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A New Class of Adiabatic Cyclic States and Geometric Phases for Non-Hermitian Hamiltonians
Ali Mostafazadeh
For a T-periodic non-Hermitian Hamiltonian H(t), we construct a class of adiabatic cyclic states of period T which are not eigenstates of the initial Hamiltonian H(0). We show that…
Perturbative Calculation of the Adiabatic Geometric Phase and Particle in a Well with Moving Walls
Ali Mostafazadeh
We use the Rayleigh-Schrödinger perturbation theory to calculate the corrections to the adiabatic geometric phase due to a perturbation of the Hamiltonian. We show that these corre…
Noncyclic geometric phase and its non-Abelian generalization
Ali Mostafazadeh
We use the theory of dynamical invariants to yield a simple derivation of noncyclic analogues of the Abelian and non-Abelian geometric phases. This derivation relies only on the pr…
Comment on Identical Motion in Classical and Quantum Mechanics
Ali Mostafazadeh
Makowski and Konkel [Phys. Rev. A 58, 4975 (1998)] have obtained certain classes of potentials which lead to identical classical and quantum Hamilton-Jacobi equations. We obtain th…
Generalized Adiabatic Product Expansion: A nonperturbative method of solving time-dependent Schroedinger equation
Ali Mostafazadeh
We outline a method based on successive canonical transformations which yields a product expansion for the evolution operator of a general (possibly non-Hermitian) Hamiltonian. For…