Tag P. Roy

Entries 4 Total

Localized exact solutions of \(\mathcal{PT}\) symmetric nonlinear Schrödinger equation with space and time modulated nonlinearities

Aug 1, ’13 1:10 AM

L. E. Arroyo Meza, M. B. Hott, A. de Souza Dutra, P. Roy

Using canonical transformations we obtain localized (in space) exact solutions of the nonlinear Schrodinger equation (NLSE) with space and time modulated nonlinearity and in the presence of an external potential depending on space and time. In particular we obtain exact solutions of NLSE in the presence of a number of non Hermitian \(\mathcal{PT}\) symmetric external potentials.

http://arxiv.org/abs/1307.7591

Pattern Formation and Solitons (nlin.PS); Mathematical Physics (math-ph)

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Pseudo Hermitian Generalized Dirac Oscillators

Jan 11, ’13 7:57 AM

D. Dutta, O. Panella, P. Roy

We study generalized Dirac oscillators with complex interactions in \((1+1)\) dimensions. It is shown that for the choice of interactions considered here, the Dirac Hamiltonians are \(\eta\) pseudo Hermitian with respect to certain metric operators \(\eta\). Exact solutions of the generalized Dirac Oscillator for some choices of the interactions have also been obtained. It is also shown that generalized Dirac oscillators can be identified with Anti Jaynes Cummings type model and by spin flip it can also be identified with Jaynes Cummings type model.

http://arxiv.org/abs/1301.2035
Mathematical Physics (math-ph); High Energy Physics – Theory (hep-th); Quantum Physics (quant-ph)

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Pseudo Hermitian formulation of Black-Scholes equation

Dec 18, ’11 6:58 PM

T. K. Jana, P. Roy

We show that the non Hermitian Black-Scholes Hamiltonian and its various generalizations are eta-pseudo Hermitian. The metric operator eta is explicitly constructed for this class of Hamitonians. It is also shown that the e?ective Black-Scholes Hamiltonian and its partner form a pseudo supersymmetric system.

http://arxiv.org/abs/1112.3217
General Finance (q-fin.GN)

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Study of classical mechanical systems with complex potentials

Jan 7, ’11 11:52 PM

A. Sinha, D. Dutta, P. Roy

We apply the factorization technique developed by Kuru and Negro [Ann. Phys. 323 (2008) 413] to study complex classical systems. As an illustration we apply the technique to study the classical analogue of the exactly solvable PT symmetric Scarf II model, which exhibits the interesting phenomenon of spontaneous breakdown of PT symmetry at some critical point. As the parameters are tuned such that energy switches from real to complex conjugate pairs, the corresponding classical trajectories display a distinct characteristic feature – the closed orbits become open ones.

http://arxiv.org/abs/1101.0909
Quantum Physics (quant-ph)
Physics Letters A : vol. 375 (2011) p 452-457

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