Spectra of PT-Symmetric Operators and Perturbation Theory

Abstract

Criteria are formulated both for the existence and for the non-existence of complex eigenvalues for a class of non self-adjoint operators in Hilbert space invarariant under a particular discrete symmetry. Applications to the PT-symmetric Schrödinger operators are discussed.

arXiv comment14 pages

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• Perturbation theory of PT-symmetric Hamiltonians
• Conditional observability
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• The resistive state in a superconducting wire: Bifurcation from the normal state
• Non-Hermitian spectral effects in a PT-symmetric waveguide
• Construction of PT-asymmetric non-Hermitian Hamiltonians with CPT-symmetry
• Kurt Symanzik - a stable fixed point beyond triviality
• PT Symmetric, Hermitian and P-Self-Adjoint Operators Related to Potentials in PT Quantum Mechanics
• Determination of the domain of the admissible matrix elements in the four-dimensional PT-symmetric anharmonic model
• On Domains of PT Symmetric Operators Related to -y''(x) + (-1)^n x^{2n}y(x)
• Kinematic and dynamic vortices in a thin film driven by an applied current and magnetic field
• The Pauli equation with complex boundary conditions
• On $J$-self-adjoint extensions of the Phillips symmetric operator
• Perturbation method for non-square Hamiltonians and its application to polynomial oscillators
• Quasi-exact minus-quartic oscillators in strong-core regime
• Analytic approximation for eigenvalues of a class of $\mathcal{P}\mathcal{T}$ symmetric Hamiltonians
• Non-real Eigenvalues for PT-Symmetric Double Wells