8,051 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
Heat Conduction in One-Dimensional chain of Hard Discs with Substrate Potential
Heat conduction of one-dimensional chain of equivalent rigid particles in the
field of external on-site potential is considered. Zero diameters of the
particles correspond to exactly integrable case with divergent heat conduction
coefficient. By means of simple analytical model it is demonstrated that for
any nonzero particle size the integrability is violated and the heat conduction
coefficient converges. The result of the analytical computation is verified by
means of numerical simulation in a plausible diapason of parameters and good
agreement is observedComment: 14 pages, 7 figure
Symmetry breaking in the self-consistent Kohn-Sham equations
The Kohn-Sham (KS) equations determine, in a self-consistent way, the
particle density of an interacting fermion system at thermal equilibrium. We
consider a situation when the KS equations are known to have a unique solution
at high temperatures and this solution is a uniform particle density. We show
that, at zero temperature, there are stable solutions that are not uniform. We
provide the general principles behind this phenomenon, namely the conditions
when it can be observed and how to construct these non-uniform solutions. Two
concrete examples are provided, including fermions on the sphere which are
shown to crystallize in a structure that resembles the C molecule.Comment: a few typos eliminate
Intervalley-Scattering Induced Electron-Phonon Energy Relaxation in Many-Valley Semiconductors at Low Temperatures
We report on the effect of elastic intervalley scattering on the energy
transport between electrons and phonons in many-valley semiconductors. We
derive a general expression for the electron-phonon energy flow rate at the
limit where elastic intervalley scattering dominates over diffusion. Electron
heating experiments on heavily doped n-type Si samples with electron
concentration in the range m are performed at
sub-1 K temperatures. We find a good agreement between the theory and the
experiment.Comment: v2: Notations changed: --> ,
removed. Eq. (1) changed, Eq. (2) added and complete derivation of Eq. (3)
included. Some further discussion about single vs. many valley added [3rd
paragraph after Eq. (7)]. End notes removed and new reference added [Kragler
and Thomas]. Typos in references correcte
Dielectronic recombination data for astrophysical applications: Plasma rate-coefficients for Fe^q+ (q=7-10, 13-22) and Ni^25+ ions from storage-ring experiments
This review summarizes the present status of an ongoing experimental effort
to provide reliable rate coefficients for dielectronic recombination of highly
charged iron ions for the modeling of astrophysical and other plasmas. The
experimental work has been carried out over more than a decade at the heavy-ion
storage-ring TSR of the Max-Planck-Institute for Nuclear Physics in Heidelberg,
Germany. The experimental and data reduction procedures are outlined. The role
of previously disregarded processes such as fine-structure core excitations and
trielectronic recombination is highlighted. Plasma rate coefficients for
dielectronic recombination of Fe^q+ ions (q=7-10, 13-22) and Ni^25+ are
presented graphically and in a simple parameterized form allowing for easy use
in plasma modeling codes. It is concluded that storage-ring experiments are
presently the only source for reliable low-temperature dielectronic
recombination rate-coefficients of complex ions.Comment: submitted for publication in the International Review of Atomic and
Molecular Physics, 8 figures, 3 tables, 68 reference
Cold electron Josephson transistor
A superconductor-normal metal-superconductor mesoscopic Josephson junction
has been realized in which the critical current is tuned through normal current
injection using a symmetric electron cooler directly connected to the weak
link. Both enhancement of the critical current by more than a factor of two,
and supercurrent suppression have been achieved by varying the cooler bias.
Furthermore, this transistor-like device demonstrates large current gain
20) and low power dissipation
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
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