Geometric Phase in composite systems .X.yⅰ Department of Physics, Dalian University of Technology With C. H. Oh, L. C Kwek, D. M. Tong e NUS Erik Sjoqvist e Uppsala Univ H. T. Cui, L. C. Wang, X L Huang e Dalian Univ of tech
Geometric Phase in composite systems 衣学喜 X. X. Yi Department of Physics, Dalian University of Technology With C. H. Oh, L. C. Kwek, D. M. Tong @ NUS; Erik Sjoqvist @ Uppsala Univ.; H. T. Cui, L. C. Wang, X. L. Huang @ Dalian Univ. of Tech
Outline Why study geometric phase Geometric phase in bipartite systems Geometric phase in open systems Geometric phase in dissipative systems Geometric phase in dephasing systems Geometric phase and QPTs Conclusion
2 Outline • Why study geometric phase • Geometric phase in bipartite systems • Geometric phase in open systems – Geometric phase in dissipative systems – Geometric phase in dephasing systems – Geometric phase and QPTs • Conclusion
Why study geometric phase Classical counterpart of berry Phase it is connected to the intrinsic curvature of the sphere Parallel transport 4 http://www.mi.infmit/manini/berryphase.html
3 Why study geometric phase Classical counterpart of Berry Phase; it is connected to the intrinsic curvature of the sphere. Parallel transport http://www.mi.infm.it/manini/berryphase.html
Parameter dependent system: H(n) 41(2,|w(2)}1() Adiabatic theorem: ()=v(()ee Geometric phase d (vn in y
4 , | n n ( ) ( ) ( ) ( ( )) ( ) 0 / | | t n n i dt i t n t t e e − − = 0 t n n n d i = Geometric phase: Adiabatic theorem: Parameter dependent system: H ( ) n ( )
Well defined for a closed path ,=乎aww
5 n n n C d i = Well defined for a closed path x y C