4,150 research outputs found
SU(3) Landau - Zener Interferometry
We consider a general theory of Landau-Zener transitions in a three-level
system. Based on a classification of three level crossings we express the
Landau - Zener Hamiltonians in terms of two bases: i) spin S=1 SU(2) operators
and ii) SU(3) Gell - Mann matrices. We show that the generic Hamiltonians being
non-linear in terms of the SU(2) group generators become linear in the SU(3)
basis. If the diabatic states of the SU(3) Landau - Zener Hamiltonian form a
triangle, the interference between two paths results in formation of "beats"
and "steps" pattern in the time-dependent transition probability. The
characteristic time scales describing the "beats" and "steps" depend on a dwell
time through the triangle. These scales are related to the geometric size of
the interferometer. We formulate the SU(3) Landau - Zener problem in terms of
Bloch dynamics of a unit vector and find a solution of eight-dimensional Bloch
equations in the limit of a non-adiabatic transition. Possible experiments in
triangular and linearly arranged triple quantum dots where Landau - Zener
interferometry can be used for finding manifestations of SU(3) symmetry are
discussed.Comment: 6 pages, 3 figure
Semi-fermionic representation of SU(N) Hamiltonians
We represent the generators of the SU(N) algebra as bilinear combinations of
Fermi operators with imaginary chemical potential. The distribution function,
consisting of a minimal set of discrete imaginary chemical potentials, is found
for arbitrary N. This representation leads to the conventional temperature
diagram technique with standard Feynman codex, except that the Matsubara
frequencies are determined by neither integer nor half-integer numbers. The
real-time Schwinger-Keldysh formalism is formulated in the framework of complex
distribution functions. We discuss the continuous large N and SU(2) large spin
limits. We illustrate the application of this technique for magnetic and
spin-liquid states of the Heisenberg model.Comment: 11 pages, 7 EPS figures included, extended versio
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