ScholarBank@NUShttps://scholarbank.nus.edu.sgThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Sun, 05 Dec 2021 11:50:57 GMT2021-12-05T11:50:57Z50261- Information-theoretic corrections to black hole area quantisationhttps://scholarbank.nus.edu.sg/handle/10635/96932Title: Information-theoretic corrections to black hole area quantisation
Authors: Parwani, R.R.
Abstract: Nonlinear corrections are proposed to the discrete equispaced area spectrum of quantum black holes obtained previously in some quantisation schemes. It is speculated that such a modified spectrum might be related to the fine structure found using the loop quantum gravity approach. © 2009 World Scientific Publishing Company.
Thu, 30 Jul 2009 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/969322009-07-30T00:00:00Z
- Exact solutions of a nonpolynomially nonlinear Schrödinger equationhttps://scholarbank.nus.edu.sg/handle/10635/96540Title: Exact solutions of a nonpolynomially nonlinear Schrödinger equation
Authors: Parwani, R.; Tan, H.S.
Abstract: A nonlinear generalisation of Schrödinger's equation had previously been obtained using information-theoretic arguments. The nonlinearities in that equation were of a nonpolynomial form, equivalent to the occurrence 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 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 Schrödinger equations in the literature and suggest some possible applications of our results in the domains of low-energy and high-energy physics. © 2006 Elsevier B.V. All rights reserved.
Thu, 26 Apr 2007 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/965402007-04-26T00:00:00Z
- Singularity avoidance in nonlinear quantum cosmologyhttps://scholarbank.nus.edu.sg/handle/10635/98879Title: Singularity avoidance in nonlinear quantum cosmology
Authors: Nguyen, L.-H.; Parwani, R.R.
Abstract: We extend our previous study on the effects of an information-theoretically motivated nonlinear correction to the Wheeler-deWitt equation in the minisuperspace scheme for FRW universes. Firstly we show that even when the geometry is hyperbolic, and matter given by a cosmological constant, the nonUnearity can stiU provide a barrier to screen the initial singidarity, just as in the case for flat universes. Secondly, in the flat case we show that singularity avoidance in the presence of a free massless scalar field is perturbatively possible for a very large class of initially unperturbed quantum states, generalising our previous discussion using Gaussian states. © 2009 American Institute of Physics.
Thu, 01 Jan 2009 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/988792009-01-01T00:00:00Z
- Why is schrödinger's equation linear?https://scholarbank.nus.edu.sg/handle/10635/98953Title: Why is schrödinger's equation linear?
Authors: Parwani, R.R.
Abstract: Information-theoretic arguments are used to obtain a link between the accurate linearity of Schrödinger's equation and Lorentz invariance: A possible violation of the latter at short distances would imply the appearance of nonlinear corrections to quantum theory. Nonlinear corrections can also appear in a Lorentz invariant theory in the form of higher derivative terms that are determined by a length scale, possibly the Planck length. It is suggested that the best place to look for evidence of such quantum nonlinear effects is in neutrino physics and cosmology.
Sat, 01 Jan 2005 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/989532005-01-01T00:00:00Z
- Nonlinear Schrödinger-Pauli equationshttps://scholarbank.nus.edu.sg/handle/10635/98814Title: Nonlinear Schrödinger-Pauli equations
Authors: Ng, W.K.; Parwani, R.R.
Abstract: We obtain novel nonlinear Schrödinger-Pauli equations through a formal non-relativistic limit of appropriately constructed nonlinear Dirac equations. This procedure automatically provides a physical regularisation of potential singularities brought forward by the nonlinear terms and suggests how to regularise previous equations studied in the literature. The enhancement of contributions coming from the regularised singularities suggests that the obtained equations might be useful for future precision tests of quantum nonlinearity.
Sat, 01 Jan 2011 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/988142011-01-01T00:00:00Z
- Common axioms for inferring classical ensemble dynamics and quantum theoryhttps://scholarbank.nus.edu.sg/handle/10635/98656Title: Common axioms for inferring classical ensemble dynamics and quantum theory
Authors: Parwani, R.R.
Abstract: The same set of physically motivated axioms can be used to construct both the classical ensemble Hamilton-Jacobi equation and Schrödingers equation. Crucial roles are played by the assumptions of universality and simplicity (Occam's Razor) which restrict the number and type of of arbitrary constants that appear in the equations of motion. In this approach, non-relativistic quantum theory is seen as the unique single parameter extension of the classical ensemble dynamics. The method is contrasted with other related constructions in the literature and some consequences of relaxing the axioms are also discussed: for example, the appearance of nonlinear higher-derivative corrections possibly related to gravity and spacetime fluctuations. Finally, some open research problems within this approach are highlighted. © 2006 American Institute of Physics.
