TY - JOUR

T1 - Nonlinear schrödinger equations and the separation property

AU - Goldin, Gerald A.

AU - Svetlichny, George

N1 - Funding Information: The authors are grateful to Professor Wolmer Vasconcelos for helpful discussions. G.S. also thanks the Department of Mathematics, Rutgers University (New Brunswick), where this work was done, for hospitality during his 1992–93 stay; and acknowledges financial support from the Secretaria de Ciência e Tecnologia (SCT) and the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), both agencies of the Brazilian government.

PY - 1995/1

Y1 - 1995/1

N2 - We investigate hierarchies of nonlinear Schrödinger equations for multiparticle systems satisfying the separation property, i.e., where product wave functions evolve by the separate evolution of each factor. Such a hierarchy defines a nonlinear derivation on tensor products of the single-particle wave-function space, and satisfies a certain homogeneity property characterized by two new universal physical constants. A canonical construction of hierarchies is derived that allows the introduction, at any particular “threshold” number of particles, of truly new physical effects absent in systems having fewer particles. In particular, if single quantum particles satisfy the usual (linear) Schrödinger equation, a system of two particles can evolve by means of a fairly simple nonlinear Schrödinger equation without violating the separation property. Examples of Galileian-invariant hierarchies are given.

AB - We investigate hierarchies of nonlinear Schrödinger equations for multiparticle systems satisfying the separation property, i.e., where product wave functions evolve by the separate evolution of each factor. Such a hierarchy defines a nonlinear derivation on tensor products of the single-particle wave-function space, and satisfies a certain homogeneity property characterized by two new universal physical constants. A canonical construction of hierarchies is derived that allows the introduction, at any particular “threshold” number of particles, of truly new physical effects absent in systems having fewer particles. In particular, if single quantum particles satisfy the usual (linear) Schrödinger equation, a system of two particles can evolve by means of a fairly simple nonlinear Schrödinger equation without violating the separation property. Examples of Galileian-invariant hierarchies are given.

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U2 - https://doi.org/10.2991/jnmp.1995.2.2.3

DO - https://doi.org/10.2991/jnmp.1995.2.2.3

M3 - Article

SN - 1402-9251

VL - 2

SP - 120

EP - 132

JO - Journal of Nonlinear Mathematical Physics

JF - Journal of Nonlinear Mathematical Physics

IS - 2

ER -