Related papers: A Nonconventional Ergodic Theorem for quantum "dia…
We address the issue of quantifying the non-Gaussian character of a bosonic quantum state and introduce a non-Gaussianity measure based on the Hilbert-Schmidt distance between the state under examination and a reference Gaussian state. We…
It is proved that to every invariant measure of a compact dynamical system one can associate a certain asymptotic pseudo orbit such that any point asymptotically tracing in average that pseudo orbit is generic for the measure. It follows…
We strengthen the maximal ergodic theorem for actions of groups of polynomial growth to a form involving jump quantity, which is the sharpest result among the family of variational or maximal ergodic theorems. As a consequence, we deduce in…
We prove a pointwise convergence result for additive ergodic averages associated with certain multiplicative actions of the Gaussian integers. We derive several applications in dynamics and number theory, including: (i) Wirsing's theorem…
The entropic dynamics (ED) approach to quantum mechanics is ideally suited to address the problem of measurement because it is based on entropic and Bayesian methods of inference that have been designed to process information and data. The…
The paper gives a systematic review of the basic ideas of (non-relativistic) quantum mechanics including all changes that result from previous work of the authors. This shows that the new theory is self-consistent and (in certain sense)…
We study a nonconventional ergodic average for asymptotically abelian weakly mixing C*-dynamical systems, related to a second iteration of Khintchine's recurrence theorem obtained by Bergelson in the measure theoretic case. A noncommutative…
We study the ergodic and non-ergodic behaviors of a clean Jaynes-Cummings-Hubbard chain for different parameters based on the average level spacings and the generalized fractal dimensions of eigenstates by using exact diagonalization. It…
Gibbs measures are the main object of study in equilibrium statistical mechanics, and are used in many other contexts, including dynamical systems and ergodic theory, and spatial statistics. However, in a large number of natural instances…
We investigate the time dynamics of quantum correlations of the anisotropic Heisenberg model in a time-dependent magnetic field, in one-dimensional, ladder, and two-dimensional lattices. We find that quantum correlation measures in the…
We consider stationary stochastic dynamical systems evolving on a compact metric space, by perturbing a deterministic dynamics with a random noise, added according to an arbitrary probabilistic distribution. We prove the maximal and…
The entropic way of formulating Heisenberg's uncertainty principle not only plays a fundamental role in applications of quantum information theory but also is essential for manifesting genuine nonclassical features of quantum systems. In…
We define a nonlinear thermodynamical formalism which translates into dynamical system theory the statistical mechanics of generalized mean-field models, extending investigation of the quadratic case by Leplaideur and Watbled. Under…
This is a review paper concerned with the global consistency of the quantum dynamics of non-commutative systems. Our point of departure is the theory of constrained systems, since it provides a unified description of the classical and…
We identify quantum geometric bounds for observables in non-Hermitian systems. We find unique bounds on non-Hermitian quantum geometric tensors, generalized two-point response correlators, conductivity tensors, and optical weights. We…
Dynamical Lie-algebraic method for the construction of local quantum invariants of motion in non-integrable many-body systems is proposed and applied to a simple but generic toy model, namely an infinite kicked $t-V$ chain of spinless…
The limits of linear electrodynamics are reviewed, and possible directions of nonlinear extension are explored. The central theme is that the qualitative character of the empirical successes of quantum electrodynamics must be used as a…
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…
I prove a theorem on the precise connection of the time and phase space average of the Boltzmann equilibrium showing that the behaviour of a dynamical system with a stationary measure and a dominant equilibrium state is qualitatively…
For classical discrete systems under constant composition, canonical average provides equilibrium configuration from a set of many-body interactions, which typically acts as nonlinear map. The nonlinearity has recently been investigated in…