Wed, 04 Jan 2006 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/986562006-01-04T00:00:00Z
- Complexity: An introductionhttps://scholarbank.nus.edu.sg/handle/10635/96045Title: Complexity: An introduction
Authors: Parwani, R.R.
Abstract: This article summarises an undergraduate level introduction to the field of Complexity Studies" by highlighting interesting complex systems in the biological, physical and social sciences, and the common tools, principles and concepts used for their study.
Thu, 01 Jan 2004 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/960452004-01-01T00:00:00Z
- Asymptotically free Û(1) Kac-Moody gauge fields in 3 + 1 dimensionshttps://scholarbank.nus.edu.sg/handle/10635/95828Title: Asymptotically free Û(1) Kac-Moody gauge fields in 3 + 1 dimensions
Authors: Baaquie, B.E.; Parwani, R.R.
Abstract: Û(1) Kac-Moody gauge fields have the infinite dimensional Û(1) Kac-Moody group as their gauge group. The pure gauge sector, unlike the usual U(1) Maxwell Lagrangian, is nonlinear and nonlocal; the Euclidean theory is defined on a (d+ 1)-dimensional manifold Rd×S1 and, hence, is also asymmetric. We quantize this theory using the background field method and examine its renormalizability at one loop by analyzing all the relevant diagrams. We find that, for a suitable choice of the gauge field propagators, this theory is one-loop renormalizable in 3+1 dimensions. This pure Û(1) Kac-Moody gauge theory in 3+1 dimensions has only one running coupling constant and the theory is asymptotically free. When fermions are added the number of independent couplings increases and a richer structure is obtained. Finally, we note some features of the theory which suggest its possible relevance to the study of anisotropic condensed matter systems, in particular, that of high-temperature superconductors.
Tue, 15 Oct 1996 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/958281996-10-15T00:00:00Z
- Asymptotically free Û(l) Kac-Moody gauge fields in 3 + 1 dimensionshttps://scholarbank.nus.edu.sg/handle/10635/95829Title: Asymptotically free Û(l) Kac-Moody gauge fields in 3 + 1 dimensions
Authors: Baaquie, B.E.; Parwani, R.R.
Abstract: Û( l ) Kac-Moody gauge fields have the infinite dimensional Û( 1 ) Kac-Moody group as their gauge group. The pure gauge sector, unlike the usual U(l) Maxwell Lagrangian, is nonlinear and nonlocal; the Euclidean theory.is defined on a (d+ l)-dimensional manifold Rd×Sl and, hence, is also asymmetric. We quantize this theory using the background field method and examine its renormalizability at one loop by analyzing all the relevant diagrams. We find that, for a suitable choice of the gauge field propagators, this theory is one-loop renormalizable in 3 + 1 dimensions. This pure Û( 1 ) Kac-Moody gauge theory in 3 + 1 dimensions has only one running coupling constant and the theory is asymptotically free. When fermions are added the number of independent couplings increases and a richer structure is obtained. Finally, we note some features of the theory which suseest its possible relevance to the studv of anisotrooic condensed matter svstems, in particular, that of high-temperature superconductors. © 1996 The American Physical Society.
Mon, 01 Jan 1996 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/958291996-01-01T00:00:00Z
- Nonlinear quantum cosmologyhttps://scholarbank.nus.edu.sg/handle/10635/97349Title: Nonlinear quantum cosmology
Authors: Nguyen, L.-H.; Parwani, R.R.
Abstract: We study the effects of an information-theoretically motivated nonlinear correction to the Wheeler-deWitt equation in the minisuperspace scheme for flat, k = 0, Friedmann-Robertson-Walker universes. When the only matter is a cosmological constant, the nonlinearity can provide a barrier that screens the original Big Bang, leading to the quantum creation of a universe through tunneling just as in the k = 1 case. When the matter is instead a free massless scalar field, the nonlinearity can again prevent a contracting classical universe from reaching zero size by creating a bounce. Our studies here are self-consistent to leading order in perturbation theory for the nonlinear effects. © Springer Science+Business Media, LLC 2009.
Tue, 01 Sep 2009 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/973492009-09-01T00:00:00Z
- Information measures for inferring quantum mechanicshttps://scholarbank.nus.edu.sg/handle/10635/96930Title: Information measures for inferring quantum mechanics
Authors: Parwani, R.R.
