Related papers: Compact and complete description of non-Markovian …
We investigate the long-time behavior of quantum Markovian dynamics generated by time-dependent Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) master equations. We introduce a notion of weak relaxation and derive sufficient conditions…
We maintain that the wavefunction is an ensemble property rather than an individual particle property. For individual particles, we propose an ontology underwritten by the Heisenberg representation. It consists of properties represented by…
Recent advances at the intersection of control theory, neuroscience, and machine learning have revealed novel mechanisms by which dynamical systems perform computation. These advances encompass a wide range of conceptual, mathematical, and…
We theoretically study a simple non-equilibrium quantum network whose dynamics can be expressed and exactly solved in terms of a time-local master equation. Specifically, we consider a pair of coupled fermionic modes, each one locally…
Memory effects in the dynamics of open systems have been the subject of significant interest in the last decades. The methods involved in quantifying this effect, however, are often difficult to compute and may lack analytical insight. With…
We construct a large class of completely positive and trace preserving non-Markovian dynamical maps for an open quantum system. These maps arise from a piecewise dynamics characterized by a continuous time evolution interrupted by jumps,…
We present a conservative/dissipative time integration scheme for nonlinear mechanical systems. Starting from a weak form, we derive algorithmic forces and velocities that guarantee the desired conservation/dissipation properties. Our…
We present a dynamical framework for modeling the motion of point-like charged particles, with or without mass, in general external electromagnetic fields. A key feature of this formulation is the treatment of time coordinate as a dynamical…
We analyze the motion of a pressure control system described by a differential equation with nonlocal dissipative force. This system is composed by an oscillator, a membrane and a constant force. We consider the dissipative memory kernel…
Effective forces -- derived from experimental or {\it in silico} molecular dynamics time traces -- are critical in developing reduced and computationally efficient descriptions of otherwise complex dynamical problems. Thus, designing…
The dynamics of open quantum system are often modeled by non-Markovian processes that account for memory effects arising from interactions with the environment. It is well-known that the memory provided by the environment can be classical…
We study a system of Maxwell's equations that describes the time evolution of electromagnetic fields with an additional electric scalar variable to make the system amenable to a mixed finite element spatial discretization. We demonstrate…
A simple pseudo-Hamiltonian formulation is proposed for the linear inhomogeneous systems of ODEs. In contrast to the usual Hamiltonian mechanics, our approach is based on the use of non-stationary Poisson brackets, i.e. corresponding…
Many physical systems are described by nonlinear differential equations that are too complicated to solve in full. A natural way to proceed is to divide the variables into those that are of direct interest and those that are not, formulate…
Differential equations containing memory terms that depend nonlinearly on past states model a variety of non-Markovian processes. In this study, we present a Markovian embedding procedure for such equations with distributed delay by…
We study the analytically solvable Ising model of a single qubit system coupled to a spin bath. The purpose of this study is to analyze and elucidate the performance of Markovian and non-Markovian master equations describing the dynamics of…
We analyze the non-Markovian dynamics of a quantum system subject to spontaneous collapse in space. After having proved, under suitable conditions, the separation of the center-of-mass and relative motions, we focus our analysis on the time…
Finding the dynamical law of observable quantities lies at the core of physics. Within the particular field of statistical mechanics, the generalized Langevin equation (GLE) comprises a general model for the evolution of observables…
Beyond the conventional quantum regression theorem, a general formula for non-Markovian correlation functions of arbitrary system operators both in the time- and frequency-domain is given. We approach the problem by transforming the…
As we typically teach in an introductory mechanics course, choosing a "good" reference frame with convenient axes may present a major simplification to a problem. Additionally, knowing some conserved quantities provides an extremely…