15,192 research outputs found
Thom form in equivariant Cech-de Rham theory
In the present paper, we provide the foundation of a -equivariant Cech-de
Rham theory for a compact Lie group by using the Cartan model of
equivariant differential forms. Our approach is quite elementary without
referring to the Mathai-Quillen framework. In particular, by a direct
computation, we give an explicit formula of the -equivariant Thom form of
C^l, which deforms the classical Bochnor-Martinelli kernel. Also we discuss a
version of equivariant Riemann-Roch formula.Comment: 26pages, no figure
Inelastic tunneling in a double quantum dot coupled to a bosonic environment
Coupling a quantum system to a bosonic environment always give rise to
inelastic processes, which reduce the coherency of the system. We measure
energy dependent rates for inelastic tunneling processes in a fully
controllable two-level system of a double quantum dot. The emission and
absorption rates are well repro-duced by Einstein's coefficients, which relate
to the spontaneous emission rate. The inelastic tunneling rate can be
comparable to the elastic tunneling rate if the boson occupation number becomes
large. In the specific semiconductor double dot, the energy dependence of the
inelastic rate suggests that acoustic phonons are coupled to the double dot
piezoelectrically.Comment: 6 pages, 4 figure
On sums of generalized Ramanujan sums
Ramanujan sums have been studied and generalized by several authors. For
example, Nowak studied these sums over quadratic number fields, and Grytczuk
defined that on semigroups. In this note, we deduce some properties on sums of
generalized Ramanujan sums and give examples on number fields. In particular,
we have a relational expression between Ramanujan sums and residues of Dedekind
zeta functions.Comment: 10 page
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