Abstract: Starting from the Hamilton-Jacobi equation describing a classical ensemble, one may infer a quantum dynamics using the principle of maximum uncertainty. That procedure requires an appropriate measure of uncertainty. Such a measure is constructed here from physically motivated constraints. It leads to a unique single parameter extension of the classical dynamics that is equivalent to the usual linear quantum mechanics. © 2005 IOP Publishing Ltd.
Fri, 08 Jul 2005 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/969302005-07-08T00:00:00Z
- An information-theoretic link between spacetime symmetries and quantum linearityhttps://scholarbank.nus.edu.sg/handle/10635/95762Title: An information-theoretic link between spacetime symmetries and quantum linearity
Authors: Parwani, R.R.
Abstract: A nonlinear generalisation of Schrodinger's equation is obtained using information-theoretic arguments. The nonlinearities are controlled by an intrinsic length scale and involve derivatives to all orders thus making the equation mildly nonlocal. The nonlinear equation is homogeneous, separable, conserves probability, but is not invariant under spacetime symmetries. Spacetime symmetries are recovered when a dimensionless parameter is tuned to vanish, whereby linearity is simultaneously established and the length scale becomes hidden. It is thus suggested that if, in the search for a more basic foundation for Nature's Laws, an inference principle is given precedence over symmetry requirements, then the symmetries of spacetime and the linearity of quantum theory might both be emergent properties that are intrinsically linked. Supporting arguments are provided for this point of view and some testable phenomenological consequences are highlighted. The generalised Klien-Gordon and Dirac equations are also studied, leading to the suggestion that nonlinear quantum dynamics with intrinsically broken spacetime symmetries might be relevant to understanding the problem of neutrino mass (lessness) and oscillations: Among other observations, this approach hints at the existence of a hidden discrete family symmetry in the Standard Model of particle physics. © 2004 Elsevier Inc. All rights reserved.
Tue, 01 Feb 2005 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/957622005-02-01T00:00:00Z
- Some thoughts on a nonlinear Schrödinger equation motivated by information theoryhttps://scholarbank.nus.edu.sg/handle/10635/98885Title: Some thoughts on a nonlinear Schrödinger equation motivated by information theory
Authors: Parwani, R.R.
Abstract: The arguments leading to a nonlinear generalization of the Schrödinger equation in the context of the maximum uncertainty principle are reviewed. The exact and perturbative properties of that equation depend on a free regulating/interpolating parameter η, which can be fixed using energetics as is shown here. A linear theory with an external potential that reproduces some unusual exact solutions of the nonlinear equation is also discussed, together with possible symmetry enhancements in the nonlinear theory. © 2007 Springer Science+Business Media, Inc.
Sun, 01 Jul 2007 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/988852007-07-01T00:00:00Z
- Information and cosmological physicshttps://scholarbank.nus.edu.sg/handle/10635/98759Title: Information and cosmological physics
Authors: Parwani, R.R.
Abstract: We have reviewed an information-theoretic approach to quantum cosmology, summarizing the key results obtained to date, including a suggestion that an accelerating universe will eventually turn around. © Published under licence by IOP Publishing Ltd.
Wed, 01 Jan 2014 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/987592014-01-01T00:00:00Z
- An approximate expression for the large angle period of a simple pendulumhttps://scholarbank.nus.edu.sg/handle/10635/95758Title: An approximate expression for the large angle period of a simple pendulum
Authors: Parwani, R.R.
Abstract: A heuristic but pedagogical derivation is given of an explicit formula which accurately reproduces the period of a simple pendulum even for large amplitudes. The formula is compared with others in the literature.
Thu, 01 Jan 2004 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/957582004-01-01T00:00:00Z
- Probing quantum nonlinearities through neutrino oscillationshttps://scholarbank.nus.edu.sg/handle/10635/97616Title: Probing quantum nonlinearities through neutrino oscillations
Authors: Ng, W.K.; Parwani, R.R.
Abstract: We investigate potential quantum nonlinear corrections to Dirac's equation through its sub-leading effect on neutrino oscillation probabilities. Working in the plane-wave approximation and in the μ - τ sector, we explore various classes of nonlinearities, with or without an accompanying Lorentz violation. The parameters in our models are first delimited by current experimental data before they are used to estimate corrections to oscillation probabilities. We find that only a small subset of the considered nonlinearities has the potential to be relevant at higher energies and thus possibly detectable in future experiments. A falsifiable prediction of our models is an energy-dependent effective mass-squared, generically involving fractional powers of the energy. © 2010 World Scientific Publishing Company.
