The nonlinear Schrödinger equation in one dimension as a solvable model displaying certain basic features of the many-body problem in the thermodynamical limit

1976 ◽  
Vol 33 (2) ◽  
pp. 467-507 ◽  
Author(s):  
F. Calogero ◽  
A. Degasperis
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Body Problem ◽  
Solvable Model ◽  
Nonlinear Schrodinger Equation ◽  
One Dimension ◽  
Many Body ◽  
Thermodynamical Limit ◽  
The Many ◽  
Basic Features

Wave equation for dissipative systems derived from a quantized many-body problem

1980 ◽  
Vol 58 (7) ◽  
pp. 1019-1025 ◽  
Author(s):  
M. Razavy
Keyword(s):  
Wave Function ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Body Problem ◽  
Body Wave ◽  
Time Dependent ◽  
Dissipative Systems ◽  
Many Body ◽  
Dependent Part ◽  
The Many

A classical many-body problem composed of an infinite number of mass points coupled together by springs is quantized. The masses and the spring constants in this system are chosen in such a way that the motion of each particle is exponentially damped. Because of the quadratic form of the Hamiltonian, the many-body wave function of the system can be written as a product of two terms: a time-dependent phase factor which contains correlations between the classical motions of the particles, and a stationary state solution of the Schrödinger equation. By assuming a Hartree type wave function for the many-particle Schrödinger equation, the contribution of the time-dependent part to the single particle wave function is determined, and it is shown that the time-dependent wave function of each mass point satisfies the nonlinear Schrödinger–Langevin equation. The characteristic decay time of any part of the subsystem, in this model, is related to the stiffness of the springs, and is the same for all particles.

scholarly journals Quantum Lattice-Gas Models for the Many-Body Schrödinger Equation

1997 ◽  
Vol 08 (04) ◽  
pp. 705-716 ◽  
Author(s):  
Bruce M. Boghosian ◽  
Washington Taylor
Keyword(s):  
Schrödinger Equation ◽  
Arbitrary Number ◽  
Schrodinger Equation ◽  
Lattice Gas ◽  
Quantum Computer ◽  
Many Body ◽  
Lattice Gas Models ◽  
Many Body Systems ◽  
The Many ◽  
Classical Computer

A general class of discrete unitary models are described whose behavior in the continuum limit corresponds to a many-body Schrödinger equation. On a quantum computer, these models could be used to simulate quantum many-body systems with an exponential speedup over analogous simulations on classical computers. On a classical computer, these models give an explicitly unitary and local prescription for discretizing the Schrödinger equation. It is shown that models of this type can be constructed for an arbitrary number of particles moving in an arbitrary number of dimensions with an arbitrary interparticle interaction.

scholarly journals Hybrid nature of the abnormal solutions of the Bethe–Salpeter equation in the Wick–Cutkosky model

2021 ◽  
Vol 81 (1) ◽  
Author(s):  
J. Carbonell ◽  
V. A. Karmanov ◽  
H. Sazdjian
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Fock Space ◽  
Form Factors ◽  
Massless Particle ◽  
Ladder Approximation ◽  
Many Body ◽  
Relativistic Limit ◽  
Elastic Form ◽  
The Many

AbstractIn the Wick–Cutkosky model, where two scalar massive constituents interact by means of the exchange of a scalar massless particle, the Bethe–Salpeter equation has solutions of two types, called “normal” and “abnormal”. In the non-relativistic limit, the normal solutions correspond to the usual Coulomb spectrum, whereas the abnormal ones do not have non-relativistic counterparts – they are absent in the Schrödinger equation framework. We have studied, in the formalism of the light-front dynamics, the Fock-space content of the abnormal solutions. It turns out that, in contrast to the normal ones, the abnormal states are dominated by the massless exchange particles (by 90 % or more), what provides a natural explanation of their decoupling from the two-body Schrödinger equation. Assuming that one of the massive constituents is charged, we have calculated the electromagnetic elastic form factors of the normal and abnormal states, as well as the transition form factors. The results on form factors confirm the many-body nature of the abnormal states, as found from the Fock-space analysis. The abnormal solutions have thus properties similar to those of hybrid states, made here essentially of two massive constituents and several or many massless exchange particles. They could also be interpreted as the Abelian scalar analogs of the QCD hybrid states. The question of the validity of the ladder approximation of the model is also examined.

scholarly journals Discrete Spectrum of 2 + 1-Dimensional Nonlinear Schrödinger Equation and Dynamics of Lumps

2016 ◽  
Vol 2016 ◽  
pp. 1-11
Author(s):  
Javier Villarroel ◽  
Julia Prada ◽  
Pilar G. Estévez
Keyword(s):  
Schrödinger Equation ◽  
Discrete Spectrum ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Body Problem ◽  
Dynamical Evolution ◽  
Nonlinear Schrodinger Equation ◽  
Spectral Operator ◽  
Nonlinear Schrödinger ◽  
Integrable Generalization

We consider a natural integrable generalization of nonlinear Schrödinger equation to2+1dimensions. By studying the associated spectral operator we discover a rich discrete spectrum associated with regular rationally decaying solutions, the lumps, which display interesting nontrivial dynamics and scattering. Particular interest is placed in the dynamical evolution of the associated pulses. For all cases under study we find that the relevant dynamics corresponds to acentral configurationof a certainN-body problem.

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