Related papers: Algebraic Quantization of Integrable Models in Dis…
Generalized Gibbs ensembles have been used as powerful tools to describe the steady state of integrable many-particle quantum systems after a sudden change of the Hamiltonian. Here we demonstrate numerically, that they can be used for a…
Functional relation for commuting quantum transfer matrices of quantum integrable models is identified with classical Hirota's bilinear difference equation. This equation is equivalent to the completely discretized classical 2D Toda lattice…
A rich variety of non-equilibrium dynamical phenomena and processes unambiguously calls for the development of general numerical techniques to probe and estimate a complex interplay between spatial and temporal degrees of freedom in…
This paper summarizes a research program that has been underway for a decade. The objective is to find a fast and accurate scheme for solving quantum problems which does not involve a Monte Carlo algorithm. We use an alternative strategy…
We introduce two new exactly solvable (stochastic) interacting particle systems which are discrete time versions of q-TASEP. We call these geometric and Bernoulli discrete time q-TASEP. We obtain concise formulas for expectations of a large…
We show that the classical mechanics of an algebraic model are implied by its quantizations. An algebraic model is defined, and the corresponding classical and quantum realizations are given in terms of a spectrum generating algebra.…
In this article we describe applications of the numerical method of discrete differential forms in computational GR. In particular we consider the initial value problem for vacuum space-times that admit plane gravitational waves. As…
Based on the well-established theory of discrete conjugate nets in discrete differential geometry, we propose and examine discrete analogues of important objects and notions in the theory of semi-Hamiltonian systems of hydrodynamic type. In…
The quantum-classical Liouville equation describes the dynamics of a quantum subsystem coupled to a classical environment. It has been simulated using various methods, notably, surface-hopping schemes. A representation of this equation in…
The homogeneous cosmological models with a Liouville scalar field are investigated in classical and quantum context of Wheeler-DeWitt geometrodynamics. In the quantum case of quintessence field with potential unbounded from below and…
For a noncommutative configuration space whose coordinate algebra is the universal enveloping algebra of a finite dimensional Lie algebra, it is known how to introduce an extension playing the role of the corresponding noncommutative phase…
We discuss umbral calculus as a method of systematically discretizing linear differential equations while preserving their point symmetries as well as generalized symmetries. The method is then applied to the Schr\"{o}dinger equation in…
Characterizing nonequilibrium dynamics in quantum many-body systems is a challenging frontier of physics. In this Letter, we systematically construct solvable nonintegrable quantum circuits that exhibit exact hidden Markovian subsystem…
In loop quantum cosmology, a difference equation for the wave function describes the evolution of a universe model. This is different from the differential equations that arise in Wheeler-DeWitt quantizations, and some aspects of general…
Motivated by the theory of Painlev\'e equations and associated hierarchies, we study non-autonomous Hamiltonian systems that are Frobenius integrable. We establish sufficient conditions under which a given finite-dimensional Lie algebra of…
In the spirit of Arthur's trace formula, we establish a general trace formula for symmetric spaces associated with the variety of involutions of a finite $D$-module where $D$ is a division algebra central over a number field $F$. Such a…
In this paper, we classify all the variational discrete-time systems in quasi-standard form in $N$ degrees of freedom admitting coalgebra symmetry with respect to the generic realisation of the Lie-Poisson algebra…
Differential flatness serves as a powerful tool for controlling continuous time nonlinear systems in problems such as motion planning and trajectory tracking. A similar notion, called difference flatness, exists for discrete-time systems.…
Two non-standard quantum deformations of the (1+1) Schr\"odinger algebra are identified with the symmetry algebras of either a space or time uniform lattice discretization of the Schr\"odinger equation. For both cases, the deformation…
A method of classification of integrable equations on quad-graphs is discussed based on algebraic ideas. We assign a Lie ring to the equation and study the function describing the dimensions of linear spaces spanned by multiple commutators…