Related papers: Deriving a kinetic uncertainty relation for piecew…
The current status of the derivation of kinetic equations from quantum many-particle dynamics is reviewed.
In this paper, we present a rigorous derivation of a new kinetic equation describing the limiting behavior of a classical system of particles with three particle elastic instantaneous interactions, which are modeled using a non-symmetric…
Partial differential equations (PDEs) are fundamental for theoretically describing numerous physical processes that are based on some input fields in spatial configurations. Understanding the physical process, in general, requires…
In this work, we study dynamic programming (DP) algorithms for partially observable Markov decision processes with jointly continuous and discrete state-spaces. We consider a class of stochastic systems which have coupled discrete and…
Scientific Machine Learning is a new class of approaches that integrate physical knowledge and mechanistic models with data-driven techniques for uncovering governing equations of complex processes. Among the available approaches, Universal…
Exotic stochastic processes are shown to emerge in the quantum evolution of complex systems. Using influence function techniques, we consider the dynamics of a system coupled to a chaotic subsystem described through random matrix theory. We…
We discuss some applications of various versions of uncertainty relations for both discrete and continuous variables in the context of quantum information theory. The Heisenberg uncertainty relation enables demonstration of the EPR paradox.…
We overview some recent results in the field of uncertainty quantification for kinetic equations and related problems with random inputs. Uncertainties may be due to various reasons, such as lack of knowledge on the microscopic interaction…
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,…
Semi-Markov processes represent a well known and widely used class of random processes in classical probability theory. Here, we develop an extension of this type of non-Markovian dynamics to the quantum regime. This extension is…
We derive a thermodynamic uncertainty relation (TUR) for first-passage times (FPTs) on continuous time Markov chains. The TUR utilizes the entropy production coming from bidirectional transitions, and the net flux coming from unidirectional…
In this paper, we present a novel framework to synthesize robust strategies for discrete-time nonlinear systems with random disturbances that are unknown, against temporal logic specifications. The proposed framework is data-driven and…
Machine learning techniques not only offer efficient tools for modelling dynamical systems from data, but can also be employed as frontline investigative instruments for the underlying physics. Nontrivial information about the original…
We derive quantum kinetic equations for fermions in a homogeneous time-dependent background in presence of decohering collisions, by use of the Schwinger-Keldysh CTP-formalism. The quantum coherence (between particles and antiparticles) is…
Difference Kinetic Equations are derived quantum mechanically in a plane wavelets representation with account of two-particle correlations. It is shown that the set of plane wavelet orthonormal functions is complete. The set of ket vectors…
The density operator of a quantum state can be represented as a complex joint probability of any two observables whose eigenstates have non-zero mutual overlap. Transformations to a new basis set are then expressed in terms of complex…
Universal relations that characterize the fluctuations of nonequilibrium systems are of fundamental importance. The thermodynamic and kinetic uncertainty relations impose upper bounds on the precision of currents solely by total entropy…
In the thermodynamics of nanoscopic systems the relation between classical and quantum mechanical description is of particular importance. To scrutinize this correspondence we have picked out two 2-dim billiard systems. Both systems are…
In this paper, the aim is to develop a quantum counterpart to classical Markov decision processes (MDPs). Firstly, we provide a very general formulation of quantum MDPs with state and action spaces in the quantum domain, quantum…
Answers to the question how a classical world emerges from underlying quantum physics are revisited, connected and extended as follows. First, three distinct concepts are compared: decoherence in open quantum systems, consistent/decoherent…