ScholarBank@NUShttps://scholarbank.nus.edu.sgThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Wed, 20 Nov 2019 23:16:46 GMT2019-11-20T23:16:46Z5051- Generalized coherent states under deformed quantum mechanics with maximum momentumhttps://scholarbank.nus.edu.sg/handle/10635/96704Title: Generalized coherent states under deformed quantum mechanics with maximum momentum
Authors: Ching, C.L.; Ng, W.K.
Abstract: Following the Gazeau-Klauder approach, we construct generalized coherent states (GCS) as the quantum simulator to examine the deformed quantum mechanics, which exhibits an intrinsic maximum momentum. We study deformed harmonic oscillators and compute their probability distribution and entropy of states exactly. Also, a particle in an infinite potential box is studied perturbatively. In particular, unlike usual quantum mechanics, the present deformed case increases the entropy of the Planck scale quantum optical system. Furthermore, for simplicity, we obtain the modified uncertainty principle (MUP) with the perturbative treatment up to leading order. MUP turns out to increase generally. However, for certain values of γ (a parameter of GCS), it is possible that the MUP will vanish and hence will exhibit the classical characteristic. This is interpreted as the manifestation of the intrinsic high-momentum cutoff at lower momentum in a perturbative treatment. Although the GCS saturates the minimal uncertainty in a simultaneous measurement of physical position and momentum operators, thus constituting the squeezed states, complete coherency is impossible in quantum gravitational physics. The Mandel Q number is calculated, and it is shown that the statistics can be Poissonian and super-/sub-Poissonian depending on γ. The equation of motion is studied, and both Ehrenfest's theorem and the correspondence principle are recovered. Fractional revival times are obtained through the autocorrelation, and they indicate that the superposition of a classical-like subwave packet is natural in GCS. We also contrast our results with the string-motivated (Snyder) type of deformed quantum mechanics, which incorporates a minimum position uncertainty rather than a maximum momentum. With the advances of quantum optics technology, it might be possible to realize some of these distinguishing quantum-gravitational features within the domain of future experiments. © 2013 American Physical Society.
Mon, 07 Oct 2013 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/967042013-10-07T00:00:00Z
- 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
- 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
- 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
- Nonlinear dirac equations with applications to neutrino oscillationshttps://scholarbank.nus.edu.sg/handle/10635/97342Title: Nonlinear dirac equations with applications to neutrino oscillations
Authors: Ng, W.K.
Abstract: We first review a method to generate nonlinear Dirac equations. The method demands the nonlinear extensions preserve several physical properties like locality, Hermiticity, Poincaré invariance and separability. The last constraint results in nonlinear extensions of non-polynomial type. A class of nonlinear extensions that simultaneously violate Lorentz invariance is also constructed. We then review, using the classes of nonlinear extensions with or without violation of Lorentz symmetry, the sub-leading modifications to the neutrino oscillation probabilities in the ν1-ντ sector. The parameters in our models are bounded using the current experimental data. These are then used to estimate corrections to the oscillation probabilities and the corresponding energies at which the corrections will be sizeable. Thus one may test quantum nonlinearities in future higher energy experiments. © 2009 World Scientific Publishing Company.
Thu, 30 Jul 2009 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/973422009-07-30T00:00:00Z