scholarly journals Comment on “Geometric phase of the gyromotion for charged particles in a time-dependent magnetic field” [Phys. Plasmas 18, 072505 (2011)]

2012 ◽  
Vol 19 (9) ◽  
pp. 094701 ◽  
Author(s):  
Alain J. Brizard ◽  
Loïc de Guillebon
Keyword(s):  
Magnetic Field ◽  
Geometric Phase ◽  
Charged Particles ◽  
Time Dependent

Algebraic dynamic study of geometric phase for a homonuclear linear spincluster

2007 ◽  
Vol 85 (8) ◽  
pp. 879-885
Author(s):  
X -X Chen ◽  
J Xue
Keyword(s):  
Magnetic Field ◽  
Coupling Strength ◽  
Geometric Phase ◽  
Time Dependent ◽  
Algebraic Dynamics ◽  
Spin Cluster ◽  
Alternative Expression ◽  
Linear Formula ◽  
External Time ◽  
The Magnetic Field

A homonuclear linear [Formula: see text] coupling spin cluster with the middle particle driven by an external time-dependent magnetic field is investigated by using the method of algebraic dynamics. The exact analytical solutions of the time-dependent Schrodinger equation of the spin cluster system are derived and employed to study the geometric phase. An alternative expression of the geometric phase in each eigenstate is obtained. It is shown that the geometric phase is related to the external magnetic-field parameter θ (the angle between the magnetic field and the Z axis) and the effective coupling strength Jn. Based on the relation, how the geometric phase depends on the coupling strength Jn in different reducible subspace is discussed.PACS Nos.: 33.20.Wr, 03.65.Fd, 03.65.Vf

GEOMETRIC PHASE IN THE CONDENSED VAPOR OF Rb UNDER PRESSURE AND EXTERNAL MAGNETIC FIELD

2010 ◽  
Vol 24 (17) ◽  
pp. 1869-1875
Author(s):  
ZHAO-XIAN YU ◽  
ZHI-YONG JIAO ◽  
XIANG-GUI LI
Keyword(s):  
Magnetic Field ◽  
Atomic Nucleus ◽  
External Magnetic Field ◽  
Invariant Theory ◽  
Geometric Phase ◽  
Time Dependent ◽  
Coupling Constant ◽  
External Time

By using the Lewis–Riesenfeld invariant theory, we have studied the geometric phase in the condensed vapor of Rb under pressure and external time-dependent magnetic field. We find that the geometric phase in the cycle case has nothing to do with the coupling constant between electron and atomic nucleus, and the external time-dependent magnetic field.

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