Non self-adjoint Hamiltonians with complex eigenvalues

Abstract

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.

in press in Journal of Physics A

References in corpus (4)

• Making Sense of Non-Hermitian Hamiltonians
• Fermionic coherent states for pseudo-Hermitian two-level systems
• Some results on the dynamics and transition probabilities for non self-adjoint hamiltonians
• Vector coherent states and intertwining operators

Cited by in corpus (5)

• A description of pseudo-bosons in terms of nilpotent Lie algebras
• Intertwining operators for non self-adjoint Hamiltonians and bicoherent states
• Quantum mechanical settings inspired by RLC circuits
• Analytic approximation for eigenvalues of a class of $\mathcal{P}\mathcal{T}$ symmetric Hamiltonians
• Eigenvalues of non-hermitian matrices: a dynamical and an iterative approach. Application to a truncated Swanson model