Related papers: Composition schemes: q-enumerations and phase tran…
The statistics of gaps between quantum energy levels is a hallmark criterion in quantum chaos and quantum integrability studies. The relevant distributions corresponding to exactly integrable vs. fully chaotic systems are universal and…
We present a description of the measurement process based on the parametric representation with environmental coherent states. This representation is specifically tailored for studying quantum systems whose environment needs being…
To elucidate ideal measurements, one must explain how individual events emerge from quantum theory which deals with statistical ensembles, and how different may end up with different final states. This so-called "measurement problem" is…
Competing styles of Statistical Mechanics have been introduced as practical succedaneous to the conventional well established Boltzmann-Gibbs statistical mechanics, when in the use of the latter the researcher is impaired in his/her…
Quantum trajectories are Markov processes modeling the evolution of a quantum system subjected to repeated independent measurements. Inspired by the theory of random products of matrices, it has been shown that these Markov processes admit…
Power-law distributions are widely observed in complex systems, yet establishing their thermodynamic consistency remains a theoretical challenge. In this paper, we present a thermodynamic framework for power-law statistics based on the…
A version of quantum theory is derived from a set of plausible assumptions related to the following general setting: For a given system there is a set of experiments that can be performed, and for each such experiment an ordinary…
In this article the statistical properties of symmetrical random matrices whose elements are drawn from a q-parameterized non-extensive statistics power-law distribution are investigated. In the limit as q->1 the well known Gaussian…
When dealing with certain kind of complex phenomena the theoretician may face some difficulties -- typically a failure to have access to information for properly characterize the system -- for applying the full power of the standard…
We study point processes on the real line whose configurations $X$ are locally finite, have a maximum and evolve through increments which are functions of correlated Gaussian variables. The correlations are intrinsic to the points and…
A scheme for constructing quantum mechanics is given that does not have Hilbert space and linear operators as its basic elements. Instead, a version of algebraic approach is considered. Elements of a noncommutative algebra (observables) and…
We study the spectral statistics for extended yet finite quasi 1-d systems which undergo a transition from periodicity to disorder. In particular we compute the spectral two-point form factor, and the resulting expression depends on the…
The statistics of chiral matrix ensembles with uncorrelated but multivariate Gaussian distributed elements is intuitively expected to be driven by many parameters. Contrary to intuition, however, our theoretical analysis reveals the…
At non-zero temperature classical systems exhibit statistical fluctuations of thermodynamic quantities arising from the variation of the system's initial conditions and its interaction with the environment. The fluctuating work, for…
The Boltzmann-Gibbs probability distribution, seen as a statistical model, belongs to the exponential family. Recently, the latter concept has been generalized. The q-exponential family has been shown to be relevant for the statistical…
There are considered some corollaries of certain hypotheses on the observation process of microphenomena. We show that an enlargement of the phase space and of its motion group and an account for the diffusion motions of microsystems in the…
Quantum circuits consisting of random unitary gates and subject to local measurements have been shown to undergo a phase transition, tuned by the rate of measurement, from a state with volume-law entanglement to an area-law state. From a…
We introduce the theoretical framework we use to study the bewildering variety of phases in condensed--matter physics. We emphasize the importance of the breaking of symmetries, and develop the idea of an order parameter through several…
The description of a measuring process, such as that which occurs when a quantum point contact (QPC) detector is influenced by a nearby external electron which can take up two possible positions, provides a interesting application of the…
This essay advocates the view that any problem that has a meaningful empirical content, can be formulated in constructive, more definitely, finite terms. We consider combinatorial models of dynamical systems and approaches to statistical…