Related papers: Generalized bit cumulants for chaotic systems: Num…
For generic Hamiltonian systems we derive predictions for dynamical tunneling from regular to chaotic phase-space regions. In contrast to previous approaches, we account for the resonance-assisted enhancement of regular-to-chaotic tunneling…
In the present Letter we show that the concept of the generalized synchronization regime in discrete maps needs refining in the same way as it has been done for the flow systems [PRE, 84 (2011) 037201]. We have shown that\alkor{, in the…
Graph compositions generalize both integer compositions and partitions of a finite set. We develop formulas, generating functions and recurrence relations for composition counting functions for several families of graphs.
Using the character expansion method, we generalize several well-known integrals over the unitary group to the case where general complex matrices appear in the integrand. These integrals are of interest in the theory of random matrices and…
We analyze a systematic algorithm for the exact computation of the current cumulants in stochastic nonequilibrium systems, recently discussed in the framework of full counting statistics for mesoscopic systems. This method is based on…
The eigenvalues of quantum chaotic systems have been conjectured to follow, in the large energy limit, the statistical distribution of eigenvalues of random ensembles of matrices of size $N\rightarrow\infty$. Here we provide semiclassical…
Motivated by applications in optics and acoustics we develop a dynamical-system approach to describe absorption in chaotic systems. We introduce an operator formalism from which we obtain (i) a general formula for the escape rate $\kappa$…
In many condensed-matter systems, it is very useful to introduce a quasi-particle approach, which is based on some sort of linearization around a suitable background state. In order to be a systematic and controlled approximation, this…
A method is presented to obtain local unitary invariants for multipartite quantum systems consisting of fermions or distinguishable particles. The invariants are organized into infinite families, in particular, the generalization to higher…
In this paper we propose an elementary topological approach which unifies and extends various different results concerning fixed points and periodic points for maps defined on sets homeomorphic to rectangles embedded in euclidean spaces. We…
We review the main ideas and results in the stationary problems of quantum chaos in generic (mixed) systems, whose classical dynamics has regular (invariant tori) and chaotic regions coexisting in the phase space. First we discuss the…
A model of interacting motile chaotic elements is proposed. The chaotic elements are distributed in space and interact with each other through interactions depending on their positions and their internal states. As the value of a governing…
In order to perform numerical studies of long-term stability in nonlinear Hamiltonian systems, one needs a numerical integration algorithm which is symplectic. Further, this algorithm should be fast and accurate. In this paper, we propose…
A new family of polynomials, called cumulant polynomial sequence, and its extensions to the multivariate case is introduced relied on a purely symbolic combinatorial method. The coefficients of these polynomials are cumulants, but depending…
In this paper we consider finite-dimensional constrained Hamiltonian systems of polynomial type. In order to compute the complete set of constraints and separate them into the first and second classes we apply the modern algorithmic methods…
The multiplicative and additive compounds of a matrix play an important role in several fields of mathematics including geometry, multi-linear algebra, combinatorics, and the analysis of nonlinear time-varying dynamical systems. There is a…
We consider a class of generalized binomials emerging in fractional calculus. After establishing some general properties, we focus on a particular yet relevant case, for which we provide several ready-for-use combinatorial identities,…
In this work, we propose a generalization to the classical logistic map. The generalized map preserves most properties of the classical map and has richer dynamics as it contains the fractional order and one more parameter. We propose the…
We derive an exact and explicit Kraus decomposition for the reduced density of a quantum system simultaneously interacting with time-dependent external fields and a chaotic environment of thermodynamic dimension. We test the accuracy of the…
In this paper it is shown that a generalized circulant matrix underlies every weakly Coupled Map Lattice (CML), independently of the form of the coupling term. Therefore, this matrix will appear always perturbative methods are used to get…