Minimum-correlation mixed quantum states

We consider states leading to the equality sign in the uncertainty inequalities associated with correlations in open quantum systems which have been recently derived by Ponomarenko and Wolf [Phys. Rev. A 63, 062106 (2001)]. The new inequalities involve fluctuations defined in terms of the square of the density operator that characterizes mixed states. We find the minimum-correlation states associated with the quadratures of single-mode and two-mode electromagnetic fields in a cavity and for the angular momentum operators which can describe atomic degrees of freedom. We show that while in the case of single-mode quadratures the functional form of the minimum-correlation state is uniquely specified, this is not so for the other pairs of noncommuting operators. In general, the states with the least amount of correlations are mixed and they exhibit squeezing

Quantum critical behaviour of the plateau-insulator transition in the quantum Hall regime

High-field magnetotransport experiments provide an excellent tool to investigate the plateau-insulator phase transition in the integral quantum Hall effect. Here we review recent low-temperature high-field magnetotransport studies carried out on several InGaAs/InP heterostructures and an InGaAs/GaAs quantum well. We find that the longitudinal resistivity $\rho_{xx}$ near the critical filling factor $\nu_{c}$ ~ 0.5 follows the universal scaling law $\rho_{xx}(\nu, T) \propto exp[-\Delta \nu/(T/T_{0})^{\kappa}]$, where $\Delta \nu =\nu -\nu_{c}$. The critical exponent $\kappa$ equals $0.56 \pm 0.02$, which indicates that the plateau-insulator transition falls in a non-Fermi liquid universality class.Comment: 8 pages, accepted for publication in Proceedings of the Yamada Conference LX on Research in High Magnetic Fields (August 16-19, 2006, Sendai

Fractional charge in transport through a 1D correlated insulator of finite length

Transport through a one channel wire of length $L$ confined between two leads is examined when the 1D electron system has an energy gap $2M$: $M > T_L \equiv v_c/L$ induced by the interaction in charge mode ($v_c$: charge velocity in the wire). In spinless case the transformation of the leads electrons into the charge density wave solitons of fractional charge $q$ entails a non-trivial low energy crossover from the Fermi liquid behavior below the crossover energy $T_x \propto \sqrt{T_L M} e^{-M /[T_L(1-q^2)]}$ to the insulator one with the fractional charge in current vs. voltage, conductance vs. temperature, and in shot noise. Similar behavior is predicted for the Mott insulator of filling factor $\nu = integer/(2 m')$.Comment: 5 twocolumn pages in RevTex, no figure

Threshold features in transport through a 1D constriction

Suppression of electron current $\Delta I$ through a 1D channel of length $L$ connecting two Fermi liquid reservoirs is studied taking into account the Umklapp electron-electron interaction induced by a periodic potential. This interaction causes Hubbard gaps $E_H$ for $L \to \infty$. In the perturbative regime where $E_H \ll v_c/L$ ($v_c:$ charge velocity), and for small deviations $\delta n$ of the electron density from its commensurate values $- \Delta I/V$ can diverge with some exponent as voltage or temperature $V,T$ decreases above $E_c=max(v_c/L,v_c \delta n)$, while it goes to zero below $E_c$. This results in a nonmonotonous behavior of the conductance.Comment: Final variant published in PRL, 79, 1714; minor correction

Construction Materials with Tailings of Quartzite Enrichment

The composition and properties of the tailings of quartzite enrichment of "Gora Karaul'naya"deposit, the possibility of its using as an aggregate in the composition of heavy and fine-aggregate concrete and dry construction mixture were determined. The introduction of quartzite tailings increases the water demand of the mixture, reduces the compressive strength of concrete and mortar, increases the bending strength compared to quartz sand. © Published under licence by IOP Publishing Ltd

The New White Flight

White charter school enclaves—defined as charter schools located in school districts that are thirty percent or less white, but that enroll a student body that is fifty percent or greater white— are emerging across the country. The emergence of white charter school enclaves is the result of a sobering and ugly truth: when given a choice, white parents as a collective tend to choose racially segregated, predominately white schools. Empirical research supports this claim. Empirical research also demonstrates that white parents as a collective will make that choice even when presented with the option of a more racially diverse school that is of good academic quality. Despite the connection between collective white parental choice and school segregation, greater choice continues to be injected into the school assignment process. School choice assignment policies, particularly charter schools, are proliferating at a substantial rate. As a result, parental choice rather than systemic design is creating new patterns of racial segregation and inequality in public schools. Yet the Supreme Court’s school desegregation jurisprudence insulates racial segregation in schools ostensibly caused by parental choice rather than systemic design from regulation. Consequently, the new patterns of racial segregation in public schools caused by collective white parental choice largely escapes regulation by courts. This article argues that the time has come to reconsider the legal and normative viability of regulating racial segregation in public schools caused by collective white parental choice. The article makes two important contributions to the legal literature on school desegregation. First, using white charter school enclaves as an example, it documents the ways in which school choice policies are being used to allow whites as a collective to satisfy their preference for segregated predominately white schools. Second, the article sets forth both constitutional and normative arguments for regulating the private choices that result in stark racial segregation patterns in public schools

Negative local resistance caused by viscous electron backflow in graphene

Graphene hosts a unique electron system in which electron-phonon scattering is extremely weak but electron-electron collisions are sufficiently frequent to provide local equilibrium above liquid nitrogen temperature. Under these conditions, electrons can behave as a viscous liquid and exhibit hydrodynamic phenomena similar to classical liquids. Here we report strong evidence for this transport regime. We find that doped graphene exhibits an anomalous (negative) voltage drop near current injection contacts, which is attributed to the formation of submicrometer-size whirlpools in the electron flow. The viscosity of graphene's electron liquid is found to be ~0.1 m$^2$ /s, an order of magnitude larger than that of honey, in agreement with many-body theory. Our work shows a possibility to study electron hydrodynamics using high quality graphene