相关论文: Integrable systems as quantum mechanics

In this paper, I try once again to cause some good-natured trouble. The issue remains, when will we ever stop burdening the taxpayer with conferences devoted to the quantum foundations? The suspicion is expressed that no end will be in…

The quantum mechanics of one degree of freedom exhibiting the exact conformal SL(2,R) symmetry is presented. The starting point is the classification of the unitary irreducible representations of the SL(2,R) group (or, to some extent, its…

Mathematical core of quantum mechanics is the theory of unitary representations of symmetries of physical systems. We argue that quantum behavior is a natural result of extraction of "observable" information about systems containing…

In the paper is considered stairway-like design of quantum computer, i.e., array of double quantum dots or wells. The model is quite general to include wide variety of physical systems from coupled quantum dots in experiments with solid…

The development of quantum information theory has renewed interest in the idea that the state vector does not represent the state of a quantum system, but rather the knowledge or information that we may have on the system. I argue that this…

We review the proof of a conjecture concerning the reality of the spectra of certain PT-symmetric quantum mechanical systems, obtained via a connection between the theories of ordinary differential equations and integrable models. Spectral…

In this article we argue that in quantum mechanics, and in opposition to classical physics, it is impossible to say that an isolated quantum system "owns" a physical property. Some properties of the system, its mass for example, belong to…

Linear quantum mechanics can be regarded as a particular example of a nonlinear Nambu-type theory. Some elements of this approach are presented.

A "dispersive quantum system" is a quantum system which is both isolated and non-time reversal invariant. This article presents precise definitions for those concepts and also a characterization of dispersive quantum systems within the…

This is an expository article for Elsevier's Encyclopedia of Mathematical Physics on the subject in the title. Comments/corrections welcome.

The dynamical systems of identical particles admitting quadratic integrals of motion are classified. The relevant integrals are explicitly constructed and their relation to separation of variables in H-J equation is clarified.

This is the second of a series of popular lectures on quantum chromodynamics. The first (introductory) lecture can be found here: https://scfh.ru/blogs/O_fizike_i_fizikah/polet-nad-kvantovoy-khromodinamikoy/ The lecture deals with the one…

The group of automorphisms of the geometry of an integrable system is considered. The geometrical structure used to obtain it is provided by a normal form representation of integrable systems that do not depend on any additional geometrical…

A pedagogical introduction is given to the quantum mechanics of closed systems, most generally the universe as a whole. Quantum mechanics aims at predicting the probabilities of alternative coarse-grained time histories of a closed system.…

A continuously measured quantum system may be described by restricted path integrals (RPI) or equivalently by non-Hermitian Hamiltonians. The measured system is then considered as an open system, the influence of the environment being taken…

In this paper we suggest to anticipate the introduction of concepts such as quantum state and the operators connected to their transformations well in advance of what is usually done.

We review very briefly the main mathematical structures and results in some important areas of Quantum Mechanics involving PDEs and formulate open problems.

Finite-dimensional Quantum Mechanics can be geometrically formulated as a proper classical-like Hamiltonian theory in a projective Hilbert space. The description of composite quantum systems within the geometric Hamiltonian framework is…

This article reviews the history of digital computation, and investigates just how far the concept of computation can be taken. In particular, I address the question of whether the universe itself is in fact a giant computer, and if so,…

This paper is devoted to the system of coupled KdV-like equations. It is shown that this apparently non-integrable system possesses an integrable reduction which is closely related to the Volterra chain. This fact is used to construct the…