Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Contemporary Physics (Armenian Academy of Sciences)

Quantum theory of nonlinear processes

T.K. Melik-Barkhudarov

Published Feb 1, 2007• 0 citations
Publisher

Abstract

Principles of development of the quantum theory of nonlinear processes on the basis of Lagrangian formulation are discussed. It is shown that in the framework of this formulation it is possible to preserve succession from the classical theory and, in particular, use these methods for studies of quantum systems. The quantum dispersion of a nonlinear oscillator excited by an external source and of a parametric generator is calculated. Its role is established in the solution of the problem of stability of oscillations.

DOI
10.3103/s1068337207020014

Related papers

The operator method of the approximate description of the quantum and classical systems

И. Д. Феранчук, L I Komarov

Systematic theory of the operator method (OM) of the approximate solution of the Schrodinger equation is considered. The eigenfunctions and eigenvalues for various one- and many-dimensional systems are calculated and the arguments of the convergence of the OM perturbation series are discussed. It is also shown that OM permits one to develop the absolute convergent approximation in the theory of nonlinear oscillations of the classical systems.

Journal of Physics A Mathematical and General•Nov 11, 1984•30 citations

Variation Principle of Linear and Nonlinear Irreversible Processes

Masakazu Ichiyanagi

A method is proposed for investigating nonequilibrium processes in an arbitrary system under an action of external perturbations. We formulate a new quantum mechanical variation principle, which is valid beyond linear irreversible processes. The definition of our variation functional is made on the basis of our recognition of the importance of a change in the internal energy of the system. In this article, we go beyond the theory of Nakano by developing our new variation principle in the framework of the closed-time-path method by Schwinger. The relationship of the thermodynamical stability criterion to the exact solution of transport problems is discussed.

Progress of Theoretical Physics•Jul 1, 1986•5 citations

Quantum Mechanics of a Nonlinear System

Minoru Omote, Haruo Sato

A procedure is given for constructing a Hamiltonian quantum theory for a system with a nonlinear (classical) Lagrangian. It is shown that the resulting formalism retains all the symmetry properties prossessed by the original Lagrangian.

Progress of Theoretical Physics•Apr 1, 1972•43 citations

Tunneling time and superposition principle

Nikolay Leonidovich Chuprikov

We show that scattering a quantum particle on a one-dimensional potential barrier as well as scattering the electromagnetic wave on a quasi-one-dimensional layered structure (both represent scattering problems with one 'source' and two 'sinks') violate the superposition principle; the role of nonlinear elements is played here by the potential barrier and the layered structure, splitting the incident (probability and electromagnetic) wave into two parts (transmitted and reflected). This explains why all attempts to solve the tunneling time problem within the framework of the standard (linear) models of these processes, both in quantum mechanics and in classical electrodynamics, have been unsuccessful. We revise the traditional formulation of the superposition principle, present a new (nonlinear) wave model, by the example of the quantum-mechanical scattering process, and show that concepts of the tunneling time developed on its basis are free from the Hartman paradox.

arXiv:1705.00897•May 2, 2017•0 citations

The Quantum Theory of Nonlinear Optics

P. D. Drummond, Mark S. Hillery

Playing a prominent role in communications, quantum science and laser physics, quantum nonlinear optics is an increasingly important field. This book presents a self-contained treatment of field quantization and covers topics such as the canonical formalism for fields, phase-space representations and the encompassing problem of quantization of electrodynamics in linear and nonlinear media. Starting with a summary of classical nonlinear optics, it then explains in detail the calculation techniques for quantum nonlinear optical systems and their applications, quantum and classical noise sources in optical fibers and applications of nonlinear optics to quantum information science. Supplemented by end-of-chapter exercises and detailed examples of calculation techniques in different systems, this book is a valuable resource for graduate students and researchers in nonlinear optics, condensed matter physics, quantum information and atomic physics. A solid foundation in quantum mechanics and classical electrodynamics is assumed, but no prior knowledge of nonlinear optics is required.

Cambridge University Press eBooks•Mar 27, 2014•162 citations

Measurement description by means of a nonlinear Schrodinger equation

Alexander N. Grigorenko

A new general formulation for nonlinear quantum mechanics is discussed. It is shown that a nonlinear deterministic evolution with random variables can model a measurement as a dynamical process. Phases of state vectors are treated as random variables of the theory.

Journal of Physics A Mathematical and General•Mar 7, 1995•14 citations
Principles of development of the quantum theory of nonlinear processes on the basis of Lagrangian formulation are discussed. It is shown that in the framework of this formulation it is possible to preserve succession from the classical theory and, in particular, use these methods for studies of quantum systems. The quantum dispersion of a nonlinear oscillator excited by an external source and of a parametric generator is calculated. Its role is established in the solution of the problem of stability of oscillations.
A method is proposed for investigating nonequilibrium processes in an arbitrary system under an action of external perturbations. We formulate a new quantum mechanical variation principle, which is valid beyond linear irreversible processes. The definition of our variation functional is made on the basis of our recognition of the importance of a change in the internal energy of the system. In this article, we go beyond the theory of Nakano by developing our new variation principle in the framework of the closed-time-path method by Schwinger. The relationship of the thermodynamical stability criterion to the exact solution of transport problems is discussed.
We show that scattering a quantum particle on a one-dimensional potential barrier as well as scattering the electromagnetic wave on a quasi-one-dimensional layered structure (both represent scattering problems with one 'source' and two 'sinks') violate the superposition principle; the role of nonlinear elements is played here by the potential barrier and the layered structure, splitting the incident (probability and electromagnetic) wave into two parts (transmitted and reflected). This explains why all attempts to solve the tunneling time problem within the framework of the standard (linear) models of these processes, both in quantum mechanics and in classical electrodynamics, have been unsuccessful. We revise the traditional formulation of the superposition principle, present a new (nonlinear) wave model, by the example of the quantum-mechanical scattering process, and show that concepts of the tunneling time developed on its basis are free from the Hartman paradox.
Playing a prominent role in communications, quantum science and laser physics, quantum nonlinear optics is an increasingly important field. This book presents a self-contained treatment of field quantization and covers topics such as the canonical formalism for fields, phase-space representations and the encompassing problem of quantization of electrodynamics in linear and nonlinear media. Starting with a summary of classical nonlinear optics, it then explains in detail the calculation techniques for quantum nonlinear optical systems and their applications, quantum and classical noise sources in optical fibers and applications of nonlinear optics to quantum information science. Supplemented by end-of-chapter exercises and detailed examples of calculation techniques in different systems, this book is a valuable resource for graduate students and researchers in nonlinear optics, condensed matter physics, quantum information and atomic physics. A solid foundation in quantum mechanics and classical electrodynamics is assumed, but no prior knowledge of nonlinear optics is required.