A new class of adiabatic cyclic states and geometric phases for non-Hermitian Hamiltonians

  title={A new class of adiabatic cyclic states and geometric phases for non-Hermitian Hamiltonians},
  author={Ali Mostafazadeh},
  journal={Physics Letters A},
Abstract 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 the corresponding adiabatic geometric phase angles are real and discuss their relationship with the conventional complex adiabatic geometric phase angles. We present a detailed calculation of the new adiabatic cyclic states and their geometric phases for a non-Hermitian analog of the spin 1/2 particle… Expand
Geometric Phase for Non-Hermitian Hamiltonians and Its Holonomy Interpretation
For an arbitrary possibly non-Hermitian matrix Hamiltonian H, that might involve exceptional points, we construct an appropriate parameter space M and the lines bundle L^n over M such that theExpand
Consistency between adiabatic and non-adiabatic geometric phases for non-self-adjoint Hamiltonians
We show that the adiabatic approximation for non-self-adjoint Hamiltonians seems to induce two non-equal expressions for the geometric phase. The first one is related to the spectral projectorExpand
Geometric phase in PT-symmetric quantum mechanics
Unitary evolution in PT-symmetric quantum mechanics (QM) with a time-dependent metric is found to yield an interesting class of adiabatic processes. As an explicit example, a Berry-like phaseExpand
A new kind of geometric phases in open quantum systems and higher gauge theory
A new approach is proposed, extending the concept of geometric phases to adiabatic open quantum systems described by density matrices (mixed states). This new approach is based on an analogy betweenExpand
The pseudo Hermitian invariant operator and time-dependent non-Hermitian Hamiltonian exhibiting a SU(1,1) and SU(2) dynamical symmetry
We study the time evolution of quantum systems with a time-dependent non-Hermitian Hamiltonian exhibiting a SU(1,1) and SU(2) dynamical symmetry. With a time-dependent metric, the pseudo-Hermitian ...
Floquet exceptional points and chirality in non-Hermitian Hamiltonians
Floquet exceptional points correspond to the coalescence of two (or more) quasi-energies and corresponding Floquet eigenstates of a time-periodic non-Hermitian Hamiltonian. They generally arise whenExpand
Piecewise Adiabatic Following in Non-Hermitian Cycling
The time evolution of periodically driven non-Hermitian systems is in general non-unitary but can be stable. It is hence of considerable interest to examine the adiabatic following dynamics inExpand
Topological phases in the non-Hermitian Su-Schrieffer-Heeger model
We address the conditions required for a $\mathbb{Z}$ topological classification in the most general form of the non-Hermitian Su-Schrieffer-Heeger (SSH) model. Any chirally symmetric SSH model willExpand
Non-Hermitian time-dependent perturbation theory: Asymmetric transitions and transitionless interactions
Abstract The ordinary time-dependent perturbation theory of quantum mechanics, that describes the interaction of a stationary system with a time-dependent perturbation, predicts that the transitionExpand
Imaginary phases in two-level model with spontaneous decay
We study a two-level model coupled to the electromagnetic vacuum and to an external classic electric field with fixed frequency. The amplitude of the external electric field is supposed to vary veryExpand


Phase change during a cyclic quantum evolution.
A new geometric phase factor is defined for any cyclic evolution of a quantum system. This is independent of the phase factor relating the initial and final state vectors and the Hamiltonian, for aExpand
Noncyclic geometric phase and its non-Abelian generalization
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 principle of gaugeExpand
Geometrical phase factor for a non-Hermitian Hamiltonian (Erratum)
In a previous paper, the measurement of an atomic Berry phase associated with two crossing levels has been suggested as a possible test for an atomic interferometry method. As one of the two levelsExpand
On the adiabatic theorem for nonself-adjoint Hamiltonians
The authors consider the evolution of a two-level system driven by a nonself-adjoint Hamiltonian H( in t) and treat the adiabatic limit in to 0. While adiabatic theorem-like results do not hold trueExpand
Non-adiabatic non-abelian geometric phase
Abstract The non-integrable geometric phase factor is generalized to a non-abelian phase factor which in the adiabatic limit is the Wilczek-Zee generalization of the Berry phase. It is then extendedExpand
Geometric angles in quantum and classical physics
Abstract The geometric angles introduced in the group theoretical treatment of Berry's phase by Anandan and Stodolsky are generalized to the non-adiabatic cyclic evolutions studied by Aharonov andExpand
Adiabatic evolution of an irreversible two level system
The adiabatic dynamics of a two level atom with spontaneous decay is studied. The existence of a complex adiabatic phase shift is established: The real part being the usual Berry’s phase. AExpand
Berry phase of a resonant state
We derive closed analytical expressions for the complex Berry phase of an open quantum system in a state which is a superposition of resonant states and evolves irreversibly due to the spontaneousExpand
Relativistic adiabatic approximation and geometric phase
A relativistic analogue of the quantum adiabatic approximation is developed for Klein-Gordon fields minimally coupled to electromagnetism, gravity and an arbitrary scalar potential. The correspondingExpand
Extending the quantal adiabatic theorem: Geometry of noncyclic motion
We show that a noncyclic phase of geometric origin has to be included in the approximate adiabatic wave function. The adiabatic noncyclic geometric phase for systems exhibiting a conical intersectionExpand