scholarly journals High-order adiabatic approximation for non-Hermitian quantum system and complexification of Berry's phase

1993 ◽  
Vol 48 (4) ◽  
pp. 393-398 ◽  
Author(s):  
Chang-Pu Sun
Keyword(s):  
Quantum System ◽  
Adiabatic Approximation ◽  
High Order ◽  
Berry's Phase ◽  
Berry’S Phase

THREE ELABORATIONS ON BERRY’S CONNECTION, CURVATURE AND PHASE

1988 ◽  
Vol 03 (02) ◽  
pp. 285-297 ◽  
Author(s):  
R. JACKIW
Keyword(s):  
Conservation Laws ◽  
Quantum System ◽  
Canonical Transformation ◽  
Time Dependent ◽  
Berry's Phase ◽  
Berry’S Phase ◽  
Gauge Transformations ◽  
Constants Of Motion ◽  
Symmetry Transformations ◽  
Higher Order Corrections

We discuss how symmetries and conservation laws are affected when Berry’s phase occurs in a quantum system: symmetry transformations of coordinates have to be supplemented by gauge transformations of Berry’s connection, and consequently constants of motion acquire terms beyond the familiar kinematical ones. We show how symmetries of a problem determine Berry’s connection, curvature and, once a specific path is chosen, the phase as well. Moreover, higher order corrections are also fixed. We demonstrate that in some instances Berry’s curvature and phase can be removed by a globally well-defined, time-dependent canonical transformation. Finally, we describe how field theoretic anomalies may be viewed as manifestations of Berry’s phase.

scholarly journals TOPOLOGICAL PROPERTIES OF BERRY'S PHASE

2005 ◽  
Vol 20 (05) ◽  
pp. 335-343 ◽  
Author(s):  
KAZUO FUJIKAWA
Keyword(s):  
Adiabatic Approximation ◽  
Time Interval ◽  
Finite Time Interval ◽  
Present Formulation ◽  
Level Crossing ◽  
Geometric Phases ◽  
Berry's Phase ◽  
Berry’S Phase ◽  
Convenient Formula ◽  
Oppenheimer Approximation

By using a second quantized formulation of level crossing, which does not assume adiabatic approximation, a convenient formula for geometric terms including off-diagonal terms is derived. The analysis of geometric phases is reduced to a simple diagonalization of the Hamiltonian in the present formulation. If one diagonalizes the geometric terms in the infinitesimal neighborhood of level crossing, the geometric phases become trivial for any finite time interval T. The topological interpretation of Berry's phase such as the topological proof of phase-change rule thus fails in the practical Born–Oppenheimer approximation, where a large but finite ratio of two time scales is involved.

scholarly journals Using Berry’s Phase to Detect the Unruh Effect at Lower Accelerations

2011 ◽  
Vol 107 (13) ◽  
Author(s):  
Eduardo Martín-Martínez ◽  
Ivette Fuentes ◽  
Robert B. Mann
Keyword(s):  
Unruh Effect ◽  
Berry's Phase ◽  
Berry’S Phase

Calculation of Berry's phase in squeezed states

1991 ◽  
Vol 54 (3) ◽  
pp. 894-900
Author(s):  
E. V. Damaskinski
Keyword(s):  
Squeezed States ◽  
Berry's Phase ◽  
Berry’S Phase
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