Related papers: Hamilton-Jacobi Formulation of KS Entropy for Clas…
The phase space Koopman-van Hove (KvH) equation can be derived from the asymptotic semiclassical analysis of partial differential equations. Semiclassical theory yields the Hamilton-Jacobi equation for the complex phase factor and the…
In this first of a series of four articles, it is shown how a hamiltonian quantum dynamics can be formulated based on a generalization of classical probability theory using the notion of quasi-invariant measures on the classical phase space…
Von Neumann entropy production rates of the quantised kicked rotor interacting with an environment are calculated. A significant correspondence is found between the entropy contours of the classical and quantised systems. This is a…
In these notes we will give an overview and road map for a definition and characterization of (relative) entropy for both classical and quantum systems. In other words, we will provide a consistent treatment of entropy which can be applied…
It has earlier been argued that there should exist a formulation of quantum mechanics which does not refer to a background spacetime. In this paper we propose that, for a relativistic particle, such a formulation is provided by a…
In this paper, we demonstrate a polynomial convergence rate for homogenization of Hamilton-Jacobi equations with quasi-periodic potentials. We establish a connection between the convergence rate of homogenization and the regularity of the…
Quantum thermodynamics has emerged as a central field for understanding how energy conversion processes occur in microscopic systems. In these systems, effects such as coherence, entanglement, and non-Markovianity play key roles. In this…
We analyze the connections between entanglement dynamics and classical trajectories in a semiclassi-cal regime for two systems: A pair of coupled oscillators and the Jaynes-Cummings model. We find that entanglement production depends on…
We give arguments for the existence of a thermodynamics of quantum complexity that includes a "Second Law of Complexity". To guide us, we derive a correspondence between the computational (circuit) complexity of a quantum system of $K$…
Observing how long a dynamical system takes to return to some state is one of the most simple ways to model and quantify its dynamics from data series. This work proposes two formulas to estimate the KS entropy and a lower bound of it, a…
The paper deals with Hawking radiation related to non-static spherically symmetric black hole. Quantum corrections are incorporated using Hamilton-Jacobi method beyond semi-classical approximation. It is found that different order…
A gauge-invariant wave equation for the dynamics of hybrid quantum-classical systems is formulated by combining the variational setting of Lagrangian paths in continuum theories with Koopman wavefunctions in classical mechanics. We identify…
There is a version of the Landau-Lifshitz equation that takes into account the Coulomb exchange interactions between atoms, expressed by the term $\sim\bm{s}\times\triangle\bm{s}$. On the other hand, ions in the magnetic materials have…
We introduce a simple quantum generalization of the spectrum of classical Lyapunov exponents. We apply it to the SYK and XXZ models, and study the Lyapunov growth and entropy production. Our numerical results suggest that a black hole is…
A density matrix formulation of classical bipartite correlations is constructed. This leads to an understanding of the appearance of classical statistical correlations intertwined with the quantum correlations as well as a physical…
In this work we show how to complete some Hamilton-Jacobi solutions of linear, nonconservative classical oscillatory systems which appeared in the literature and we extend these complete solutions to the quantum mechanical case. In…
The general forms of Quantum Hamilton Jacobi Equation for a particle of constant mass, position dependent effective mass and non-Hermitian Effective mass Swanson model have been considered. It has been found that the said equations can be…
Covariant classical particle dynamics is described, and the associated covariant relativistic particle quantum mechanics is derived. The invariant symmetric bracket is defined on the space of quantum amplitudes, and its relation to a…
A framework for statistical-mechanical analysis of quantum Hamiltonians is introduced. The approach is based upon a gradient flow equation in the space of Hamiltonians such that the eigenvectors of the initial Hamiltonian evolve toward…
We consider quantum trajectories of composite systems as generated by the stochastic unraveling of the respective Lindblad-master-equation. Their classical limit is taken to correspond to local jumps between orthogonal states. Based on…