Criticality and entanglement in random quantum systems

We review studies of entanglement entropy in systems with quenched randomness, concentrating on universal behavior at strongly random quantum critical points. The disorder-averaged entanglement entropy provides insight into the quantum criticality of these systems and an understanding of their relationship to non-random ("pure") quantum criticality. The entanglement near many such critical points in one dimension shows a logarithmic divergence in subsystem size, similar to that in the pure case but with a different universal coefficient. Such universal coefficients are examples of universal critical amplitudes in a random system. Possible measurements are reviewed along with the one-particle entanglement scaling at certain Anderson localization transitions. We also comment briefly on higher dimensions and challenges for the future.Comment: Review article for the special issue "Entanglement entropy in extended systems" in J. Phys.

Helical liquids and Majorana bound states in quantum wires

We show that the combination of spin-orbit coupling with a Zeeman field or strong interactions may lead to the formation of a helical liquid in single-channel quantum wires. In a helical liquid, electrons with opposite velocities have opposite spin precession. We argue that zero-energy Majorana bound states are formed in various situations when the wire is situated in proximity to a conventional s-wave superconductor. This occurs when the external magnetic field, the superconducting gap, or, in particular, the chemical potential vary along the wire. We discuss experimental consequences of the formation of the helical liquid and the Majorana bound states.Comment: 4+epsilon page

How Beliefs About HIV Status affect Risky Behaviors: Evidence From Malawi, Second Version

This paper examines how beliefs about own HIV status affect sexual behavior. Risky behavior is measured as the propensity to engage in extramarital affairs or not use condoms. The empirical analysis is based on 2004 and 2006 data from the Malawi Diffusion and Ideational Change Project. Controlling for endogeneity between beliefs and risk-taking, we find that downward revisions in the belief of being HIV positive lead to a lower propensity to engage in extramarital affairs but have no effect on condom use. We show that the estimates provide a lower bound when there is measurement error in reported extra-marital affairs.Beliefs,AIDS,Malawi

How Beliefs about HIV Status Affect Risky Behaviors: Evidence from Malawi, Second Version

This paper examines whether and to what extent changes in beliefs about own HIV status induce changes in risky sexual behavior using data from married males living in three regions of Malawi. Risky behavior is measured as the propensity to engage in extramarital affairs. The empirical analysis is based on panel surveys for years 2006 and 2008 from the Malawi Diffusion and Ideational Change Project (MDICP), which contain detailed information on beliefs about HIV status and on sexual behaviors. Many individuals change their beliefs over time, because of opportunities to get tested for HIV and informational campaigns. We estimate the effect of belief revisions on the propensity to engage in extra-marital affairs using a panel data estimator developed by Arellano and Carrasco (2003), which accommodates unobserved heterogeneity as well as belief endogeneity arising from the dependence of current beliefs on lagged behaviors. We find that downward revisions in the belief of being HIV positive lead to an increased propensity to engage in extra-marital affairs and upward revisions to a decreased propensity. The estimates are shown to be robust to underreporting of affairs. Using our estimates and a standard epidemeological model of disease transmission, we find that increasing the responsiveness of beliefs to test results would reduce the HIV transmission rate as infected individuals reduce sexual behavior and decrease the likelihood that uninfected persons have contact with an HIV-positive person.AIDS, Malawi, Beliefs