Physics – Quantum Physics
Scientific paper
2008-06-23
J.Phys.A41:485304,2008
Physics
Quantum Physics
29 pages, 21 figures
Scientific paper
10.1088/1751-8113/41/48/485304
We consider the geometric phase and quantum tunneling in vicinity of diabolic and exceptional points. We show that the geometric phase associated with the degeneracy points is defined by the flux of complex magnetic monopole. In weak-coupling limit the leading contribution to the real part of geometric phase is given by the flux of the Dirac monopole plus quadrupole term, and the expansion for its imaginary part starts with the dipolelike field. For a two-level system governed by the generic non-Hermitian Hamiltonian, we derive a formula to compute the non-adiabatic complex geometric phase by integral over the complex Bloch sphere. We apply our results to to study a two-level dissipative system driven by periodic electromagnetic field and show that in the vicinity of the exceptional point the complex geometric phase behaves as step-like function. Studying tunneling process near and at exceptional point, we find two different regimes: coherent and incoherent. The coherent regime is characterized by the Rabi oscillations and one-sheeted hyperbolic monopole emerges in this region of the parameters. In turn with the incoherent regime the two-sheeted hyperbolic monopole is associated. The exceptional point is the critical point of the system where the topological transition occurs and both of the regimes yield the quadratic dependence on time. We show that the dissipation brings into existence of pulses in the complex geometric phase and the pulses are disappeared when dissipation dies out. Such a strong coupling effect of the environment is beyond of the conventional adiabatic treatment of the Berry phase.
la Cruz Fermin Aceves de
Nesterov Alexander I.
No associations
LandOfFree
Complex magnetic monopoles, geometric phases and quantum evolution in vicinity of diabolic and exceptional points does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Complex magnetic monopoles, geometric phases and quantum evolution in vicinity of diabolic and exceptional points, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Complex magnetic monopoles, geometric phases and quantum evolution in vicinity of diabolic and exceptional points will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-674149