相关论文: A statistical formalism of Causal Dynamical Triang…
A block spin renormalization group approach is proposed for the dynamical triangulation formulation of quantum gravity in arbitrary dimensions. Renormalization group flow diagrams are presented for the three-dimensional and four-dimensional…
In this paper, we give the definition of the random periodic solutions of random dynamical systems. We prove the existence of such periodic solutions for a $C^1$ perfect cocycle on a cylinder using a random invariant set, the Lyapunov…
We study in a rigorous way the XYZ spin model by Renormalization Group methods.
Various versions of the Dynamical Systems Method (DSM) are proposed for solving linear ill-posed problems with bounded and unbounded operators. Convergence of the proposed methods is proved. Some new results concerning discrepancy principle…
The generalization of Kasteleyn and Fortuin clusters formalism is introduced in XY (or more generally O(n)) models. Clusters geometrical structure may be linked to spin physical properties as correlation functions. To investigate…
We present a new chaotic system of three coupled ordinary differential equations, limited to quadratic nonlinear terms. A wide variety of dynamical regimes are reported. For some parameters, chaotic reversals of the amplitudes are produced…
The Relativistic Dynamical Inversion technique, a novel tool for finding analytical solutions to the Dirac equation, is written in explicitly covariant form. It is then shown how the technique can be used to make a change from Cartesian to…
We extend the 2 dimensional Causal Dynamical Triangulation (CDT) model from the usual model of closed string to the one of open-closed string. The matrix-vector model describing the loop gas model is modified so as to possess the nature of…
We show how, and under which conditions, the equilibrium states of a first-order Ordinary Differential Equation (ODE) system can be described with a deterministic Structural Causal Model (SCM). Our exposition sheds more light on the concept…
We show how, and under which conditions, the equilibrium states of a first-order Ordinary Differential Equation (ODE) system can be described with a deterministic Structural Causal Model (SCM). Our exposition sheds more light on the concept…
Evolution of the z-component of a single spin in the finite cyclic XY spin 1/2 chain is studied. Initially one selected spin is polarized while other spins are completely unpolarized and uncorrelated. Polarization of the selected spin as a…
A method to approximately close the dynamic cavity equations for synchronous reversible dynamics on a locally tree-like topology is presented. The method builds on $(a)$ a graph expansion to eliminate loops from the normalizations of each…
In the former article "Formal mathematical systems including a structural induction principle" we have presented a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the…
Complex Schroedinger equation is transformed to spinor or coupled scalar field equations replacing the imaginary unit $i$ by a matrix $\begin{bmatrix} 0 & 1 \\-1 & 0 \end{bmatrix}$. New perspecive on stochasic approach is developed with…
In this note, we present a new numerical method for solving backward stochastic differential equations. Our method can be viewed as an analogue of the classical finite element method solving deterministic partial differential equations.
We perform a non-perturbative sum over geometries in a (2+1)-dimensional quantum gravity model given in terms of Causal Dynamical Triangulations. Inspired by the concept of triangulations of product type introduced previously, we impose an…
We generalize the number theoretic spin chain, a one-dimensional statistical model based on the Farey fractions, by introducing a new parameter x>=0. This allows us to write recursion relations in the length of the chain. These relations…
Recent results for rotations expressed as polynomials of spin matrices are derived here by elementary differential equation methods. Structural features of the results are then examined in the framework of biorthogonal systems, to obtain an…
We relate a large class of classical spin models, including the inhomogeneous Ising, Potts, and clock models of q-state spins on arbitrary graphs, to problems in quantum physics. More precisely, we show how to express partition functions as…
Classical Bianchi-Lie, Backlund and Darboux transformations are considered. Their generalizations for the dynamical systems are discussed. For the transformation being the generalization of the normal shift the special class of dynamical…