Electronic Mach-Zehnder interferometer as a tool to probe fractional statistics

We study transport through an electronic Mach-Zehnder interferometer recently devised at the Weizmann Institute. We show that this device can be used to probe statistics of quasiparticles in the fractional quantum Hall regime. We calculate the tunneling current through the interferometer as the function of the Aharonov-Bohm flux, temperature and voltage bias, and demonstrate that its flux-dependent component is strongly sensitive to the statistics of tunneling quasiparticles. More specifically, the flux-dependent and flux-independent contributions to the current are related by a power law, the exponent being a function of the quasiparticle statistics.Comment: 22 pages; 8 figure

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.Comment: 4 pages (2 fig) v2: extensive improvements to "readability" & references adde

Shot Noise in Anyonic Mach-Zehnder Interferometer

We show how shot noise in an electronic Mach-Zehnder interferometer in the fractional quantum Hall regime probes the charge and statistics of quantum Hall quasiparticles. The dependence of the noise on the magnetic flux through the interferometer allows for a simple way to distinguish Abelian from non-Abelian quasiparticle statistics. In the Abelian case, the Fano factor (in units of the electron charge) is always lower than unity. In the non-Abelian case, the maximal Fano factor as a function of the magnetic flux exceeds one.Comment: references adde

Dimer coverings on the Sierpinski gasket with possible vacancies on the outmost vertices

We present the number of dimers $N_d(n)$ on the Sierpinski gasket $SG_d(n)$ at stage $n$ with dimension $d$ equal to two, three, four or five, where one of the outmost vertices is not covered when the number of vertices $v(n)$ is an odd number. The entropy of absorption of diatomic molecules per site, defined as $S_{SG_d}=\lim_{n \to \infty} \ln N_d(n)/v(n)$, is calculated to be $\ln(2)/3$ exactly for $SG_2(n)$. The numbers of dimers on the generalized Sierpinski gasket $SG_{d,b}(n)$ with $d=2$ and $b=3,4,5$ are also obtained exactly. Their entropies are equal to $\ln(6)/7$, $\ln(28)/12$, $\ln(200)/18$, respectively. The upper and lower bounds for the entropy are derived in terms of the results at a certain stage for $SG_d(n)$ with $d=3,4,5$. As the difference between these bounds converges quickly to zero as the calculated stage increases, the numerical value of $S_{SG_d}$ with $d=3,4,5$ can be evaluated with more than a hundred significant figures accurate.Comment: 35 pages, 20 figures and 1 tabl

Metric characterization of cluster dynamics on the Sierpinski gasket

We develop and implement an algorithm for the quantitative characterization of cluster dynamics occurring on cellular automata defined on an arbitrary structure. As a prototype for such systems we focus on the Ising model on a finite Sierpsinski Gasket, which is known to possess a complex thermodynamic behavior. Our algorithm requires the projection of evolving configurations into an appropriate partition space, where an information-based metrics (Rohlin distance) can be naturally defined and worked out in order to detect the changing and the stable components of clusters. The analysis highlights the existence of different temperature regimes according to the size and the rate of change of clusters. Such regimes are, in turn, related to the correlation length and the emerging "critical" fluctuations, in agreement with previous thermodynamic analysis, hence providing a non-trivial geometric description of the peculiar critical-like behavior exhibited by the system. Moreover, at high temperatures, we highlight the existence of different time scales controlling the evolution towards chaos.Comment: 20 pages, 8 figure