Dual oscillators and Quantum Pendulums: spectrum and correlators

Abstract

We outline the nonlinear transformation in the path integral representation for partition function of O(N) symmetric oscillator systems bringing their duality to certain one-dimensional oscillators with unstable potential shapes. This duality transformation realizes the equivalence between spectra of a Hermitian and a non-Hermitian Hamiltonians. It is exploited to calculate exactly the spectra of quantum rotators . The zero-temperature limit is considered and the dual representation of n-point correlators of coordinate operators is obtained.

12 pages, substantial changes: calculation of correlators added

References in corpus (12)

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• Complex Extension of Quantum Mechanics
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• Supersymmetry without hermiticity
• An Equivalent Hermitian Hamiltonian for the non-Hermitian -x^4 Potential
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• The disappearing $Q$ operator
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Cited by in corpus (10)

• General solution of scalar field cosmology with a (piecewise) exponential potential
• Electronic properties of bilayer graphene catenoid bridge
• Nonunique C operator in PT Quantum Mechanics
• PT Symmetry in Classical and Quantum Statistical Mechanics
• Exact Isospectral Pairs of PT-Symmetric Hamiltonians
• Generalized Ellis-Bronnikov graphene wormhole
• Position-dependent mass effects on a bilayer graphene catenoid bridge
• Phantom without phantom or how the PT symmetry saves us from the Big Rip
• PT symmetry and large-N models
• The Large-N Limit of PT-Symmetric O(N) Models