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Open Quantum Systems Decoherence Quantum Simulation

Mapping between Hamiltonians with attractive and repulsive potentials on a lattice

arXiv
Authors: Yogesh N. Joglekar

Year

2010

Paper ID

11384

Status

Preprint

Abstract Read

~2 min

Abstract Words

114

Citations

N/A

Abstract

Through a simple and exact analytical derivation, we show that for a particle on a lattice, there is a one-to-one correspondence between the spectra in the presence of an attractive potential hat{V} and its repulsive counterpart -hat{V}. For a Hermitian potential, this result implies that the number of localized states is the same in both, attractive and repulsive, cases although these states occur above (below) the band-continnum for the repulsive (attractive) case. For a mPmT-symmetric potential that is odd under parity, our result implies that in the mPmT-unbroken phase, the energy eigenvalues are symmetric around zero, and that the corresponding eigenfunctions are closely related to each other.

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  • This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
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  • Through a simple and exact analytical derivation, we show that for a particle on a lattice, there is a one-to-one correspondence between the spectra in the presence of an...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1009.1366 [2] arXiv https://arxiv.org/abs/1009.1366 [3] Publisher https://arxiv.org/abs/1009.1366

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