Suppression of Shot Noise in Quantum Point Contacts in the "0.7" Regime

Experimental investigations of current shot noise in quantum point contacts show a reduction of the noise near the 0.7 anomaly. It is demonstrated that such a reduction naturally arises in a model proposed recently to explain the characteristics of the 0.7 anomaly in quantum point contacts in terms of a quasi-bound state, due to the emergence of two conducting channels. We calculate the shot noise as a function of temperature, applied voltage and magnetic field, and demonstrate an excellent agreement with experiments. It is predicted that with decreasing temperature, voltage and magnetic field, the dip in the shot noise is suppressed due to the Kondo effect.Comment: 4 pages, 1 figur

A Variational Ground-State for the ν=2/3\nu=2/3 Fractional Quantum Hall Regime

A variational $\nu=2/3$ state, which unifies the sharp edge picture of MacDonald with the soft edge picture of Chang and of Beenakker is presented and studied in detail. Using an exact relation between correlation functions of this state and those of the Laughlin $\nu=1/3$ wavefunction, the correlation functions of the $\nu=2/3$ state are determined via a classical Monte Carlo calculation, for systems up to $50$ electrons. It is found that as a function of the slope of the confining potential there is a sharp transition of the ground state from one description to the other. This transition should be observable in tunneling experiments through quantum dots.Comment: 14 pages + 4 uuencoded figure

Descent, fields of invariants and generic forms via symmetric monoidal categories

Let $W$ be a finite dimensional algebraic structure (e.g. an algebra) over a field $K$ of characteristic zero. We study forms of $W$ by using Deligne's Theory of symmetric monoidal categories. We construct a category $\mathcal{C}_W$, which gives rise to a subfield $K_0\subseteq K$, which we call the field of invariants of $W$. This field will be contained in any subfield of $K$ over which $W$ has a form. The category $\mathcal{C}_W$ is a $K_0$-form of $Rep_{\bar{K}}(Aut(W))$, and we use it to construct a generic form $\widetilde{W}$ over a commutative $K_0$ algebra $B_W$ (so that forms of $W$ are exactly the specializations of $\widetilde{W}$). This generalizes some generic constructions for central simple algebras and for $H$-comodule algebras. We give some concrete examples arising from associative algebras and $H$-comodule algebras. As an application, we also explain how can one use the construction to classify two-cocycles on some finite dimensional Hopf algebras.Comment: 47 pages. A more detailed description of the kernel completion was adde

Plurality Voting under Uncertainty

Understanding the nature of strategic voting is the holy grail of social choice theory, where game-theory, social science and recently computational approaches are all applied in order to model the incentives and behavior of voters. In a recent paper, Meir et al.[EC'14] made another step in this direction, by suggesting a behavioral game-theoretic model for voters under uncertainty. For a specific variation of best-response heuristics, they proved initial existence and convergence results in the Plurality voting system. In this paper, we extend the model in multiple directions, considering voters with different uncertainty levels, simultaneous strategic decisions, and a more permissive notion of best-response. We prove that a voting equilibrium exists even in the most general case. Further, any society voting in an iterative setting is guaranteed to converge. We also analyze an alternative behavior where voters try to minimize their worst-case regret. We show that the two behaviors coincide in the simple setting of Meir et al., but not in the general case.Comment: The full version of a paper from AAAI'15 (to appear

The cohomological restriction map and FP-infinity groups

We ask, following Bartholdi, whether it is true that the kernel of the restriction map from the cohomology of a group G to the cohomology of a finite index subgroup H is finitely generated as an ideal. We show that in case the group has virtual finite cohomological dimension it is true, and we will show that if G does not have virtual finite cohomological dimension it might not be true, even in case G is an FP infinity group.Comment: 17 pagee