Related papers: Quantum L_p and Orlicz spaces
We study the statistical mechanics of classical and quantum systems in non-equilibrium steady states. Emphasis is placed on systems in strong thermal gradients. Various measures and functional forms of observables are presented. The quantum…
In this paper we: 1) show how the smooth geometry of spaces of normal quantum states over W*-algebras (generalised spaces of density matrices) may be used to substantially enrich the description of quantum dynamics in the algebraic and path…
Any realist interpretation of quantum theory must grapple with the measurement problem and the status of state-vector collapse. In a no-collapse approach, measurement is typically modeled as a dynamical process involving decoherence. We…
We study some basic and interesting quantum mechanical systems in dynamical noncommutative spaces in which the space- space commutation relations are position dependent. It is observed that the fundamental objects in the dynamical…
In this paper we present a unified algebraic framework to discuss the reduction of classical and quantum systems. The underlying algebraic structure is a Lie-Jordan algebra supplemented, in the quantum case, with a Banach structure. We…
Classical Bianchi-Lie, Backlund and Darboux transformations are considered. Their generalizations for the dynamical systems are discussed. For the transformation being the generalization of the normal shift the special class of dynamical…
Deterministic dynamical models are discussed which can be described in quantum mechanical terms. -- In particular, a local quantum field theory is presented which is a supersymmetric classical model. The Hilbert space approach of Koopman…
Computational methods are indispensable to study the quantum dynamics of relativistic light-matter interactions in parameter regimes where analytical methods become inapplicable. We present numerical methods for solving the time-dependent…
The non-commutativity of the position and momentum operators is formulated as an effective potential in classical phase space and expanded as a series of successive many-body terms, with the pair term being dominant. A non-linear partial…
Noting the important role the abstract $L^p$ space has played in the development of random normed modules, in this paper we introduce and study the Orlicz space generated from a random normed module. First, we give a basic dual space…
The formalism of linear response theory can be extended to encompass physical situations where an open quantum system evolves towards a non-equilibrium steady-state. Here, we use the framework put forward by Konopik and Lutz [Phys. Rev.…
We present a general approach to the classical dynamical systems simulation. This approach is based on classical systems extension to quantum states. The proposed theory can be applied to analysis of multiple (including non-Hamiltonian)…
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…
A dynamical system with discrete time is studied by means of algebraic geometry. The system admits a reduction that is interpreted as a classical field theory in 2+1-dimensional wholly discrete space-time. The integrals of motion of a…
This work develops a symplectic framework for quantum computing to be applied to classical Hamiltonian systems, exploiting the intrinsic geometric compatibility between unitary quantum evolution and symplectic phase-space dynamics in a…
To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…
In this paper we relate the geometry of Banach spaces to the theory of differential equations, apparently in a new way. We will construct Banach function space norms arising as weak solutions to ordinary differential equations of first…
Many quantitative approaches to the dynamical scrambling of information in quantum systems involve the study of out-of-time-ordered correlators (OTOCs). In this paper, we introduce an algebraic OTOC ($\mathcal{A}$-OTOC) that allows us to…
This paper is a review of our recent work on three notorious problems of non-relativistic quantum mechanics: realist interpretation, quantum theory of classical properties and the problem of quantum measurement. A considerable progress has…
In this paper we shall re-visit the well-known Schr\"odinger and Lindblad dynamics of quantum mechanics. However, these equations may be realized as the consequence of a more general, underlying dynamical process. In both cases we shall see…