Non-Abelian geometric phase, Floquet theory and periodic dynamical invariants
نویسندگان
چکیده
منابع مشابه
Non-Abelian Geometric Phase, Floquet Theory, and Periodic Dynamical Invariants
For a periodic Hamiltonian, periodic dynamical invariants may be used to obtain non-degenerate cyclic states. This observation is generalized to the degenerate cyclic states, and the relation between the periodic dynamical invariants and the Floquet decompositions of the time-evolution operator is elucidated. In particular, a necessary condition for the occurrence of cyclic non-adiabatic non-Ab...
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We study the geometric phase phenomenon in the context of the adiabatic Floquet theory (the so-called the (t, t) Floquet theory). A double integration appears in the geometric phase formula because of the presence of two time variables within the theory. We show that the geometric phases are then identified with horizontal lifts of surfaces in an abelian gerbe with connection, rather than with ...
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We use the theory of dynamical invariants to yield a simple derivation of noncyclic analogues of the Abelian and non-Abelian geometric phases. This derivation relies only on the principle of gauge invariance and elucidates the existing definitions of the Abelian noncyclic geometric phase. We also discuss the adiabatic limit of the noncyclic geometric phase and compute the adiabatic non-Abelian ...
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Mark A. Kowarsky,1,2,3 Lloyd C. L. Hollenberg,1,2 and Andrew M. Martin1 1School of Physics, The University of Melbourne, Parkville 3010, Australia 2Center for Quantum Computation and Communication Technology, School of Physics, The University of Melbourne, Parkville 3010, Australia 3Department of Physics, Stanford University, Stanford, California 94305, USA (Received 6 February 2014; published ...
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Adiabatic U(2) geometric phases are studied for arbitrary quantum systems with a three-dimensional Hilbert space. Necessary and sufficient conditions for the occurrence of the non-Abelian geometrical phases are obtained without actually solving the full eigenvalue problem for the instantaneous Hamiltonian. The parameter space of such systems which has the structure of CP 2 is explicitly constru...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and General
سال: 1998
ISSN: 0305-4470,1361-6447
DOI: 10.1088/0305-4470/31/49/015