Related papers: Path Integral Solubility of a General Two-Dimensio…
The path integral of the relativistic Coulomb system is solved, and the wave functions are extracted from the resulting amplitude.
The work deals with the existence of solutions of a certain system of quadratic integral equations in H^2(R^d,R^N), d = 2, 3. We demonstrate the existence of a perturbed solution by virtue of a fixed point technique.
In the context of two illustrative examples from supersymmetric quantum mechanics we show that the semi-classical analysis of the path integral requires complexification of the configuration space and action, and the inclusion of complex…
A simplified model of tachyon matter in classical and quantum mechanics is constructed. p-Adic path integral quantization of the model is considered. Recent results in using p-adic analysis, as well as perspectives of an adelic…
Model complexity is a fundamental problem in deep learning. In this paper we conduct a systematic overview of the latest studies on model complexity in deep learning. Model complexity of deep learning can be categorized into expressive…
We present a path - integral approach to treat a 2D model of a quantum bifurcation. The model potential has two equivalent minima separated by one or two saddle points, depending on the value of a continuous parameter. Tunneling is…
The generalized recurrence plot is a modern tool for quantification of complex spatial patterns. Its application spans the analysis of trabecular bone structures, Turing patterns, turbulent spatial plankton patterns, and fractals.…
Abstract inner automorphisms can be used to promote any category into a 2-category, and we study two-dimensional limits and colimits in the resulting 2-categories. Existing connected colimits and limits in the starting category become…
Two formulations of quantum mechanics, inequivalent in the presence of closed timelike curves, are studied in the context of a soluable system. It illustrates how quantum field nonlinearities lead to a breakdown of unitarity, causality, and…
We investigate some general machinery for describing semidualizing modules over generic constructions like ladder determinantal rings with coefficients in a normal domain. We also pose and investigate natural localization questions that…
We investigate global properties of the mappings entering the description of symmetries of integrable spin and vertex models, by exploiting their nature of birational transformations of projective spaces. We give an algorithmic analysis of…
An approximate equation for the effective conductivity sigma_eff of systems with a finite maximal scale of inhomogeneities is deduced. An exact solution of this equation is found and its physical meaning is discussed. A two-phase randomly…
The theory of matrix models is reviewed from the point of view of its relation to integrable hierarchies. Discrete 1-matrix, 2-matrix, ``conformal'' (multicomponent) and Kontsevich models are considered in some detail, together with the…
We review the developments of a recently proposed approach to study integrable theories in any dimension. The basic idea consists in generalizing the zero curvature representation for two-dimensional integrable models to space-times of…
We study orbit-finite systems of linear equations, in the setting of sets with atoms. Our principal contribution is a decision procedure for solvability of such systems. The procedure works for every field (and even commutative ring) under…
We prove that the integral closedness of any ideal of height at least two is compatible with specialization by a generic element. This opens the possibility for proofs using induction on the height of an ideal. Also, with additional…
We briefly review a hamiltonian path integral formalism developed earlier by one of us. An important feature of this formalism is that the path integral quantization in arbitrary co-ordinates is set up making use of only classical…
We define and study a higher-dimensional version of model theoretic internality, and relate it to higher-dimensional definable groupoids in the base theory.
Relativistic generalization of Path Integral Monte-Carlo method has been proposed and some possible applications have been discussed.
In this work we develop an alternative approach for solution of Quantum Trajectories using the Path Integral method. The state-of-the-art technique in the field is to solve a set of non-linear, coupled partial differential equations (PDEs)…