Related papers: On quantum averaging, quantum KAM and quantum diff…
Quantum mechanics for a four-state-system is derived from classical statistics. Entanglement, interference, the difference between identical fermions or bosons and the unitary time evolution find an interpretation within a classical…
Concepts like `typicality' and the `eigenstate thermalization hypothesis' aim at explaining the apparent equilibration of quantum systems, possibly after a very long time. However, these concepts are not concerned with the specific way in…
Three existing interpretations of quantum mechanics, given by Heisenberg, Bohm and Madelung, are examined to describe dissipative quantum systems as well. It is found that the Madelung quantum hydrodynamics is the only correct approach. A…
This colloquium gives an overview of recent theoretical and experimental progress in the area of nonequilibrium dynamics of isolated quantum systems. We particularly focus on quantum quenches: the temporal evolution following a sudden or…
A system of quantum computing structures is introduced and proven capable of making emerge, on average, the orbits of classical bounded nonlinear maps on \mathbb{C} through the iterative action of path-dependent quantum gates. The effects…
Recent developments concerning canonical quantisation and gauge invariant quantum mechanical systems and quantum field theories are briefly discussed. On the one hand, it is shown how diffeomorphic covariant representations of the…
We explain the ubiquity and extremely slow evolution of non gaussian out-of-equilibrium distributions for the Hamiltonian Mean-Field model, by means of traditional kinetic theory. Deriving the Fokker-Planck equation for a test particle, one…
This article traces the development of fluctuation theory and its deep connection to irreversibility, from equilibrium to near-equilibrium, and finally to far-from-equilibrium systems. Classical fluctuation theorems, which capture the…
We study diffusion processes in anomalous spacetimes regarded as models of quantum geometry. Several types of diffusion equation and their solutions are presented and the associated stochastic processes are identified. These results are…
Experiments with trapped atomic gases have opened novel possibilities for studying the evolution of nonequilibrium finite quantum systems, which revived the necessity of reconsidering and developing the theory of such processes. This review…
In this paper, we study high-dimensional nonlinear quantum harmonic oscillator equation. We show the equation admits many time quasi-periodic solutions by establishing an abstract infinite dimensional KAM theorem with multiple normal…
Non-Hermitian Hamiltonians possessing a discrete real spectrum motivated a remarkable research activity in quantum physics and new insights have emerged. In this paper we formulate concepts of statistical thermodynamics for systems…
A unified conceptual foundation of classical and quantum physics is given, free of undefined terms. Ensembles are defined by extending the `probability via expectation' approach of Whittle to noncommuting quantities. This approach carries…
We derive general evolution equations describing the ensemble-average quantum dynamics generated by disordered Hamiltonians. The disorder average affects the coherence of the evolution and can be accounted for by suitably tailored effective…
We consider how to characterize the dynamics of a quantum system from a restricted set of initial states and measurements using Bayesian analysis. Previous work has shown that Hamiltonian systems can be well estimated from analysis of noisy…
The representation of a Schrodinger equations as a classic Hamiltonian system allows to construct a unified perturbation theory both in classic, and in a quantum mechanics grounded on the theory of canonical transformations, and also to…
In this paper we aim at characterizing the effect of stochastic fluctuations on the distribution of the energy exchanged by a quantum system with an external environment under sequences of quantum measurements performed at random times.…
Beyond H\"{o}lder's type, this paper mainly concerns the persistence and remaining regularity of an individual frequency-preserving KAM torus in a finitely differentiable Hamiltonian system, even allows the non-integrable part being…
Classical dynamics is formulated as a Hamiltonian flow on phase space, while quantum mechanics is formulated as a unitary dynamics in Hilbert space. These different formulations have made it difficult to directly compare quantum and…
This paper presents a useful compact formula for deriving an effective Hamiltonian describing the time-averaged dynamics of detuned quantum systems. The formalism also works for ensemble-averaged dynamics of stochastic systems. To…