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Browsing by Author "Pathak, Rajeev K."
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Item Exactly solvable PT -symmetric models in two dimensions(IOP, 2015-11) Agarwal, Kaustubh S.; Pathak, Rajeev K.; Joglekar, Yogesh N.; Department of Physics, School of ScienceNon-Hermitian, $\mathcal{PT}$ -symmetric Hamiltonians, experimentally realized in optical systems, accurately model the properties of open, bosonic systems with balanced, spatially separated gain and loss. We present a family of exactly solvable, two-dimensional, $\mathcal{PT}$ potentials for a non-relativistic particle confined in a circular geometry. We show that the $\mathcal{PT}$ -symmetry threshold can be tuned by introducing a second gain-loss potential or its Hermitian counterpart. Our results explicitly demonstrate that $\mathcal{PT}$ breaking in two dimensions has a rich phase diagram, with multiple re-entrant $\mathcal{PT}$ -symmetric phases.Item Raising the PT -transition threshold by strong coupling to neutral chains(Wiley, 2018) Agarwal, Kaustubh S.; Pathak, Rajeev K.; Joglekar, Yogesh N.; Physics, School of ScienceThe PT-symmetry-breaking threshold in discrete realizations of systems with balanced gain and loss is determined by the effective coupling between the gain and loss sites. In one-dimensional chains, this threshold is maximum when the two sites are closest to each other or the farthest. We investigate the fate of this threshold in the presence of parallel, strongly coupled, Hermitian (neutral) chains and find that it is increased by a factor proportional to the number of neutral chains. We present numerical results and analytical arguments for this enhancement. We then consider the effects of adding neutral sites to PT-symmetric dimer and trimer configurations and show that the threshold is more than doubled, or tripled by their presence. Our results provide a surprising way to engineer the PT threshold in experimentally accessible samples.