231 research outputs found
Heat Kernel Expansion for Operators of the Type of the Square Root of the Laplace Operator
A method is suggested for the calculation of the DeWitt-Seeley-Gilkey (DWSG)
coefficients for the operator basing on a
generalization of the pseudodifferential operator technique. The lowest DWSG
coefficients for the operator are calculated by using
the method proposed. It is shown that the method admits a generalization to the
case of operators of the type , where m is an
arbitrary rational number. A more simple method is proposed for the calculation
of the DWSG coefficients for the case of strictly positive operators under the
sign of root. By using this method, it is shown that the problem of the
calculation of the DWSG coefficients for such operators is exactly solvable.
Namely, an explicit formula expressing the DWSG coefficients for operators with
root through the DWSG coefficients for operators without root is deduced.Comment: 17 pages, LaTeX, no figure
Dynamics and phase diagram of the quantum Hall state in bilayer graphene
Utilizing the Baym-Kadanoff formalism with the polarization function
calculated in the random phase approximation, the dynamics of the
quantum Hall state in bilayer graphene is analyzed. Two phases with nonzero
energy gap, the ferromagnetic and layer asymmetric ones, are found. The phase
diagram in the plane , where is a
top-bottom gates voltage imbalance, is described. It is shown that the energy
gaps in these phases scale linearly, $\Delta E\sim 10 B[T]K, with magnetic
field. The comparison of these results with recent experiments in bilayer
graphene is presented.Comment: 14 pages, 4 figure
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