Completely Integrable Equation for the Quantum Correlation Function of Nonlinear Schrödinger Eqaution

نویسنده

  • T. Kojima
چکیده

Correlation functions of exactly solvable models can be described by differential equations [1]. In this paper we show that for non free fermionic case differential equations should be replaced by integro-differential equations. We derive an integro-differential equation, which describes time and temperature dependent correlation function 〈ψ(0, 0)ψ(x, t)〉T of penetrable Bose gas. The integrodifferential equation turns out be the continuum generalization of classical nonlinear Schrödinger equation. PACS : 02.30.Jr; 02.30.Rz; 05.30.Jp; 05.50.+q; 51.30.+i; 65.50.+m

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Well-posedness and standing waves for the fourth-order non-linear Schrödinger-type equation

We consider the initial value problem for the fourth-order non-linear Schrödinger-type equation (4NLS) which describes the motion of an isolated vortex filament. In the first part of this note we review some recent results on the time local well-posedness of (4NLS) and give the alternative proof of those results. In the second part of this note we consider the stability of a standing wave solut...

متن کامل

On the quantum KP hierarchy and its relation to the non-linear Schrödinger equation

We establish a relation between the classical non-linear Schrödinger equation and the KP hierarchy, and we extend this relation to the quantum case by defining a quantum KP hierarchy. We also present evidence that an integrable hierarchy of equations is obtained by quantizing the first Hamiltonian structure of the KdV equation. The connection between infinite-dimensional algebras and integrable...

متن کامل

Solutions structure of integrable families of Riccati equations and their applications to the perturbed nonlinear fractional Schrodinger equation

Some preliminaries about the integrable families of Riccati equations and solutions structure of these equations in several cases are presented in this paper, then by using of definitions for fractional derivative we apply the new extended of tanh method to the perturbed nonlinear fractional Schrodinger equation with the kerr law nonlinearity. Finally by using of this method and solutions of Ri...

متن کامل

Localized Solitons of a (2+1)-dimensional Nonlocal Nonlinear Schrödinger Equation

A new integrable (2+1)-dimensional nonlocal nonlinear Schrödinger equation is proposed. The N-soliton solution is given by Gram type determinant. It is found that the localized N-soliton solution has interesting interaction behavior which shows change of amplitude of localized pulses after collisions .

متن کامل

Quantum Coupled Nonlinear Schrödinger System with Different Masses

Abstract. In this letter, I have considered one-dimensional quantum system with different masses m and M , which does not appear integrable in general. However I have found an exact two-body wave function and due to the extension of the integrable system to more general system, it was concluded that the rapidity or quasi-momentum in the integrable system should be regarded as a modification of ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1996