Related papers: Generalized Number Theoretic Spin Chain-Connection…
Starting from the characterization of the past time evolution of market prices in terms of two fundamental indicators, price velocity and price acceleration, we construct a general classification of the possible patterns characterizing the…
In this paper, we introduce an algorithm that provides approximate solutions to semi-linear ordinary differential equations with highly oscillatory solutions, which, after an appropriate change of variables, can be rewritten as…
A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative…
The off-diagonal Bethe ansatz method is generalized to the high spin integrable systems associated with the su(2) algebra by employing the spin-s isotropic Heisenberg chain model with generic integrable boundaries as an example. With the…
In this paper we point out that the generalized statistics of Tsallis-Havrda-Charv\'at can be conveniently used as a conceptual framework for statistical treatment of random chains. In particular, we use the path-integral approach to show…
We study an open quantum spin chain with non-reciprocal dissipation using a theoretical approach known as time-dependent generalized Gibbs ensemble. In the regime of weak dissipation the system is fully characterized by its rapidity…
We suggest a generalization of the Feynman path integral to an integral over random surfaces. The proposed action is proportional to the linear size of the random surfaces and is called gonihedric. The convergence and the properties of the…
We study non-interacting fermionic systems dissipatively driven at their boundaries, focusing in particular on the case of a non-number-conserving Hamiltonian, which for example describes an $XY$ spin chain. We show that despite the lack of…
The spin-statistics connection is obtained for a simple formulation of a classical field theory containing even and odd Grassmann variables. To that end, the construction of irreducible canonical realizations of the rotation group…
We combine the method of exchangeable pairs with Stein's method for functional approximation. As a result, we give a general linearity condition under which an abstract Gaussian approximation theorem for stochastic processes holds. We apply…
A field theory with generalized statistics in one space dimension is introduced. The statistics enters the scene through the coupling of the matter fields to a statistical gauge field, as it happens in the Chern-Simons theory in two…
We investigate the application of the line-graph operator to one-dimensional spin models with periodic boundary conditions. The spins (or interactions) in the original spin structure become the interactions (or spins) in the resulting spin…
We compare the structures and methods in the theory of causal fermion systems with generalized trace dynamics and non-commutative geometry. Although the three theories differ on many aspects, they agree in that the geometric structure to be…
We present a discussion of generalized statistics based on Renyi's, Fisher's and Tsallis's measures of information. The unifying conceptual framework which we employ here is provided by information theory. Important applications of…
The basic mathematical properties of Green's functions used in statistical mechanics as well as the equations defining these functions and the techniques of solving these equations are reviewed. An approach is presented called the…
We consider an $XYZ$ spin chain within the framework of the generalized algebraic Bethe ansatz. We study form factors of local operators corresponding to the singlet states in the limit of free fermions. We obtain explicit representations…
We study the entropy of entanglement of the ground state in a wide family of one-dimensional quantum spin chains whose interaction is of finite range and translation invariant. Such systems can be thought of as generalizations of the XY…
Linear Response theory aims to predict how added forcing alters the statistical properties of an unforced system. These kinds of questions have been studied predominantly for autonomous dynamical systems, yet many systems in the physical,…
The present article is devoted to one class of generalizations of the Salem functions. To construct such functions by systems of functional equations, the generalized shift operator is used.
Here I will review the theoretical results that have been obtained for spin glasses. I will concentrate my attention on the predictions of the mean field approach in three dimensional systems and on its numerical and experimental…