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We consider Markovian open quantum dynamics with weak unitary symmetries. Starting from the quantum master equation for the system alone, it is known that the joint dynamics of the system and its environment can be obtained by dilation,…
We study a graph partitioning problem motivated by the simulation of the physical movement of multi-body systems on an atomistic level, where the forces are calculated from a quantum mechanical description of the electrons. Several advanced…
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…
Correlations between different partitions of quantum systems play a central role in a variety of many-body quantum systems, and they have been studied exhaustively in experimental and theoretical research. Here, we investigate dynamical…
The most general evolution of the density matrix of a quantum system with a finite-dimensional state space is by stochastic maps which take a density matrix linearly into the set of density matrices. These dynamical stochastic maps form a…
Invisible particles frequently appear in final state in studying physics at colliders. Experimental precision is also low in measuring missing energy. In this paper, we propose a general approach for studying process involving invisible…
Special exotic class of dynamical systems~ -- the implicit maps~ -- is considered. Such maps, particularly, can appear as a result of using of implicit and semi-implicit iterative numerical methods. In the present work we propose the…
Positive maps applied to a subsystem of a bipartite quantum state constitute a central tool in characterising entanglement. In the multipartite case, however, the direct application of a positive but not completely positive map cannot…
This article surveys the burgeoning area at the intersection of dynamical systems theory and algorithms for NP-hard problems. Traditionally, computational complexity and the analysis of non-deterministic polynomial-time (NP)-hard problems…
For spatiotemporal chaos described by partial differential equations, there are generally locations where the dynamical variable achieves its local extremum or where the time partial derivative of the variable vanishes instantaneously. To a…
Two major deviations from causality in the existing formulations of quantum mechanics, related respectively to quantum chaos and indeterminate wave reduction, are eliminated within the new, universal concept of dynamic complexity. The…
Characterizing those quantum channels that correspond to Markovian time evolutions is an open problem in quantum information theory, even different notions of quantum Markovianity exist. One such notion is that of infinitesimal Markovian…
For finite-dimensional quantum systems, such as qubits, a well established strategy to protect such systems from decoherence is dynamical decoupling. However many promising quantum devices, such as oscillators, are infinite dimensional, for…
I investigate the problem of optimally discriminating between two open quantum dynamical processes in a single-shot scenario, with the goal of minimizing the error probability of identification. This task involves optimising both the input…
Driven particles in presence of crowded environment, obstacles or kinetic constraints often exhibit negative differential mobility (NDM) due to their decreased dynamical activity. We propose a new mechanism for complex many-particle systems…
The dynamics of local observables in a quantum many-body system can be formally described in the language of open systems. The problem is that the bath representing the complement of the local subsystem generally does not allow the common…
The essence of the path integral method in quantum physics can be expressed in terms of two relations between unitary propagators, describing perturbations of the underlying system. They inherit the causal structure of the theory and its…
This paper discusses the evolution of probability distributions for certain time-dependent dynamical systems. Exponential loss of memory is proved for expanding maps and for one-dimensional piecewise expanding maps with slowly varying…
It is shown in "SIAM J. Sci. Comput. 39 (2017):B424-B441" that free-form curves used in computer aided geometric design can usually be represented as the solutions of linear differential systems and points and derivatives on the curves can…
A model of interacting motile chaotic elements is proposed. The chaotic elements are distributed in space and interact with each other through interactions depending on their positions and their internal states. As the value of a governing…