Some results on the dynamics and transition probabilities for non self-adjoint hamiltonians
arXiv:1502.07175 · doi:10.1016/j.aop.2015.02.034
Abstract
We discuss systematically several possible inequivalent ways to describe the dynamics and the transition probabilities of a quantum system when its hamiltonian is not self-adjoint. In order to simplify the treatment, we mainly restrict our analysis to finite dimensional Hilbert spaces. In particular, we propose some experiments which could discriminate between the various possibilities considered in the paper. An example taken from the literature is discussed in detail.
arXiv commentin press in Annals of Physics
References in corpus (26)
- Making Sense of Non-Hermitian Hamiltonians
- Pseudo-Hermitian Representation of Quantum Mechanics
- Biorthogonal Quantum Mechanics
- Physical Aspects of Pseudo-Hermitian and -Symmetric Quantum Mechanics
- On the metric operator for the imaginary cubic oscillator
- Time-Dependent Pseudo-Hermitian Hamiltonians Defining a Unitary Quantum System and Uniqueness of the Metric Operator
- Three-Hilbert-Space Formulation of Quantum Mechanics
- Two families of superintegrable and isospectral potentials in two dimensions
- Pseudo-Unitary Operators and Pseudo-Unitary Quantum Dynamics
- Intertwined isospectral potentials in an arbitrary dimension
- Intertwined Hamiltonians in Two Dimensional Curved Spaces
- Fermionic coherent states for pseudo-Hermitian two-level systems
- Wave packet evolution in non-Hermitian quantum systems
- Intertwining Operator Realization of Non-Relativistic Holography
- Pseudo-Hermitian Quantum Mechanics with Unbounded Metric Operators
- Linear Pseudo-fermions
- Position Dependent Mass Schroedinger Equation and Isospectral Potentials : Intertwining Operator approach
- Crypto-unitary forms of quantum evolution operators
- PT-Symmetric Representations of Fermionic Algebras
- Model pseudofermionic systems: connections with exceptional points
- Non linear pseudo-bosons versus hidden Hermiticity. II: The case of unbounded operators
- Unbounded C-symmetries and their nonuniqueness
- Symmetry and Intertwining Operators for the Nonlocal Gross-Pitaevskii Equation
- Damping and Pseudo-fermions
- Non-Hermitian Quantum Systems and Time-Optimal Quantum Evolution
- Non-Hermitian Model for Asymmetrical Tunneling
Cited by in corpus (11)
- Non-hermitian operator modelling of basic cancer cell dynamics
- Transition Probabilities in the Two-Level Quantum System with PT-Symmetric Non-Hermitian Hamiltonians
- Bi-squeezed states arising from pseudo-bosons
- Coordinate representation for non Hermitian position and momentum operators
- A chain of solvable non-Hermitian Hamiltonians constructed by a series of metric operators
- Non self-adjoint Hamiltonians with complex eigenvalues
- Transition Probabilities for Flavor Eigenstates of Non-Hermitian Hamiltonians in the PT-Broken Phase
- Gibbs states defined by biorthogonal sequences
- Non self-adjoint operators with real spectra and extensions of quantum mechanics
- Heisenberg dynamics for non self-adjoint Hamiltonians: symmetries and derivations
- Decomposition of a system in pseudo-Hermitian quantum mechanics