Geometric Phase in a Time-Dependent Coupled Atom-Heteronuclear-Molecule Condensate

2011 ◽  
Vol 50 (6) ◽  
pp. 1719-1725
Author(s):  
An-Ling Wang ◽  
Fu-Ping Liu ◽  
Zhao-Xian Yu
Keyword(s):  
Geometric Phase ◽  
Time Dependent

scholarly journals Exact time-dependent decoherence factor and its adiabatic classical limit

2003 ◽  
Vol 81 (10) ◽  
pp. 1185-1191
Author(s):  
J -Q Shen ◽  
P Chen ◽  
H Mao
Keyword(s):  
Invariant Theory ◽  
Geometric Phase ◽  
Classical Limit ◽  
Unitary Transformation ◽  
Time Dependent ◽  
Quantum Decoherence ◽  
Dynamical Models ◽  
Complete Set ◽  
General Time ◽  
03.65 Ge

The present paper finds the complete set of exact solutions of the general time-dependent dynamical models for quantum decoherence, by making use of the Lewis–Riesenfeld invariant theory and the invariant-related unitary transformation formulation. Based on this, the general explicit expression for the decoherence factor is then obtained and the adiabatic classical limit of an illustrative example is discussed. The result (i.e., the adiabatic classical limit) obtained in this paper is consistent with what is obtained by other authors, and furthermore we obtain more general results concerning time-dependent nonadiabatic quantum decoherence. It is shown that the invariant theory is appropriate for treating both the time-dependent quantum decoherence and the geometric phase factor. PACS Nos.: 03.65.Ge, 03.65.Bz

Invariants and geometric phase for systems with non-Hermitian time-dependent Hamiltonians

1992 ◽  
Vol 46 (7) ◽  
pp. 3626-3630 ◽  
Author(s):  
Xiao-Chun Gao ◽  
Jing-Bo Xu ◽  
Tie-Zheng Qian
Keyword(s):  
Geometric Phase ◽  
Time Dependent

Geometric Phase in a Time-Dependent Λ-Type Jaynes–Cummings Model

2009 ◽  
Vol 51 (3) ◽  
pp. 407-410 ◽  
Author(s):  
Qin Xian-Ming ◽  
Yu Zhao-Xian ◽  
Jiao Zhi-Yong ◽  
Xie Bing-Hao
Keyword(s):  
Geometric Phase ◽  
Time Dependent

Geometric phase of cosmological scalar and tensor perturbations in f(R) gravity

2018 ◽  
Vol 33 (14) ◽  
pp. 1850077
Author(s):  
Hamideh Balajany ◽  
Mohammad Mehrafarin
Keyword(s):  
Scalar Field ◽  
Harmonic Oscillator ◽  
Geometric Phase ◽  
Berry Phase ◽  
Time Dependent ◽  
Einstein Theory ◽  
Tensor Perturbations ◽  
Cosmological Scalar ◽  
Conformal Equivalence

By using the conformal equivalence of f(R) gravity in vacuum and the usual Einstein theory with scalar-field matter, we derive the Hamiltonian of the linear cosmological scalar and tensor perturbations in f(R) gravity in the form of time-dependent harmonic oscillator Hamiltonians. We find the invariant operators of the resulting Hamiltonians and use their eigenstates to calculate the adiabatic Berry phase for sub-horizon modes as a Lewis–Riesenfeld phase.

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

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