597 research outputs found
Quantum oscillations and decoherence due to electron-electron interaction in metallic networks and hollow cylinders
We have studied the quantum oscillations of the conductance for arrays of
connected mesoscopic metallic rings, in the presence of an external magnetic
field. Several geometries have been considered: a linear array of rings
connected with short or long wires compared to the phase coherence length,
square networks and hollow cylinders. Compared to the well-known case of the
isolated ring, we show that for connected rings, the winding of the Brownian
trajectories around the rings is modified, leading to a different harmonics
content of the quantum oscillations. We relate this harmonics content to the
distribution of winding numbers. We consider the limits where coherence length
is small or large compared to the perimeter of each ring
constituting the network. In the latter case, the coherent diffusive
trajectories explore a region larger than , whence a network dependent
harmonics content. Our analysis is based on the calculation of the spectral
determinant of the diffusion equation for which we have a simple expression on
any network. It is also based on the hypothesis that the time dependence of the
dephasing between diffusive trajectories can be described by an exponential
decay with a single characteristic time (model A) .
At low temperature, decoherence is limited by electron-electron interaction,
and can be modelled in a one-electron picture by the fluctuating electric field
created by other electrons (model B). It is described by a functional of the
trajectories and thus the dependence on geometry is crucial. Expressions for
the magnetoconductance oscillations are derived within this model and compared
to the results of model A. It is shown that they involve several
temperature-dependent length scales.Comment: 35 pages, revtex4, 25 figures (34 pdf files
State Sum Models and Simplicial Cohomology
We study a class of subdivision invariant lattice models based on the gauge
group , with particular emphasis on the four dimensional example. This
model is based upon the assignment of field variables to both the - and
-dimensional simplices of the simplicial complex. The property of
subdivision invariance is achieved when the coupling parameter is quantized and
the field configurations are restricted to satisfy a type of mod- flatness
condition. By explicit computation of the partition function for the manifold
, we establish that the theory has a quantum Hilbert space
which differs from the classical one.Comment: 28 pages, Latex, ITFA-94-13, (Expanded version with two new sections
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