Analytic structure of eigenvalues of coupled quantum systems

Abstract

By analytically continuing the coupling constant $g$ of a coupled quantum theory, one can, at least in principle, arrive at a state whose energy is lower than the ground state of the theory. The idea is to begin with the uncoupled $g=0$ theory in its ground state, to analytically continue around an exceptional point (square-root singularity) in the complex-coupling-constant plane, and finally to return to the point $g=0$. In the course of this analytic continuation, the uncoupled theory ends up in an unconventional state whose energy is lower than the original ground state energy. However, it is unclear whether one can use this analytic continuation to extract energy from the conventional vacuum state; this process appears to be exothermic but one must do work to vary the coupling constant $g$.

11 pages, 5 figures

References in corpus (11)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• The physics of exceptional points
• Dynamically encircling exceptional points in a waveguide: asymmetric mode switching from the breakdown of adiabaticity
• Topological energy transfer in an optomechanical system with exceptional points
• PT symmetry and spontaneous symmetry breaking in a microwave billiard
• Twofold Transition in PT-Symmetric Coupled Oscillators
• Radiative coupling and weak lasing of exciton-polariton condensates
• Coupled Oscillator Systems Having Partial PT Symmetry
• Systems of coupled PT-symmetric oscillators
• Families of particles with different masses in PT-symmetric quantum field theory
• Generation of families of spectra in PT-symmetric quantum mechanics and scalar bosonic field theory

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• Stochastic Representation of the Quantum Quartic Oscillator
• Oscillators with imaginary coupling: spectral functions in quantum mechanics and quantum field theory
• Continuous quantum phase transition in the fermionic mass solutions of the Nambu-Jona-Lasinio model
• The quantum harmonic oscillator and the real Hilbert space