Geometric phase around exceptional points
Mailybaev, A. A. ; Kirillov, O. N. ; Seyranian, A. P.
arXiv, 0501040 / Harvested from arXiv
Text on arXiv
A wave function picks up, in addition to the dynamic phase, the geometric (Berry) phase when traversing adiabatically a closed cycle in parameter space. We develop a general multidimensional theory of the geometric phase for (double) cycles around exceptional degeneracies in non-Hermitian Hamiltonians. We show that the geometric phase is exactly $\pi$ for symmetric complex Hamiltonians of arbitrary dimension and for nonsymmetric non-Hermitian Hamiltonians of dimension 2. For nonsymmetric non-Hermitian Hamiltonians of higher dimension, the geometric phase tends to $\pi$ for small cycles and changes as the cycle size and shape are varied. We find explicitly the leading asymptotic term of this dependence, and describe it in terms of interaction of different energy levels.
Publié le : 2005-01-10
Classification:  Quantum Physics,  Mathematical Physics 
@article{0501040,
     author = {Mailybaev, A. A. and Kirillov, O. N. and Seyranian, A. P.},
     title = {Geometric phase around exceptional points},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0501040}
}

Mailybaev, A. A.; Kirillov, O. N.; Seyranian, A. P. Geometric phase around exceptional points. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0501040/