Related papers: Ergodicity in randomly perturbed quantum systems
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…
Measurement is a fundamental notion in the usual approximate quantum mechanics of measured subsystems. Probabilities are predicted for the outcomes of measurements. State vectors evolve unitarily in between measurements and by reduction of…
We characterize the points that satisfy Birkhoff's ergodic theorem under certain computability conditions in terms of algorithmic randomness. First, we use the method of cutting and stacking to show that if an element x of the Cantor space…
Nonlocality lies at the core of quantum mechanics from both a fundamental and applicative point of view. It is typically revealed by a Bell test, that is by violation of a Bell inequality, whose success depends both on the state of the…
If we prepare an isolated, interacting quantum system in an eigenstate and perturb a local observable at an initial time, its expectation value will relax towards a thermal expectation value, even though the time evolution of the system is…
The variational method is very important in mathematical and theoretical physics because it allows us to describe the natural systems by physical quantities independently from the frame of reference used. A global and statistical approach…
There exist extensive studies on periodic and random perturbations of various continuous maps investigating their dynamics. This paper presents a random piecewise smooth map derived from a simple inductor-less switching circuit. The…
If a macroscopic (random) classical system is put into a random state in phase space, it will of course the most likely have an almost maximal entropy according to second law of thermodynamics. We will show, however, the following theorem:…
Statistical mechanics is one of the most comprehensive theories in physics. From a boiling pot of water to the complex dynamics of quantum many-body systems it provides a successful connection between the microscopic dynamics of atoms and…
The Edwards hypothesis of ergodicity of blocked configurations for gently tapped granular materials is tested for abstract models of spin systems on random graphs and spin chains with kinetic constraints. The tapping dynamics is modeled by…
Recently probabilistic hysteresis in isolated Hamiltonian systems of ultracold atoms has been studied in the limit of large particle numbers, where a semiclassical treatment is adequate. The origin of irreversibility in these sweep…
Quantum dynamics retains a permanent and universal memory of its initial conditions, even in systems whose spectra display fully chaotic, random-matrix behavior. This effect, known as the quantum birthmark, appears as an enhancement of the…
In statistical mechanics, measuring the number of available states and their probabilities, and thus the system's entropy, enables the prediction of the macroscopic properties of a physical system at equilibrium. This predictive capacity…
We present a statistical mechanics description to study the ground state of quantum systems. In this approach, averages for the complete system are calculated over the non-interacting energy levels. Taking different interaction parameter,…
The fundamental assumption of statistical mechanics is that the system is equally likely in any of the accessible microstates. Based on this assumption, the Boltzmann distribution is derived and the full theory of statistical thermodynamics…
Correlations between the parts of a many-body system, and its time dynamics, lie at the heart of sciences, and they can be classical as well as quantum. Quantum correlations are traditionally viewed as constituted out of classical…
We study ergodic properties of partially hyperbolic systems whose central direction is mostly contracting. Earlier work of Bonatti, Viana about existence and finitude of physical measures is extended to the case of local diffeomorphisms.…
It is shown that statistical mechanics is applicable to isolated quantum systems with finite numbers of particles, such as complex atoms, atomic clusters, or quantum dots in solids, where the residual two-body interaction is sufficiently…
Quantum many-body systems can exhibit distinct regimes where dynamics is either ergodic, dynamically exploring an extensive region of available state-space, or non-ergodic, where the dynamics may be restricted. An example is the many-body…
In quantum physics, all measured observables are subject to statistical uncertainties, which arise from the quantum nature as well as the experimental technique. We consider the statistical uncertainty of the so-called sampling method, in…