A generalized nonlinear Schrodinger equation: Classical field-theoretic approach

作者：Nobre F D^*; Rego Monteiro M A; Tsallis C

来源：EPL, 2012, 97(4): 41001.

DOI：10.1209/0295-5075/97/41001

An exact classical field theory, for a recently proposed nonlinear generalization of the Schrodinger equation, is presented. In this generalization, a nonlinearity depending on an index q appears in the kinetic term, such that the free-particle linear Schrodinger equation is recovered in the limit q -> 1. It is shown that besides the usual Psi((x) over right arrow, t), a new field Phi((x) over right arrow, t) must be introduced, which becomes Psi*((x) over right arrow, t) only when q -> 1. In analogy to the linear case, rho((x) over right arrow, t) = 1/2V[Psi((x) over right arrow, t) Phi((x) over right arrow, t)+ Psi*((x) over right arrow, t) Phi*((x) over right arrow, t)] is interpreted as the probability density for finding the particle at time t, in a given position (x) over right arrow inside an arbitrary finite volume V, for any q. The possible physical consequences are discussed, and, in particular, the important property that the fields Psi((x) over right arrow, t) and Phi((x) over right arrow, t) do not interact with light.

• 出版日期2012-2