相关论文: Hybrid Koopman C*-formalism and the hybrid quantum…

Quantum and classical systems can consistently be coupled via non-unitary time-irreversible mechanisms. In this paper we characterize which kind of corresponding dynamics converge in the stationary regime to a thermal hybrid state, that is,…

Descriptions of classical mechanics in Hilbert space go back to the work of Koopman and von Neumann in the 1930s. Decades later, van Hove derived a unitary representation of the group of contact transformations which recently has been used…

We discuss hybrid master equations of composite systems which are hybrids of classical and quantum subsystems. A fairly general form of hybrid master equations is suggested, its consistency is derived from the consistency of Lindblad…

In the past ten-fifteen years, stochastic models of continuous wave function collapse were being proposed to describe the continuous emergence of classicality from quantum. We advocate that the hybrid dynamics of canonically coupled quantum…

A formalism is presented in which quantum particle dynamics can be developed on its own rather than `quantization' of an underlying classical theory. It is proposed that the unification of probability and dynamics should be considered as…

We introduce a hybrid classical-quantum algorithm to compute dynamical correlation functions and excitation spectra in many-body quantum systems, with a focus on molecular systems. The method combines classical preparation of a perturbed…

The design and analysis of optimal control policies for dynamical systems can be complicated by nonlinear dependence in the state variables. Koopman operators have been used to simplify the analysis of dynamical systems by mapping the flow…

We show that all non-relativistic quantum processes, whether open or closed, are either unitary or probabilistic unitary, i.e., probabilistic combination of unitary evolutions. This means that for open quantum systems, its continuous…

We discuss the possibility to modify many-body Hilbert quantum formalism that is necessary for the representation of quantum systems dynamics. The notion of effective classical algorithm and visualization of quantum dynamics play the key…

We propose a scheme for data-driven parameterization of unresolved dimensions of dynamical systems based on the mathematical framework of quantum mechanics and Koopman operator theory. Given a system in which some components of the state…

We construct C*-dynamical systems for the dynamics of classical infinite particle systems describing harmonic oscillators interacting with arbitrarily many neighbors on lattices, as well on more general structures. Our approach allows…

The study of mathematical connections between operator-theoretic formulations of classical dynamics and quantum mechanics began at least as early as the 1930s in work of Koopman and von Neumann and was developed in later decades by many…

A recent formalism capturing the classical-quantum coupling in a Hamiltonian theory for probabilistic classical mechanics has been proposed: the Koopman-van Hove formulation. The aims of this report are twofolds. First, we rigourously…

A filtering problem for a class of quantum systems disturbed by a classical stochastic process is investigated in this paper. The classical disturbance process, which is assumed to be described by a linear stochastic differential equation,…

We develop a Koopman operator framework for studying the {computational properties} of dynamical systems. Specifically, we show that the resolvent of the Koopman operator provides a natural abstraction of halting, yielding a ``Koopman…

We examine the theory of the KMS states on Pimsner algebras arising from multivariable unital C*-dynamical systems. As an application we show that Pimsner algebras of piecewise conjugate classical systems attain the same KMS states, even…

In this paper, we develop the framework for quantum integrable systems on an integrable classical background. We call them hybrid quantum integrable systems (hybrid integrable systems), and we show that they occur naturally in the…

This work is devoted to giving a geometric framework for describing higher-order non-autonomous mechanical systems. The starting point is to extend the Lagrangian-Hamiltonian unified formalism of Skinner and Rusk for these kinds of systems,…

A generalization of classical mechanics is obtained from a complex parametrization of the phase space. The formalism supports complex Hamiltonian functions describing non-conservative classical mechanical systems. A quantization scheme that…

We present a detailed exposition (for a Dynamical System audience) of the content of the paper: R. Exel and A. Lopes, $C^*$ Algebras, approximately proper equivalence relations and Thermodynamic Formalism, {\it Erg. Theo. and Dyn. Syst.},…