dorsal/arxiv
View SchemaExact Solutions of a Non-Polynomially Nonlinear Schrodinger Equation
| Authors | R. Parwani, H. S. Tan |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0605123 |
| URL | https://arxiv.org/abs/quant-ph/0605123 |
| DOI | 10.1016/j.physleta.2006.11.002 |
| Journal | Phys.Lett. A363 (2007) 197-201 |
Abstract
A nonlinear generalisation of Schrodinger's equation had previously been obtained using information-theoretic arguments. The nonlinearities in that equation were of a nonpolynomial form, equivalent to the occurence of higher-derivative nonlinear terms at all orders. Here we construct some exact solutions to that equation in 1+1 dimensions. On the half-line, the solutions resemble exponentially damped Bloch waves even though no external periodic potential is included: the periodicity is induced by the nonpolynomiality. The solutions are nonperturbative as they do not reduce to solutions of the linear theory in the limit that the nonlinearity parameter vanishes. An intriguing feature of the solutions is their infinite degeneracy: for a given energy, there exists a very large arbitrariness in the normalisable wavefunctions. We also consider solutions to a q-deformed version of the nonlinear equation and discuss a natural discretisation implied by the nonpolynomiality. Finally, we contrast the properties of our solutions with other solutions of nonlinear Schrodinger equations in the literature and suggest some possible applications of our results in the domains of low-energy and high-energy physics.
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"abstract": "A nonlinear generalisation of Schrodinger\u0027s equation had previously been\nobtained using information-theoretic arguments. The nonlinearities in that\nequation were of a nonpolynomial form, equivalent to the occurence of\nhigher-derivative nonlinear terms at all orders. Here we construct some exact\nsolutions to that equation in 1+1 dimensions. On the half-line, the solutions\nresemble exponentially damped Bloch waves even though no external periodic\npotential is included: the periodicity is induced by the nonpolynomiality. The\nsolutions are nonperturbative as they do not reduce to solutions of the linear\ntheory in the limit that the nonlinearity parameter vanishes. An intriguing\nfeature of the solutions is their infinite degeneracy: for a given energy,\nthere exists a very large arbitrariness in the normalisable wavefunctions. We\nalso consider solutions to a q-deformed version of the nonlinear equation and\ndiscuss a natural discretisation implied by the nonpolynomiality. Finally, we\ncontrast the properties of our solutions with other solutions of nonlinear\nSchrodinger equations in the literature and suggest some possible applications\nof our results in the domains of low-energy and high-energy physics.",
"arxiv_id": "quant-ph/0605123",
"authors": [
"R. Parwani",
"H. S. Tan"
],
"categories": [
"quant-ph",
"hep-th",
"nlin.PS"
],
"doi": "10.1016/j.physleta.2006.11.002",
"journal_ref": "Phys.Lett. A363 (2007) 197-201",
"title": "Exact Solutions of a Non-Polynomially Nonlinear Schrodinger Equation",
"url": "https://arxiv.org/abs/quant-ph/0605123"
},
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