Biorthogonal Quantum Systems

Abstract

Models of PT symmetric quantum mechanics provide examples of biorthogonal quantum systems. The latter incorporporate all the structure of PT symmetric models, and allow for generalizations, especially in situations where the PT construction of the dual space fails. The formalism is illustrated by a few exact results for models of the form H=(p+ν)^2+\sum_{k>0}μ_{k}exp(ikx). In some non-trivial cases, equivalent hermitian theories are obtained and shown to be very simple: They are just free (chiral) particles. Field theory extensions are briefly considered.

34 pages, 5 eps figures; references added and other changes made to conform to journal version

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Cited by in corpus (44)

• Pseudo-Hermitian Representation of Quantum Mechanics
• Biorthogonal Quantum Mechanics
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• Invisibility and PT-symmetry
• Nonlinear Supersymmetric Quantum Mechanics: concepts and realizations
• Consistency of PT-symmetric quantum mechanics
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• Wave packet evolution in non-Hermitian quantum systems
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• Non-Hermitian interaction representation and its use in relativistic quantum mechanics
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• Engineering Yang-Lee anyons via Majorana bound states
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• Bosonic pair creation and the Schiff-Snyder-Weinberg effect
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• Exact propagators for complex SUSY partners of real potentials
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• Galois conjugates of String-net Model
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• On Rotations as Spin Matrix Polynomials
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