High-order quantum adiabatic approximation and Berry's phase factor

1988 ◽  
Vol 21 (7) ◽  
pp. 1595-1599 ◽  
Author(s):  
Chang-Pu Sun
Keyword(s):  
Adiabatic Approximation ◽  
High Order ◽  
Phase Factor ◽  
Berry's Phase ◽  
Berry’S Phase

AN APPROXIMATE METHOD TREATING A THREE BODY FORCE IN THE (d, p) REACTION

1988 ◽  
Vol 03 (10) ◽  
pp. 981-987
Author(s):  
NAOKI HASHIMOTO
Keyword(s):  
Approximate Method ◽  
Body Force ◽  
Phase Factor ◽  
Simple Method ◽  
Berry's Phase ◽  
Berry’S Phase ◽  
Three Body

We propose a very simple method to calculate the (d, p) reaction including a three body force, and discuss briefly the non-integrable phase factor like Berry’s phase associated to the three body force.

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
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