Related papers: Piecewise Deterministic Quantum Dynamics and Quant…
We numerically analyse quantum survival probability fluctuations in an open, classically chaotic system. In a quasi-classical regime, and in the presence of classical mixed phase space, such fluctuations are believed to exhibit a fractal…
A quantum system subjected to a strong continuous monitoring undergoes quantum jumps. This very well known fact hides a neglected subtlety: sharp scale-invariant fluctuations invariably decorate the jump process even in the limit where the…
We consider a class of stochastic dynamical systems, called piecewise deterministic Markov processes, with states $(x, \s)\in \O\times \G$, $\O$ being a region in $\bbR^d$ or the $d$--dimensional torus, $\G$ being a finite set. The…
The quantum ferromagnetic transition at zero temperature in disordered itinerant electron systems is considered. Nonmagnetic quenched disorder leads to diffusive electron dynamics that induces an effective long-range interaction between the…
One of approaches to quantum gravity is different models of a discrete pregeometry. An example of a discrete pregeometry on a microscopic scale is introduced. This is the particular case of a causal set. The causal set is a locally finite…
Fractals define a new and interesting realm for a discussion of basic phenomena in quantum field theory and statistical mechanics. This interest results from specific properties of fractals, e.g., their dilatation symmetry and the…
In closed quantum systems, a dynamical phase transition is identified by nonanalytic behaviors of the return probability as a function of time. In this work, we study the nonunitary dynamics following quenches across exceptional points in a…
The time-dependent variational principle using generalized Gaussian trial functions yields a finite dimensional approximation to the full quantum dynamics and is used in many disciplines. It is shown how these 'semi-quantum' dynamics may be…
Quantum theory is extremely successful in explaining most physical phenomena, and is not contradicted by any experiment. Yet, the theory has many puzzling features : the occurrence of probabilities, the unclear distinction between the…
Two-dimensional arrays of periodically driven qubits can host inherently dynamical topological phases with anomalous chiral edge dynamics. These chiral Floquet phases are formally characterized by a dynamical topological invariant, the…
We define a modification of LQG in which graphs are required to consist in piecewise linear edges, which we call piecewise linear LQG (plLQG). At the diffeomorphism invariant level, we prove that plLQG is equivalent to standard LQG, as long…
If a point particle moves chaotically through a periodic array of scatterers the associated transport coefficients are typically irregular functions under variation of control parameters. For a piecewise linear two-parameter map we analyze…
To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…
The dynamical behavior for a quantum Brownian particle is investigated under a random potential of the fractional iterative map on a one-dimensional lattice. For our case, the quantum expectation values can be obtained numerically from the…
In this paper we focus our attention on a particle that follows a unidirectional quantum walk, an alternative version of the nowadays widespread discrete-time quantum walk on a line. Here the walker at each time step can either remain in…
The multichannel quantum defect theory (MQDT) can be reinterpreted as a quantum Poincare map in representation of angular momentum. This has two important implications: we have a paradigm of a true quantum Poincare map without…
Canonical variables for the Poisson algebra of quantum moments are introduced here, expressing semiclassical quantum mechanics as a canonical dynamical system that extends the classical phase space. New realizations for up to fourth order…
We propose the assumption of quantum mechanics on a discrete space and time, which implies the modification of mathematical expressions for some postulates of quantum mechanics. In particular we have a Hilbert space where the vectors are…
This letter extends previous findings on the modified Schr\"odinger evolution inspired by quantum gravity phenomenology. By establishing a connection between this approach and fractional quantum mechanics, we provide insights into a…
We study a formal extension of the Dirac equation in the framework of a non-commutative two-sheeted space-time. It is shown that this approach naturally extends the classical Dirac theory by doubling the number of fermionic states, which…