Related papers: A Magnus approximation approach to harmonic system…
We show how a large family of master equations, describing quantum Brownian motion of a harmonic oscillator with translationally invariant damping, can be derived within a phenomenological approach, based on the assumption that an…
We discuss the connection between the out-of-time-ordered correlator and the number of harmonics of the phase-space Wigner distribution function. In particular, we show that both quantities grow exponentially for chaotic dynamics, with a…
Linear mechanical systems with time-modulated parameters can harbor oscillations with amplitudes that grow or decay exponentially with time due to the phenomenon of parametric resonance. While the resonance properties of individual…
We study resonances of nonlinear systems of differential equations, including but not limited to the equations of motion of a particle moving in a potential. We use the calculus of variations to determine the minimal additive forcing…
Quantum systems coupled to environments exhibit intricate dynamics. The master equation gives a Markov approximation of the dynamics, allowing for analytic and numerical treatments. It is ubiquitous in theoretical and applied quantum…
The solutions of Hamiltonian equations are known to describe the underlying phase space of a mechanical system. In this article, we propose a novel spatio-temporal model using a strategic modification of the Hamiltonian equations,…
We consider the numerical integration of the Gross-Pitaevskii equation with a potential trap given by a time-dependent harmonic potential or a small perturbation thereof. Splitting methods are frequently used with Fourier techniques since…
The non-Markovian behaviour of open quantum systems interacting with a reservoir can often be described in terms of a time-local master equation involving a time-dependent generator which is not in Lindblad form. A systematic perturbation…
The calculation of quantum canonical time correlation functions is considered in this paper. Transport properties, such as diffusion and reaction rate coefficients, can be determined from time integrals of these correlation functions.…
We microscopically model the decoherence dynamics of entangled coherent states under the influence of vacuum fluctuation. We derive an exact master equation with time-dependent coefficients reflecting the memory effect of the environment,…
Of primary interest in this paper is the numerical approximation of a time dependent fractional, in space, diffusion equation where the domain is assumed to be nonhomogeneous, having different axial diffusion coefficients. This work is…
I show that the dynamics of the weakly interacting bose gas can be described by a modified time dependent Bogoliubov theory. The novelty of the approach is to include decoherence steps that gradually transform the entanglement entropy of…
A general non-linear response theory is derived for an arbitrary time-dependent Hamiltonian, not necessarily obeying time-reversal symmetry. This allows us to obtain a greatly generalized Kubo type formula. Applied to a mesoscopic system…
We propose a new approximation-technique to deal with the exact macroscopic integro-differential evolution equations of statistical systems which self-consistently accounts for dissipative effects. Concentrating on one and two point…
Highly oscillatory differential equations present significant challenges in numerical treatments. The Modulated Fourier Expansion (MFE), used as an ansatz, is a commonly employed tool as a numerical approximation method. In this article,…
We introduce a scalable variational method for simulating the dynamics of interacting open quantum bosonic systems deep in the quantum regime. The method is based on a multi-dimensional Wigner phase-space representation and employs a…
The problem of analytical estimation of the Lyapunov exponents and Lyapunov timescales of the motion in multiplets of interacting nonlinear resonances is considered. To this end, we elaborate a unified framework, based on the separatrix map…
It is well known that a spinning body moving in a fluid suffers a force orthogonal to its velocity and rotation axis --- it is called the Magnus effect. Recent simulations of spinning black holes and (indirect) theoretical predictions,…
We apply our recently developed resonance perturbation theory to describe the dynamics of magnetization in paramagnetic spin systems interacting simultaneously with local and collective bosonic environments. We derive explicit expressions…
In this paper, we consider a Diophantine quasi-periodic time-dependent analytic perturbation of a convex integrable Hamiltonian system, and we prove a result of stability of the action variables for an exponentially long interval of time.…