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Open Quantum Systems Decoherence Quantum Simulation

A selection rule for transitions in PT-symmetric quantum theory

arXiv

Authors: Lawrence R. Mead, David Garfinkle

Year

2016

Paper ID

42982

Status

Preprint

Abstract Read

~2 min

Abstract Words

108

Citations

N/A

Abstract

Carl Bender and collaborators have developed a quantum theory governed by Hamiltonians that are PT-symmetric rather than Hermitian. To implement this theory, the inner product was redefined to guarantee positive norms of eigenstates of the Hamiltonian. In the general case, which includes arbitrary time-dependence in the Hamiltonian, a modification of the Schrodinger equation is necessary as shown by Gong and Wang to conserve probability. In this paper, we derive the following selection rule: transitions induced by time dependence in a PT-symmetric Hamiltonian cannot occur between normalized states of differing PT-norm. We show three examples of this selection rule in action: two matrix models and one in the continuum.

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Carl Bender and collaborators have developed a quantum theory governed by Hamiltonians that are PT-symmetric rather than Hermitian.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1610.03801 [2] arXiv https://arxiv.org/abs/1610.03801 [3] Publisher https://arxiv.org/abs/1610.03801

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