474 research outputs found
Phase transitions in soft-committee machines
Equilibrium statistical physics is applied to layered neural networks with
differentiable activation functions. A first analysis of off-line learning in
soft-committee machines with a finite number (K) of hidden units learning a
perfectly matching rule is performed. Our results are exact in the limit of
high training temperatures. For K=2 we find a second order phase transition
from unspecialized to specialized student configurations at a critical size P
of the training set, whereas for K > 2 the transition is first order. Monte
Carlo simulations indicate that our results are also valid for moderately low
temperatures qualitatively. The limit K to infinity can be performed
analytically, the transition occurs after presenting on the order of N K
examples. However, an unspecialized metastable state persists up to P= O (N
K^2).Comment: 8 pages, 4 figure
A Laterally Modulated 2D Electron System in the Extreme Quantum Limit
We report on magnetotransport of a two-dimensional electron system (2DES),
located 32 nm below the surface, with a surface superlattice gate structure of
periodicity 39 nm imposing a periodic modulation of its potential. For low
Landau level fillings , the diagonal resistivity displays a rich pattern
of fluctuations, even though the disorder dominates over the periodic
modulation. Theoretical arguments based on the combined effects of the
long-wavelength, strong disorder and the short-wavelength, weak periodic
modulation present in the 2DES qualitatively explain the data.Comment: 4 pages, 5 figures. to appear in Phys. Rev. Let
Light scattering from a periodically modulated two dimensional electron gas with partially filled Landau levels
We study light scattering from a periodically modulated two dimensional
electron gas in a perpendicular magnetic field. If a subband is partially
filled, the imaginary part of the dielectric function as a function of
frequency contains additional discontinuities to the case of completely filled
subbands. The positions of the discontinuities may be determined from the
partial filling factor and the height of the discontinuity can be directly
related to the modulation potential. The light scattering cross section
contains a new peak which is absent for integer filling.Comment: RevTex, 4 figures. To appear in Phys. Rev. B as a brief repor
Monitoring of tritium purity during long-term circulation in the KATRIN test experiment LOOPINO using laser Raman spectroscopy
The gas circulation loop LOOPINO has been set up and commissioned at Tritium
Laboratory Karlsruhe (TLK) to perform Raman measurements of circulating tritium
mixtures under conditions similar to the inner loop system of the neutrino-mass
experiment KATRIN, which is currently under construction. A custom-made
interface is used to connect the tritium containing measurement cell, located
inside a glove box, with the Raman setup standing on the outside. A tritium
sample (purity > 95%, 20 kPa total pressure) was circulated in LOOPINO for more
than three weeks with a total throughput of 770 g of tritium. Compositional
changes in the sample and the formation of tritiated and deuterated methanes
CT_(4-n)X_n (X=H,D; n=0,1) were observed. Both effects are caused by hydrogen
isotope exchange reactions and gas-wall interactions, due to tritium {\beta}
decay. A precision of 0.1% was achieved for the monitoring of the T_2
Q_1-branch, which fulfills the requirements for the KATRIN experiment and
demonstrates the feasibility of high-precision Raman measurements with tritium
inside a glove box
Duality Relation among Periodic Potential Problems in the Lowest Landau Level
Using a momentum representation of a magnetic von Neumann lattice, we study a
two-dimensional electron in a uniform magnetic field and obtain one-particle
spectra of various periodic short-range potential problems in the lowest Landau
level.We find that the energy spectra satisfy a duality relation between a
period of the potential and a magnetic length. The energy spectra consist of
the Hofstadter-type bands and flat bands. We also study the connection between
a periodic short-range potential problem and a tight-binding model.Comment: 6 pages, 3 figures, final version to appear in PR
Magnetization in short-period mesoscopic electron systems
We calculate the magnetization of the two-dimensional electron gas in a
short-period lateral superlattice, with the Coulomb interaction included in
Hartree and Hartree-Fock approximations. We compare the results for a finite,
mesoscopic system modulated by a periodic potential, with the results for the
infinite periodic system. In addition to the expected strong exchange effects,
the size of the system, the type and the strength of the lateral modulation
leave their fingerprints on the magnetization.Comment: RevTeX4, 10 pages with 14 included postscript figures To be published
in PRB. Replaced to repair figure
Bloch Electrons in a Magnetic Field - Why Does Chaos Send Electrons the Hard Way?
We find that a 2D periodic potential with different modulation amplitudes in
x- and y-direction and a perpendicular magnetic field may lead to a transition
to electron transport along the direction of stronger modulation and to
localization in the direction of weaker modulation. In the experimentally
accessible regime we relate this new quantum transport phenomenon to avoided
band crossing due to classical chaos.Comment: 4 pages, 3 figures, minor modifications, PRL to appea
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