Related papers: Operator-sum representation of time-dependent dens…
For H a separable infinite dimensional complex Hilbert space, we prove that every B(H) operator has a basis with respect to which its matrix representation has a universal block tridiagonal form with block sizes given by a simple…
We study the existence and uniqueness of (locally) absolutely continuous trajectories of a dynamical system governed by a nonexpansive operator. The weak convergence of the orbits to a fixed point of the operator is investigated by relying…
Starting from a general operator representation in the time-frequency domain, this paper addresses the problem of approximating linear operators by operators that are diagonal or band-diagonal with respect to Gabor frames. A…
In this study, we present a tensor--train framework for nonintrusive operator inference aimed at learning discrete operators and using them to predict solutions of physical governing equations. Our framework comprises three approaches:…
We define an infinite dimensional modification of lower-semicomputability of density operators by G\'acs with an attempt to fix some problem in the paper. Our attempt is partly achieved by showing the existence of universal operator under…
We prove that a bounded operator $T$ on a separable Banach space $X$ satisfying a strong form of the Frequent Hypercyclicity Criterion (which implies in particular that the operator is universal in the sense of Glasner and Weiss) admits…
We construct Baxter operators for the homogeneous closed $\mathrm{XXX}$ spin chain with the quantum space carrying infinite or finite dimensional $s\ell_2$ representations. All algebraic relations of Baxter operators and transfer matrices…
Nonlinear dynamical systems with symmetries exhibit a rich variety of behaviors, including complex attractor-basin portraits and enhanced and suppressed bifurcations. Symmetry arguments provide a way to study these collective behaviors and…
We analyze the separability properties of density operators supported on $\C^2\otimes \C^N$ whose partial transposes are positive operators. We show that if the rank of $\rho$ equals N then it is separable, and that bound entangled states…
While several numerical techniques are available for predicting the dynamics of non-Markovian open quantum systems, most struggle with simulations for very long memory and propagation times, e.g., due to superlinear scaling with the number…
This article presents microscopic derivation of the Kraus operators for (the generalized) amplitude and phase damping process. Derivation is based on the recently developed method [Andersson et al, J. Mod.Opt. 54, 1695 (2007)] which…
To simulate the quantum systems at classical or quantum computers, it is necessary to reduce continuous observables (e.g. coordinate and momentum or energy and time) to discrete ones. In this work we consider the continuous observables…
Dynamical maps describe general transformations of the state of a physical system, and their iteration can be interpreted as generating a discrete time evolution. Prime examples include classical nonlinear systems undergoing transitions to…
We propose the consistent statistical approach to consider a wide class of classical open systems whose states are specified by a set of positive integers(occupation numbers).Such systems are often encountered in physics, chemistry,…
Transfer operators offer linear representations and global, physically meaningful features of nonlinear dynamical systems. Discovering transfer operators, such as the Koopman operator, require careful crafted dictionaries of observables,…
The literature on time series of functional data has focused on processes of which the probabilistic law is either constant over time or constant up to its second-order structure. Especially for long stretches of data it is desirable to be…
Our main theorem is in the generality of the axioms of Hilbert space, and the theory of unbounded operators. Consider two Hilbert spaces such that their intersection contains a fixed vector space D. It is of interest to make a precise…
We discuss time dependent quantum systems on bounded domains. Our work may be viewed as a framework for several models, including linear iterations involved in time dependent density functional theory (TDDFT), the Hartree-Fock model, or…
We study operator complexity on various time scales with emphasis on those much larger than the scrambling period. We use, for systems with a large but finite number of degrees of freedom, the notion of K-complexity employed in…
The dynamics of an open quantum system can be fully described and tomographically reconstructed if the experimenter has complete control over the system of interest. Most real-world experiments do not fulfill this assumption, and the amount…