15,343 research outputs found
Quantum Hall Conductivity in a Landau Type Model with a Realistic Geometry
In this paper, we revisit some quantum mechanical aspects related to the
Quantum Hall Effect. We consider a Landau type model, paying a special
attention to the experimental and geometrical features of Quantum Hall
experiments. The resulting formalism is then used to compute explicitely the
Hall conductivity from a Kubo formula.Comment: LaTeX, 1 eps figur
Two qubit copying machine for economical quantum eavesdropping
We study the mapping which occurs when a single qubit in an arbitrary state
interacts with another qubit in a given, fixed state resulting in some unitary
transformation on the two qubit system which, in effect, makes two copies of
the first qubit. The general problem of the quality of the resulting copies is
discussed using a special representation, a generalization of the usual Schmidt
decomposition, of an arbitrary two-dimensional subspace of a tensor product of
two 2-dimensional Hilbert spaces. We exhibit quantum circuits which can
reproduce the results of any two qubit copying machine of this type. A simple
stochastic generalization (using a ``classical'' random signal) of the copying
machine is also considered. These copying machines provide simple embodiments
of previously proposed optimal eavesdropping schemes for the BB84 and B92
quantum cryptography protocols.Comment: Minor changes. 26 pages RevTex including 7 PS figure
Interaction broadening of Wannier functions and Mott transitions in atomic BEC
Superfluid to Mott-insulator transitions in atomic BEC in optical lattices
are investigated for the case of number of atoms per site larger than one. To
account for mean field repulsion between the atoms in each well, we construct
an orthogonal set of Wannier functions. The resulting hopping amplitude and
on-site interaction may be substantially different from those calculated with
single-atom Wannier functions. As illustrations of the approach we consider
lattices of various dimensionality and different mean occupations. We find that
in three-dimensional optical lattices the correction to the critical lattice
depth is significant to be measured experimentally even for small number of
atoms. Finally, we discuss validity of the single band model.Comment: A co-author(AMD) added, paper lengthened (7 pages, 8 figures now) to
extend the description of the method and add discussion of its validit
Vanishing viscosity limits for the degenerate lake equations with Navier boundary conditions
The paper is concerned with the vanishing viscosity limit of the
two-dimensional degenerate viscous lake equations when the Navier slip
conditions are prescribed on the impermeable boundary of a simply connected
bounded regular domain. When the initial vorticity is in the Lebesgue space
with , we show the degenerate viscous lake equations
possess a unique global solution and the solution converges to a corresponding
weak solution of the inviscid lake equations. In the special case when the
vorticity is in , an explicit convergence rate is obtained
Non-adiabaticity and single-electron transport driven by surface acoustic waves
Single-electron transport driven by surface acoustic waves (SAW) through a
narrow constriction, formed in two-dimensional electron gas, is studied
theoretically. Due to long-range Coulomb interaction, the tunneling coupling
between the electron gas and the moving minimum of the SAW-induced potential
rapidly decays with time. As a result, nonadiabaticiy sets a limit for the
accuracy of the quantization of acoustoelectric current
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