5,463 research outputs found
Elliptic operators in odd subspaces
An elliptic theory is constructed for operators acting in subspaces defined
via odd pseudodifferential projections. Subspaces of this type arise as
Calderon subspaces for first order elliptic differential operators on manifolds
with boundary, or as spectral subspaces for self-adjoint elliptic differential
operators of odd order. Index formulas are obtained for operators in odd
subspaces on closed manifolds and for general boundary value problems. We prove
that the eta-invariant of operators of odd order on even-dimesional manifolds
is a dyadic rational number.Comment: 27 page
Elliptic operators in even subspaces
In the paper we consider the theory of elliptic operators acting in subspaces
defined by pseudodifferential projections. This theory on closed manifolds is
connected with the theory of boundary value problems for operators violating
Atiyah-Bott condition. We prove an index formula for elliptic operators in
subspaces defined by even projections on odd-dimensional manifolds and for
boundary value problems, generalizing the classical result of Atiyah-Bott.
Besides a topological contribution of Atiyah-Singer type, the index formulas
contain an invariant of subspaces defined by even projections. This homotopy
invariant can be expressed in terms of the eta-invariant. The results also shed
new light on P.Gilkey's work on eta-invariants of even-order operators.Comment: 39 pages, 2 figure
Parity effect in Al and Nb single electron transistors in a tunable environment
Two different types of Cooper pair transistors, with Al and Nb islands, have
been investigated in a tunable electromagnetic environment. The device with an
Al island demonstrates gate charge modulation with 2e-periodicity in a wide
range of environmental impedances at bath temperatures below 340 mK. Contrary
to the results of the Al sample, we were not able to detect 2e-periodicity
under any conditions on similar samples with Nb island. We attribute this to
the material properties of Nb.Comment: 3 pages, 3 figure
- …