Quantum Complex Henon-Heiles Potentials

Abstract

Quantum-mechanical PT-symmetric theories associated with complex cubic potentials such as V=x^2+y^2+igxy^2 and V=x^2+y^2+z^2+igxyz, where g is a real parameter, are investigated. These theories appear to possess real, positive spectra. Low-lying energy levels are calculated to very high order in perturbation theory. The large-order behavior of the perturbation coefficients is determined using multidimensional WKB tunneling techniques. This approach is also applied to the complex Henon-Heiles potential V=x^2+y^2+ig(xy^2-x^3/3).

14 pp, 4 figs

Cited by in corpus (42)

• Making Sense of Non-Hermitian Hamiltonians
• Complex Extension of Quantum Mechanics
• Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
• Pseudo-Hermiticity versus PT-Symmetry II: A complete characterizatio n of non-Hermitian Hamiltonians with a real spectrum
• Pseudo-Hermiticity versus PT-Symmetry III: Equivalence of pseudo-Her miticity and the presence of antilinear symmetries
• Must a Hamiltonian be Hermitian?
• Extension of PT-Symmetric Quantum Mechanics to Quantum Field Theory with Cubic Interaction
• Pseudo-Supersymmetric Quantum Mechanics and Isospectral Pseudo-Hermi tian Hamiltonians
• Multi-Instantons and Exact Results III: Unified Description of the Resonances of Even and Odd Anharmonic Oscillators
• The C Operator in PT-Symmetric Quantum Theories
• New Methods for Two-Dimensional Schrödinger Equation: SUSY-separation of Variables and Shape Invariance
• Bound states of the Dirac equation for the PT-symmetric generalized Hulthen potential by the Nikiforov-Uvarov method
• Spontaneous breakdown of PT symmetry in the solvable square-well model
• Complex Optical Potentials and Pseudo-Hermitian Hamiltonians
• Exponential Type Complex and non-Hermitian Potentials in PT-Symmetric Quantum Mechanics
• Semiclassical Calculation of the C Operator in PT-Symmetric Quantum Mechanics
• Nonlinear supersymmetry on the plane in magnetic field and quasi-exactly solvable systems
• Two-dimensional SUSY-pseudo-Hermiticity without separation of variables
• Bound States of Non-Hermitian Quantum Field Theories
• Coupled-channel version of PT-symmetric square well
• Eigenstate entanglement entropy in $PT$ invariant non-Hermitian system
• Two-Point Green's Function in PT-Symmetric Theories
• Deconfinement to Confinement as PT phase transition
• Non-hermitean hamiltonians with unitary and antiunitary symmetry
• Supersymmetric solution of PT-/non-PT-symmetric and non-Hermitian Morse potential is studied to get real and Supersymmetric Solution of PT-/Non-PT-Symmetric and Non-Hermitian Morse Potential via Hamiltonian Hierarchy Method
• PT symmetric models in more dimensions and solvable square-well versions of their angular Schroedinger equations
• PT phase transition in a (2+1)-d relativistic system
• PT-symmetry broken by point-group symmetry
• Structure, Time Propagation and Dissipative Terms for Resonances
• Exactly Solvable Non-Separable and Non-Diagonalizable 2-Dim Model with Quadratic Complex Interaction
• Is space-time symmetry a suitable generalization of parity-time symmetry?
• Approximate Dirac solutions of complex -symmetric Pöschl-Teller potential in view of spin and pseudospin symmetries
• Non-Hermitian oscillators with $T_d$ symmetry
• Non-perturbative calculations for the effective potential of the $PT$ symmetric and non-Hermitian $(-g{\varphi }^4)$ field theoretic model
• Conjecture on the analyticity of PT-symmetric potentials and the reality of their spectra
• Equidistance of the Complex 2-Dim Anharmonic Oscillator Spectrum: Exact Solution
• Level Crossings in Complex Two-Dimensional Potentials
• New Ansatz for Metric Operator Calculation in Pseudo-Hermitian Field Theory
• Dynamical symmetry algebra of two superintegrable two-dimensional systems
• Ladder Operators and Hidden Algebras for Shape Invariant Nonseparable and Nondiagonalizable Modelswith Quadratic Complex Interaction. I. Two-Dimensional Model
• The effective potential and resummation procedure to multidimensional complex cubic potentials for weak and strong-coupling
• Ladder Operators and Hidden Algebras for Shape Invariant Nonseparable and Nondiagonalizable Modelswith Quadratic Complex Interaction. II. Three-Dimensional Model