Towards a dephasing diode: asymmetric and geometric dephasing

We study the effect of a noisy environment on spin and charge transport in ballistic quantum wires with spin-orbit coupling (Rashba coupling). We find that the wire then acts as a dephasing diode, inducing very different dephasing of the spins of right and left movers. We also show how Berry phase (geometric phase) in a curved wire can induce such asymmetric dephasing, in addition to purely geometric dephasing. We propose ways to measure these effects through spin detectors, spin-echo techniques, and Aharanov-Bohm interferometry.     

Random walks in varying dimensions

We establish recurrence criteria for sums of independent random variables which take values in Euclidean lattices of varying dimension. In particular, we describe transient inhomogeneous random walks in the plane which interlace two symmetric step distributions of bounded support.Research partially supported by the U.S. Army Research Office through the Mathematical Sciences Institute of Cornell University.Research supported in part by National Science Foundation Grant No. DMS 9300191, by a Sloan Foundation Fellowship, and by a Presidential Faculty Fellowship.     

Self-similar amplification in fiber Bragg gratings written in fiber amplifiers

We show, by using numerical simulations, that self-similar pulses with a duration on the order of few nanoseconds and an energy on the order of 10?μJ can be obtained at the output of a fiber Bragg grating (FBG) written in a fiber amplifier. The evolution of the amplified pulses is determined by the combined effect of Kerr nonlinearity, normal-dispersion, gain, and gain saturation, which limit the pulse energy. The output pulse mainly depends on the initial pulse energy rather than on the initial pulse profile. The reduced group velocity in FBGs can significantly increase the total gain for a given amplifier length. Hence we find that the proposed amplification scheme can be highly advantageous for amplification of nanosecond-scale pulses in fiber amplifiers.     

Boolean constant degree functions on the slice are juntas

We show that a Boolean degree $d$ function on the “slice” $\left(\genfrac{}{}{0ex}{}{\left[n\right]}{k}\right)?\{(x_1,\dots ,x_n)\in \{0,1\}:{\sum }_{i=1}^n{x}_i=k\}$ is a junta (depends on a constant number $\gamma \left(d\right)$ of coordinates), assuming that $k,n?k$ are large enough. This generalizes a classical result of Nisan and Szegedy on the hypercube ${\{0,1\}}^n$. Moreover, we show that the maximum number of coordinates that a Boolean degree $d$ function can depend on is the same on the slice and on the hypercube.     

Edward Teller, the Hungarian, American and Jew, too

As explained on p. 57 of George Marx’ comprehensive treatiseThe Voice of the Martians [1] (a pun on Leo Szilárd’sVoice of the Dolphins [2]), the titleThe Martians refers to another Szilárd joke, namely to his reply to a question of Fermi’s. In end-of-the-Century parlance, Fermi’s question would be formulated as follows: —With the galaxy presumably full of planetary systems, thereby also of life and thus of intelligence, where are all those extraterrestrials? [3] — to which Szilárd answered —They are among us, but they call themselves Hungarian… — One of these individuals of high intellectual stature, is (“let him be distinguished by a long life” as we would add in such cases by Jewish custom)Edward Teller.     

The Direction of Time: Seven Arrows for One Stream? A Program

I review the role of entropy in the Second Law of Thermodynamics in providing time with a direction and explaining irreversibility. I then list seven seemingly different features, each characterizing an additional arrow. In one case, connected to Black Hole Physics, the arrow has been successfully merged with the thermodynamical and may serve as model; in another case, that of the Evolutionary drive, the adequate function has been identified as complexity. We define the aims of the program and also provide information for an alternative, geometrical (effective) approach.     

Leptogenesis from supersymmetry breaking

We show that soft supersymmetry breaking terms involving the heavy sneutrinos can lead to sneutrino-antisneutrino mixing and to new sources of CP violation, which are present even if a single generation is considered. These terms are naturally present in supersymmetric versions of leptogenesis scenarios, and they induce indirect CP violation in the decays of the heavy sneutrinos, eventually generating a baryon asymmetry. This new contribution can be comparable to or even dominate over the asymmetry produced in traditional leptogenesis scenarios.     

Two-channel Kondo effect in a modified single electron transistor

We suggest a simple system of two electron droplets which should display two-channel Kondo behavior at experimentally accessible temperatures. Stabilization of the two-channel Kondo fixed point requires fine control of the electrochemical potential in each droplet, which can be achieved by adjusting voltages on nearby gate electrodes. We study the conditions for obtaining this type of two-channel Kondo behavior, discuss the experimentally observable consequences, and explore the generalization to the multichannel Kondo case.     

The sharp Hausdorff measure condition for length of projections

In a recent paper, Pertti Mattila asked which gauge functions have the property that for any Borel set with Hausdorff measure 0$">, the projection of to almost every line has positive length. We show that finiteness of , which is known to be sufficient for this property, is also necessary for regularly varying . Our proof is based on a random construction adapted to the gauge function.