115,215 research outputs found
Influence of e-e scattering on the temperature dependence of the resistance of a classical ballistic point contact in a two-dimensional electron system
We experimentally investigate the temperature (T) dependence of the
resistance of a classical ballistic point contact (PC) in a two-dimensional
electron system (2DES). The split-gate PC is realized in a high-quality
AlGaAs/GaAs heterostructure. The PC resistance is found to drop by more than
10% as T is raised from 0.5 K to 4.2 K. In the absence of a magnetic field, the
T dependence is roughly linear below 2 K and tends to saturate at higher T.
Perpendicular magnetic fields on the order of a few 10 mT suppress the
T-dependent contribution dR. This effect is more pronounced at lower
temperatures, causing a crossover to a nearly parabolic T dependence in a
magnetic field. The normalized magnetic field dependencies dR(B) permit an
empiric single parameter scaling in a wide range of PC gate voltages. These
observations give strong evidence for the influence of electron-electron (e-e)
scattering on the resistance of ballistic PCs. Our results are in qualitative
agreement with a recent theory of the e-e scattering based T dependence of the
conductance of classical ballistic PCs [ Phys. Rev. Lett. 101 216807 (2008) and
Phys. Rev. B 81 125316 (2010)].Comment: as publishe
On the variance of the number of occupied boxes
We consider the occupancy problem where balls are thrown independently at
infinitely many boxes with fixed positive frequencies. It is well known that
the random number of boxes occupied by the first n balls is asymptotically
normal if its variance V_n tends to infinity. In this work, we mainly focus on
the opposite case where V_n is bounded, and derive a simple necessary and
sufficient condition for convergence of V_n to a finite limit, thus settling a
long-standing question raised by Karlin in the seminal paper of 1967. One
striking consequence of our result is that the possible limit may only be a
positive integer number. Some new conditions for other types of behavior of the
variance, like boundedness or convergence to infinity, are also obtained. The
proofs are based on the poissonization techniques.Comment: 34 page
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