Related papers: Reversible part of a quantum dynamical system
By an \emph{assignment} we mean a mapping from a Choquet simplex $K$ to probability measure-preserving systems, obeying some natural restrictions. We prove that if $\Phi$ is an aperiodic assignment on a Choquet simplex $K$ such that the set…
A generalization of the Gibbs-von Neumann relative entropy is proposed based on the quantum BBGKY [Bogolyubov-Born-Green-Kirkwood-Yvon] hierarchy as the nonequilibrium entropy for an N-body system. By using a generalization of the…
For an ergodic system, the time average of a classical observable coincides with that obtained via the Liouville probability density, a delta-function on the energy shell. Reinterpreting this distribution as a Wigner function, that is, the…
We derive a systematic approach to the thermodynamics of quantum systems based on the underlying symmetry groups. We show that the entropy of a system can be described in terms of group-theoretical quantities that are largely independent of…
Quantum ergodic restriction (QER) is the problem of finding conditions on a hypersurface $H$ so that restrictions $\phi_j |_H$ to $H$ of $\Delta$-eigenfunctions of Riemannian manifolds $(M, g)$ with ergodic geodesic flow are quantum ergodic…
It is offered that $F(R)-$modified gravities can be considered as nonperturbative quantum effects arising from Einstein gravity. It is assumed that nonperturbative quantum effects gives rise to the fact that the connection becomes…
We study the irreversibility \`a la Maxwell from a quantum point of view, involving an arbitrarily large ensemble of independent particles, with a daemonic potential that is capable of inducing asymmetries in the evolution, exhibiting new…
In this paper we develope the main ideas of the quantized version of affinely-rigid (homogeneously deformable) motion. We base our consideration on the usual Schr\"odinger formulation of quantum mechanics in the configuration manifold which…
We evaluate the phase diagram of quantum gravity within a fully diffeomorphism-invariant renormalisation group approach. The construction is based on the geometrical or Vilkovisky-DeWitt effective action. We also resolve the difference…
Given positive integers n and m, we consider dynamical systems in which n copies of a topological space is homeomorphic to m copies of that same space. The universal such system is shown to arise naturally from the study of a C*-algebra we…
This paper is concerned with the ergodic subspaces of the state spaces of isolated quantum systems. We prove a new ergodic theorem for closed quantum systems which shows that the equilibrium state of the system takes the form of a grand…
We develop a novel approach to Quantum Mechanics that we call Curved Quantum Mechanics. We introduce an infinite-dimensional K\"ahler manifold ${\cal M}$, that we call the state manifold, such that the cotangent space $T_z^*{\cal M}$ is a…
Quantum mechanics is potentially advantageous for certain information-processing tasks, but its probabilistic nature and requirement of measurement back action often limit the precision of conventional classical information-processing…
This paper addresses structures of state space in quasiperiodically forced dynamical systems. We develop a theory of ergodic partition of state space in a class of measure-preserving and dissipative flows, which is a natural extension of…
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…
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…
We explore how the quantum geometric properties of the Bloch wave function, characterized by the Hilbert-Schmidt quantum distance, impact magnetic phases in solid-state systems. To this end, we investigate the spin susceptibility within the…
The manifold of pure quantum states is a complex projective space endowed with the unitary-invariant geometry of Fubini and Study. According to the principles of geometric quantum mechanics, the detailed physical characteristics of a given…
We review the construction of a quantum version of the exponential statistical manifold over the set of all faithful normal positive functionals on a von Neumann algebra. The construction is based on the relative entropy approach to state…
An understanding of quantum theory in terms of new, underlying descriptions capable of explaining the existence of non-classical correlations, non-commutativity of measurements and other unique and counter-intuitive phenomena remains still…