Sun, 28 Mar 2010 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/976162010-03-28T00:00:00Z
- The large nonlinearity scale limit of an information-theoretically motivated nonlinear Schrödinger equationhttps://scholarbank.nus.edu.sg/handle/10635/98292Title: The large nonlinearity scale limit of an information-theoretically motivated nonlinear Schrödinger equation
Authors: Nguyen, L.-H.; Tan, H.-S.; Parwani, R.R.
Abstract: A nonlinear Schrodinger equation, that had been obtained within the context of the maximum uncertainty principle, has the form of a difference-differential equation and exhibits some interesting properties. Here we discuss that equation in the regime where the nonlinearity length scale is large compared to the deBroglie wavelength; just as in the perturbative regime, the equation again displays some universality. We also briefly discuss stationary solutions to a naturally induced discretisation of that equation. © 2008 IOP Publishing Ltd.
Tue, 01 Jan 2008 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/982922008-01-01T00:00:00Z
- Constraints and spectra of a deformed quantum mechanicshttps://scholarbank.nus.edu.sg/handle/10635/52843Title: Constraints and spectra of a deformed quantum mechanics
Authors: Ching, C.-L.; Parwani, R.R.; Singh, K.
Abstract: We examine a deformed quantum mechanics in which the commutator between coordinates and momenta is a function of momenta. The Jacobi identity constraint on a two-parameter class of such modified commutation relations (MCR's) shows that they encode an intrinsic maximum momentum; a subclass of which also implies a minimum position uncertainty. Maximum momentum causes the bound state spectrum of the one-dimensional harmonic oscillator to terminate at finite energy, whereby classical characteristics are observed for the studied cases. We then use a semiclassical analysis to discuss general concave potentials in one dimension and isotropic power-law potentials in higher dimensions. Among other conclusions, we find that in a subset of the studied MCR's, the leading order energy shifts of bound states are of opposite sign compared to those obtained using string-theory motivated MCR's, and thus these two cases are more easily distinguishable in potential experiments. © 2012 American Physical Society.
Wed, 31 Oct 2012 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/528432012-10-31T00:00:00Z
- Nonlinear Dirac equationshttps://scholarbank.nus.edu.sg/handle/10635/97341Title: Nonlinear Dirac equations
Authors: Ng, W.K.; Parwani, R.R.
Abstract: We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincaré invariance. We determine the constraints that the nonlinear term must obey and classify the resultant non-polynomial nonlinearities in a double expansion in the degree of nonlinearity and number of derivatives. We give explicit examples of such nonlinear equations, studying their discrete symmetries and other properties. Motivated by some previously suggested applications we then consider nonlinear terms that simultaneously violate Lorentz covariance and again study various explicit examples. We contrast our equations and construction procedure with others in the literature and also show that our equations are not gauge equivalent to the linear Dirac equation. Finally we outline various physical applications for these equations.
Thu, 01 Jan 2009 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/973412009-01-01T00:00:00Z
- A physical axiomatic approach to schrodinger's equationhttps://scholarbank.nus.edu.sg/handle/10635/95667Title: A physical axiomatic approach to schrodinger's equation
Authors: Parwani, R.R.
Abstract: The Schrodinger equation for non-relativistic quantum systems is derived from some classical physics axioms within an ensemble hamiltonian framework. Such an approach enables one to understand the structure of the equation, in particular its linearity, in intuitive terms. Furthermore it allows for a physically motivated and systematic investigation of potential generalisations which are briefly discussed. © 2006 Springer Science+Business Media, Inc.
Sun, 01 Oct 2006 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/956672006-10-01T00:00:00Z
- Universality in an information-theoretic motivated nonlinear Schrodinger equationhttps://scholarbank.nus.edu.sg/handle/10635/98532Title: Universality in an information-theoretic motivated nonlinear Schrodinger equation
Authors: Parwani, R.; Tabia, G.
Abstract: Using perturbative methods, we analyse a nonlinear generalization 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 realized. © 2007 IOP Publishing Ltd.
Fri, 25 May 2007 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/985322007-05-25T00:00:00Z
- Can degenerate bound states occur in one-dimensional quantum mechanics?https://scholarbank.nus.edu.sg/handle/10635/95918Title: Can degenerate bound states occur in one-dimensional quantum mechanics?
Authors: Kar, S.; Parwani, R.R.
Abstract: We point out that bound states, degenerate in energy but differing in parity, may form in one-dimensional quantum systems even if the potential is non-singular in any finite domain. Such potentials are necessarily unbounded from below at infinity and occur in several different contexts, such as in the study of localised states in brane-world scenarios. We describe how to construct large classes of such potentials and give explicit analytic expressions for the degenerate bound states. Some of these bound states occur above the potential maximum while some are below. Various unusual features of the bound states are described and after highlighting those that are ansatz independent, we suggest that it might be possible to observe such parity-paired degenerate bound states in specific mesoscopic systems. © Europhysics Letters Association.
