hamiltonian flow on phase space, while quantum mechanics is formulated as a unitary dynamics in Hilbert space. These different formulations have made it difficult to directly compare quantum and…
Nelson's stochastic mechanics links quantum mechanics to an underlying Brownian motion with the identification $\hbar = m\sigma$. Ghose's interpolating equation introduces a continuous parameter $\lambda$ that suppresses the quantum…
This memoir attempts at a systematic study of convergence to stationary state for certain classes of degenerate diffusive equations, by means of well-chosen Lyapunov functionals. Typical examples are the kinetic Fokker--Planck and Boltzmann…
We consider a scalar particle in a background formed by two counter-propagating plane waves. Two cases are studied: i) dynamics at a magnetic node and ii) zero initial transverse canonical momentum. The Lorentz and Klein-Gordon equations…
A system of spins coupled to a bath is a traditional setup in open quantum systems. Through Heisenberg's equation, the spin dynamics can be modeled by a set of first-order differential equations. Interpreting the terms as colored noise and…
The complex processes leading to the collisional population of ultra-long-lived Rydberg states with very high angular momentum can be explained surprisingly well using classical mechanics. In this article, we explain the reason behind this…