Universality in an Information-theoretic Motivated Nonlinear Schrodinger Equation

Simple item page
dc.creatorParwani, R.
dc.creatorTabia, G.
dc.date2006-07-31
dc.date2007-05-24
dc.date.accessioned2026-07-07T10:26:39Z
dc.date.available2026-07-07T10:26:39Z
dc.descriptionUsing perturbative methods, we analyse a nonlinear generalisation of Schrodinger's equation that had previously been obtained through information-theoretic arguments. We obtain analytical expressions for the leading correction, in terms of the nonlinearity scale, to the energy eigenvalues of the linear Schrodinger equation in the presence of an external potential and observe some generic features. In one space dimension these are: (i) For nodeless ground states, the energy shifts are subleading in the nonlinearity parameter compared to the shifts for the excited states, (ii) the shifts for the excited states are due predominantly to contribution from the nodes of the unperturbed wavefunctions and (iii) the energy shifts for excited states are positive for small values of a regulating parameter and negative at large values, vanishing at a universal critical value that is not manifest in the equation. Some of these features hold true for higher dimensional problems. We also study two exactly solved nonlinear Schrodinger equations so as to contrast our observations. Finally, we comment on the possible significance of our results if the nonlinearity is physically realised.
dc.descriptionFinal Journal Version; 23 pages inclusive of 3 figures
dc.identifierhttps://arxiv.org/abs/quant-ph/0607222
dc.identifierhttp://arxiv.org/abs/quant-ph/0607222
dc.identifierJ.Phys.A40:5621-5636,2007
dc.identifierdoi:10.1088/1751-8113/40/21/012
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/176952
dc.subjectQuantum Physics
dc.subjectHigh Energy Physics - Theory
dc.subjectPattern Formation and Solitons
dc.titleUniversality in an Information-theoretic Motivated Nonlinear Schrodinger Equation
dc.typetext

Files

Collections

arXiv