6533b85ffe1ef96bd12c1d61
RESEARCH PRODUCT
Non-self-adjoint Hamiltonians with complex eigenvalues
Fabio Bagarellosubject
Statistics and ProbabilityPure mathematicsDiagonalizable matrixPhysical systemFOS: Physical sciencesGeneral Physics and Astronomyintertwining relation01 natural sciencesModeling and simulationPhysics and Astronomy (all)symbols.namesakePT-quantum mechanic0103 physical sciencesMathematical Physic010306 general physicsSettore MAT/07 - Fisica Matematicaantilinear operatorMathematical PhysicsEigenvalues and eigenvectorsMathematicsQuantum Physics010308 nuclear & particles physicsHilbert spaceStatistical and Nonlinear PhysicsProbability and statisticsMathematical Physics (math-ph)Modeling and SimulationsymbolsQuantum Physics (quant-ph)Hamiltonian (quantum mechanics)Self-adjoint operatorStatistical and Nonlinear Physicdescription
Motivated by what one observes dealing with PT-symmetric quantum mechanics, we discuss what happens if a physical system is driven by a diagonalizable Hamiltonian with not all real eigenvalues. In particular, we consider the functional structure related to systems living in finite-dimensional Hilbert spaces, and we show that certain intertwining relations can be deduced also in this case if we introduce suitable antilinear operators. We also analyze a simple model, computing the transition probabilities in the broken and in the unbroken regime.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2016-01-01 | Journal of Physics A: Mathematical and Theoretical |