Complex Correspondence Principle

Abstract

Quantum mechanics and classical mechanics are two very different theories, but the correspondence principle states that quantum particles behave classically in the limit of high quantum number. In recent years much research has been done on extending both quantum mechanics and classical mechanics into the complex domain. This letter shows that these complex extensions continue to exhibit a correspondence, and that this correspondence becomes more pronounced in the complex domain. The association between complex quantum mechanics and complex classical mechanics is subtle and demonstrating this relationship prequires the use of asymptotics beyond all orders.

4 pages, 6 figures

References in corpus (8)

• Making Sense of Non-Hermitian Hamiltonians
• The ODE/IM Correspondence
• Mean-field dynamics of a non-Hermitian Bose-Hubbard dimer
• PT-symmetric Deformations of the Korteweg-de Vries Equation
• Classical Trajectories for Complex Hamiltonians
• Complexified Dynamical Systems
• Spontaneous Breaking of Classical PT Symmetry
• Exceptional points in quantum and classical dynamics

Cited by in corpus (34)

• The physics of exceptional points
• Observation of Fast Evolution in Parity-Time-Symmetric System
• Quantum Classical Correspondence for a non-Hermitian Bose-Hubbard Dimer
• Complex Worldline Instantons and Quantum Interference in Vacuum Pair Production
• Stationary states of a PT-symmetric two-mode Bose-Einstein condensate
• On complexified mechanics and coquaternions
• Wave packet evolution in non-Hermitian quantum systems
• Nonperturbative pair production in interpolating fields
• Experimental observation of information flow in the anti-$\mathcal{P}\mathcal{T}$-symmetric system
• Conceptual Aspects of PT-Symmetry and Pseudo-Hermiticity: A status report
• Probability-preserving evolution in a non-Hermitian two-band model
• PT-symmetry breaking in complex nonlinear wave equations and their deformations
• Quantum tunneling as a classical anomaly
• Stable States with Non-Zero Entropy under Broken $\mathcal{P}\mathcal{T}$-Symmetry
• Scaling behavior and phase diagram of a PT-symmetric non-Hermitian Bose-Hubbard system
• Probability Density in the Complex Plane
• Information retrieval and eigenstates coalescence in a non-Hermitian quantum system with anti-$\mathcal{P}\mathcal{T}$ symmetry
• Various Scattering Properties of a New PT-symmetric non-Hermitian potential
• Resonances in Extreme Mass-Ratio Inspirals: Asymptotic and Hyperasymptotic Analysis
• Quantum tunneling from paths in complex time
• Classical Particle in a Complex Elliptic Potential
• Periodic orbits for classical particles having complex energy
• Lorentzian path integral for quantum tunneling and WKB approximation for wave-function
• Scaling laws of the out-of-time-order correlators at the transition to the spontaneous $\mathcal{P}\mathcal{T}$-symmetry breaking in a Floquet system
• Competing PT potentials and re-entrant PT symmetric phase for a particle in a box
• Nonlinear eigenvalue problems
• PT-symmetrically deformed shock waves
• Extreme Synchronization Transitions
• Aharonov-Bohm effect with an effective complex-valued vector potential
• Theory Including Future Not Excluded -- Formulation of Complex Action Theory II --
• Analytic approximation for eigenvalues of a class of $\mathcal{P}\mathcal{T}$ symmetric Hamiltonians
• Trajectory Interpretation of Correspondence Principle: Solution of Nodal Issue
• Two dimensional non-Hermitian harmonic oscillator: coherent states
• $\mathcal{P}\mathcal{T}$-Symmetric Generalized Extended Momentum Operator