相关论文: Quantized Lax Equations and Their Solutions
This paper studies the structure of Lax pairs associated with integrable lattice systems (where space is a one-dimensional lattice, and time is continuous). It describes a procedure for generating examples of such systems, and emphasizes…
A new non-perturbative method of solution of the nonlinear Heisenberg equations in the finite-dimensional subspace is illustrated. The method, being a counterpart of the traditional Schrodinger picture method, is based on a finite operator…
A four-wave mixing Hamiltonian system on the classical as well as on the quantum level is investigated. In the classical case, if one assumes the frequency resonance condition of the form $\omega_0 -\omega_1 +\omega_2 -\omega_3=0$, this…
We examine certain classical continuum long wave-length limits of prototype integrable quantum spin chains. We define the corresponding construction of classical continuum Lax operators. Our discussion starts with the XXX chain, the…
The main notions of the quantum groups: coproduct, action and coaction, representation and corepresentation are discussed using simplest examples: $GL_q(2)$, $sl_q(2)$, $q$-oscillator algebra ${\cal A}(q)$, and reflection equation algebra.…
An algebraic construction more general and intimately connected with that of Faddeev$^1$, along with its application for generating different classes of quantum integrable models are summarised to complement the recent results of ref. 1 (…
Quantum entanglement is a key resource for quantum technologies, including emerging ground-to-satellite quantum communication. In such a scenario, an important challenge to be overcome is to consider entanglement between two or more quantum…
Motivated by recent work on quantum integrable models without U(1) symmetry, we show that the sl(2) Hirota equation admits a Lax representation with inhomogeneous terms. The compatibility of the auxiliary linear problem leads to a new…
The quantum reality problem is that of finding a mathematically precise definition of a sample space of configurations of beables, events, histories, paths, or other mathematical objects, and a corresponding probability distribution, for…
We express the solutions to quadratic equations with two variables in the ring of integers using EDT0L languages. We use this to show that EDT0L languages can be used to describe the solutions to one-variable equations in the Heisenberg…
We establish Holder continuity of the horizontal gradient of weak solutions to quasi-linear p-Laplacian type non-homogeneous equations in the Heisenberg Group.
A new method is proposed to generate nonlinear integrable systems by starting with existing Lax pair and a new form of Kr\"onecker product. It is observed that such equation can be generated with the help of a Hamiltonian structure.…
We consider a constructive modification of quantum-mechanical formalism. Replacement of a general unitary group by unitary representations of finite groups makes it possible to reproduce quantum formalism without loss of its empirical…
We generalize some classical results for the Schlesinger system of partial differential equations and give the explicit form of its solution, associated with rational matrix functions in general position.
These notes describe some links between the group $\mathrm{SL}_2(\mathbb{R})$, the Heisenberg group and hypercomplex numbers---complex, dual and double numbers. Relations between quantum and classical mechanics are clarified in this…
We study the Lie point symmetries of semilinear Kohn-Laplace equations on the Heisenberg group H^1 and obtain a complete group classification of these equations.
A hierarchy of pairwise commuting Hamiltonians for the quantum periodic Benjamin-Ono equation is constructed by using the Lax matrix. The eigenvectors of these Hamiltonians are Jack symmetric functions of infinitely many variables…
In its most general formulation a quantum kinematical system is described by a Heisenberg group; the "configuration space" in this case corresponds to a maximal isotropic subgroup. We study irreducible models for Heisenberg groups based on…
Finding solutions to systems of linear equations is a common prob\-lem in many areas of science and engineering, with much potential for a speedup on quantum devices. While the Harrow-Hassidim-Lloyd (HHL) quantum algorithm yields up to an…
Quantum mechanics has about a dozen exactly solvable potentials. Normally, the time-independent Schroedinger equation for them is solved by using a generalized series solution for the bound states (using the Froebenius method) and then an…