Entanglement entropy of dispersive media from thermodynamic entropy in one higher dimension

A dispersive medium becomes entangled with zero-point fluctuations in the vacuum. We consider an arbitrary array of material bodies weakly interacting with a quantum field and compute the quantum mutual information between them. It is shown that the mutual information in D dimensions can be mapped to classical thermodynamic entropy in D+1 dimensions. As a specific example, we compute the mutual information both analytically and numerically for a range of separation distances between two bodies in D=2 dimensions and find a logarithmic correction to the area law at short separations. A key advantage of our method is that it allows the strong subadditivity property---notoriously difficult to prove for quantum systems---to be easily verified.Comment: Corrected typos. Added reference

On the Complexity of Quantum ACC

For any $q > 1$, let \MOD_q be a quantum gate that determines if the number of 1's in the input is divisible by $q$. We show that for any $q,t > 1$, \MOD_q is equivalent to \MOD_t (up to constant depth). Based on the case $q=2$, Moore \cite{moore99} has shown that quantum analogs of AC$^{(0)}$, ACC$[q]$, and ACC, denoted QAC$^{(0)}_{wf}$, QACC$[2]$, QACC respectively, define the same class of operators, leaving $q > 2$ as an open question. Our result resolves this question, proving that QAC$^{(0)}_{wf} =$ QACC$[q] =$ QACC for all $q$. We also develop techniques for proving upper bounds for QACC in terms of related language classes. We define classes of languages EQACC, NQACC and BQACC_{\rats}. We define a notion $\log$-planar QACC operators and show the appropriately restricted versions of EQACC and NQACC are contained in P/poly. We also define a notion of $\log$-gate restricted QACC operators and show the appropriately restricted versions of EQACC and NQACC are contained in TC$^{(0)}$. To do this last proof, we show that TC$^{(0)}$ can perform iterated addition and multiplication in certain field extensions. We also introduce the notion of a polynomial-size tensor graph and show that families of such graphs can encode the amplitudes resulting from apply an arbitrary QACC operator to an initial state.Comment: 22 pages, 4 figures This version will appear in the July 2000 Computational Complexity conference. Section 4 has been significantly revised and many typos correcte

Nanoplasmonic near-field synthesis

The temporal response of resonances in nanoplasmonic structures typically converts an incoming few-cycle field into a much longer near-field at the spot where non-linear physical phenomena including electron emission, recollision and high-harmonic generation can take place. We show that for practically useful structures pulse shaping of the incoming pulse can be used to synthesize the plasmon-enhanced field and enable single-cycle driven nonlinear physical phenomena. Our method is demonstrated for the generation of an isolated attosecond pulse by plasmon-enhanced high harmonic generation. We furthermore show that optimal control techniques can be used even if the response of the plasmonic structure is not known a priori.Comment: 6 page

Serrated wire for welded wire fabric

The Wire Reinforcement Institute, Inc., is concerned, primarily, with gathering data and technical information to substantiate the following: That welded wire fabric, when used as a reinforcement in concrete, distributes the stresses throughout the concrete slab, as has been maintained by engineers during the past 40 years. That welded wire fabric provides adequate crack control within the working limits of the fabric. In order to efficiently accomplish Objectives 1 and 2 above, we wish to establish: The safe working stress that we can safely recommend for welded wire fabric -- both in bond and tension. The proper spacing of longitudinal and transverse wires --Object of Test, page 11

What You Do in High School Matters: The Effects of High School GPA on Educational Attainment and Labor Market Earnings in Adulthood

Using abstracted grades and other data from Add Health, we investigate the effects of cumulative high school GPA on educational attainment and labor market earnings among a sample of young adults (ages 24-34). We estimate several models with an extensive list of control variables and high school fixed effects. Results consistently show that high school GPA is a positive and statistically significant predictor of educational attainment and earnings in adulthood. Moreover, the effects are large and economically important for each gender. Interesting and somewhat unexpected findings emerge for race. Various sensitivity tests support the stability of the core findings.High school grades; Educational attainment; Earnings; Panel data