NDLI: $\mathcal{PT}$ -symmetric rational Calogero model with balanced loss and gain

Content Provider	Springer Nature Link
Author	Sinha, Debdeep Ghosh, Pijush K.
Copyright Year	2017
Abstract	A two-body rational Calogero model with balanced loss and gain is investigated. The system yields a Hamiltonian which is symmetric under the combined operation of parity ( $\mathcal{P}$ ) and time reversal ( $\mathcal{T}$ ) symmetry. It is shown that the system is integrable and exact, stable classical solutions are obtained for particular ranges of the parameters. The corresponding quantum system admits bound state solutions for the exactly same ranges of the parameters for which the classical solutions are stable. The eigenspectrum of the system is presented with a discussion on the normalization of the wave functions in proper Stokes wedges. Finally, the Calogero model with balanced loss and gain is studied classically, when the pair-wise harmonic interaction term is replaced by a common confining harmonic potential. The system admits stable solutions for particular ranges of the parameters. However, the integrability and/or exact solvability of the system is obscure due to the presence of the loss and gain terms. The perturbative solutions are obtained and are compared with the numerical results.
Starting Page	1
Ending Page	9
Page Count	9
File Format	PDF
Journal	The European Physical Journal Plus
Volume Number	132
Issue Number	11
e-ISSN	21905444
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2017-11-07
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Applied and Technical Physics Theoretical, Mathematical and Computational Physics Complex Systems Condensed Matter Physics Atomic, Molecular, Optical and Plasma Physics
Content Type	Text
Resource Type	Article

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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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