Non-orthogonal “resonances”, modified geometric phase and geometric dephasing
(i.e.W e i r d dynamics of a non-isolated spin-1/2) Rob Whitney1 Yu. Makhlin2, A. Shnirman3, and Y. Gefen4 1. 2. 3. 4.
Univ. Oxford, UK Univ. Karlsruhe, Germany Univ. Karlsruhe, Germany Weizmann Institute, Israel
! Univ. Genéve, Switzerland ! Landau Inst. Russia
11th November 2004
For those readers who were not present during this seminar: This talk divides into two independent pieces of work: slides 4-18 : spin dynamics in a time-independent field slides 20-33 : Berry phase experiment (slow time-dependent field) The only connection between these two parts is made (rather briefly) on slide 31, it is not a central point of either piece of work
For those readers who were present during this seminar: For pedagogical reasons, the two sections of the talk are in the reverse order to the way I presented them in Trieste.
Techical stuff: A brief summary of the technique we use is given on slides 15-17. This includes a brief presentation of the analogy between the diagrams and terms in a Lindblad-style Master equation. Note: This is an analogy not a mathematical equivalence, in-other-words I do not know of a proof of the equivalence.
16th November 2004
Outline Static Hamiltonian " Pictures of dynamics of dissipative spin-half (spin+environment # trace out environment)
$ Choose “resonance-states” ! density matrices associated with resonances (will be non-orthogonal)
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