dorsal/arxiv
View SchemaUniversality in an Information-theoretic Motivated Nonlinear Schrodinger Equation
| Authors | R. Parwani, G. Tabia |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0607222 |
| URL | https://arxiv.org/abs/quant-ph/0607222 |
| DOI | 10.1088/1751-8113/40/21/012 |
| Journal | J.Phys.A40:5621-5636,2007 |
Abstract
Using 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.
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"abstract": "Using perturbative methods, we analyse a nonlinear generalisation of\nSchrodinger\u0027s equation that had previously been obtained through\ninformation-theoretic arguments. We obtain analytical expressions for the\nleading correction, in terms of the nonlinearity scale, to the energy\neigenvalues of the linear Schrodinger equation in the presence of an external\npotential and observe some generic features. In one space dimension these are:\n(i) For nodeless ground states, the energy shifts are subleading in the\nnonlinearity parameter compared to the shifts for the excited states, (ii) the\nshifts for the excited states are due predominantly to contribution from the\nnodes of the unperturbed wavefunctions and (iii) the energy shifts for excited\nstates are positive for small values of a regulating parameter and negative at\nlarge values, vanishing at a universal critical value that is not manifest in\nthe equation. Some of these features hold true for higher dimensional problems.\nWe also study two exactly solved nonlinear Schrodinger equations so as to\ncontrast our observations. Finally, we comment on the possible significance of\nour results if the nonlinearity is physically realised.",
"arxiv_id": "quant-ph/0607222",
"authors": [
"R. Parwani",
"G. Tabia"
],
"categories": [
"quant-ph",
"hep-th",
"nlin.PS"
],
"doi": "10.1088/1751-8113/40/21/012",
"journal_ref": "J.Phys.A40:5621-5636,2007",
"title": "Universality in an Information-theoretic Motivated Nonlinear Schrodinger Equation",
"url": "https://arxiv.org/abs/quant-ph/0607222"
},
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