Thu, 01 Nov 2007 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/959182007-11-01T00:00:00Z
- Splitting of degenerate states in one-dimensional quantum mechanicshttps://scholarbank.nus.edu.sg/handle/10635/98001Title: Splitting of degenerate states in one-dimensional quantum mechanics
Authors: Dutt, A.; Nath, T.; Kar, S.; Parwani, R.
Abstract: A classic "no-go" theorem in one-dimensional quantum mechanics can be evaded when the potentials are unbounded below, thus allowing for novel parity-paired degenerate energy bound states. We numerically determine the spectrum of one such potential and study the parametric variation of the transition wavelength between a bound state lying inside the valley of the potential and another, von Neumann-Wigner-like state, appearing above the potential maximum. We then construct a modified potential which is bounded below except when a parameter is tuned to vanish. We show how the spacing between certain energy levels gradually decreases as we tune the parameter to approach the value for which unboundedness arises, thus quantitatively linking the closeness of degeneracy to the steepness of the potential. Our results are generic to a large class of such potentials. Apart from their conceptual interest, such potentials might be realisable in mesoscopic systems thus allowing for the experimental study of the novel states. The numerical spectrum in this study is determined using the asymptotic iteration method which we briefly review. © 2012 Società Italiana di Fisica / Springer-Verlag.
Thu, 01 Mar 2012 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/980012012-03-01T00:00:00Z
- Integrable hierarchies and information measureshttps://scholarbank.nus.edu.sg/handle/10635/96944Title: Integrable hierarchies and information measures
Authors: Parwani, R.R.; Pashaev, O.K.
Abstract: In this paper we investigate integrable models from the perspective of information theory, exhibiting various connections. We begin by showing that compressible hydrodynamics for a one-dimensional isentropic fluid, with an appropriately motivated information theoretic extension, is described by a general nonlinear Schrödinger (NLS) equation. Depending on the choice of the enthalpy function, one obtains the cubic NLS or other modified NLS equations that have applications in various fields. Next, by considering the integrable hierarchy associated with the NLS model, we propose higher order information measures which include the Fisher measure as their first member. The lowest members of the hierarchy are shown to be included in the expansion of a regularized Kullback-Leibler measure while, on the other hand, a suitable combination of the NLS hierarchy leads to a Wootters type measure related to a NLS equation with a relativistic dispersion relation. Finally, through our approach, we are led to construct integrable relativistic NLS equations. © 2008 IOP Publishing Ltd.
Tue, 03 Jun 2008 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/969442008-06-03T00:00:00Z
- Information and particle physicshttps://scholarbank.nus.edu.sg/handle/10635/96928Title: Information and particle physics
Authors: Ng, W.K.; Parwani, R.R.
Abstract: Information measures for relativistic quantum spinors are constructed to satisfy various postulated properties such as normalization invariance and positivity. Those measures are then used to motivate generalized Lagrangians meant to probe shorter distance physics within the maximum uncertainty framework. The modified evolution equations that follow are necessarily nonlinear and simultaneously violate Lorentz invariance, supporting previous heuristic arguments linking quantum nonlinearity with Lorentz violation. The nonlinear equations also break discrete symmetries. We discuss the implications of our results for physics in the neutrino sector and cosmology. © 2011 World Scientific Publishing Company.
Mon, 21 Mar 2011 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/969282011-03-21T00:00:00Z
- Properties of some nonlinear Schrödinger equations motivated through information theoryhttps://scholarbank.nus.edu.sg/handle/10635/98845Title: Properties of some nonlinear Schrödinger equations motivated through information theory
Authors: Yuan, L.D.; Parwani, R.R.
Abstract: We update our understanding of nonlinear Schrödinger equations motivated through information theory. In particular we show that a q-deformation of the basic nonlinear equation leads to a perturbative increase in the energy of a system, thus favouring the simplest q - 1 case. Furthermore the energy minimisation criterion is shown to be equivalent, at leading order, to an uncertainty maximisation argument. The special value t] - 1/4 for the interpolation parameter, where leading order energy shifts vanish, implies the preservation of existing supersymmetry in nonlinearised supersymmetric quantum mechanics. Physically, t] might be encoding relativistic effects. © 2009 IOP Publishing Ltd.
Thu, 01 Jan 2009 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/988452009-01-01T00:00:00Z