Decay of Correlations in Fermi Systems at Non-zero Temperature

The locality of correlation functions is considered for Fermi systems at non-zero temperature. We show that for all short-range, lattice Hamiltonians, the correlation function of any two fermionic operators decays exponentially with a correlation length which is of order the inverse temperature for small temperature. We discuss applications to numerical simulation of quantum systems at non-zero temperature.Comment: 3 pages, 0 figure

Lieb-Robinson Bounds and the Generation of Correlations and Topological Quantum Order

The Lieb-Robinson bound states that local Hamiltonian evolution in nonrelativistic quantum mechanical theories gives rise to the notion of an effective light cone with exponentially decaying tails. We discuss several consequences of this result in the context of quantum information theory. First, we show that the information that leaks out to spacelike separated regions is negligible and that there is a finite speed at which correlations and entanglement can be distributed. Second, we discuss how these ideas can be used to prove lower bounds on the time it takes to convert states without topological quantum order to states with that property. Finally, we show that the rate at which entropy can be created in a block of spins scales like the boundary of that block

No Child Left Behind: Estimating the Impact on Choices and Student Outcomes

Several recent education reform measures, including the federal No Child Left Behind Act (NCLB), couple school choice with accountability measures to allow parents of children in under-performing schools the opportunity to choose higher-performing schools. We use the introduction of NCLB in the Charlotte-Mecklenburg School District to determine if the choice component had an impact on the schools parents chose and if those changed choices led to academic gains. We find that 16% of parents responded to NCLB notification by choosing schools that had on average 1 standard deviation higher average test scores than their current NCLB school. We then use the lottery assignment of students to chosen schools to test if changed choices led to improved academic outcomes. On average, lottery winners experience a significant decline in suspension rates relative to lottery losers. We also find that students winning lotteries to attend substantially better (above-median) schools experience significant gains in test scores. Because proximity to high-scoring schools drives both the probability of choosing an alternative school and the average test score at the school chosen, our results suggest that the availability of proximate and high-scoring schools is an important factor in determining the degree to which school choice and accountability programs can succeed at increasing choice and immediate academic outcomes for students at under-performing schools.

Information, School Choice, and Academic Achievement: Evidence from Two Experiments

We analyze two experiments that provided direct information on school test scores to lower-income families in a public school choice plan. We find that receiving information significantly increases the fraction of parents choosing higher-performing schools. Parents with high-scoring alternatives nearby were more likely to choose non-guaranteed schools with higher test scores. Using random variation from each experiment, we find evidence that attending a higher-scoring school increases student test scores. The results imply that school choice will most effectively increase academic achievement for disadvantaged students when parents have easy access to test score information and have good options to choose from.

Disordered Topological Insulators via C∗C^*-Algebras

The theory of almost commuting matrices can be used to quantify topological obstructions to the existence of localized Wannier functions with time-reversal symmetry in systems with time-reversal symmetry and strong spin-orbit coupling. We present a numerical procedure that calculates a Z_2 invariant using these techniques, and apply it to a model of HgTe. This numerical procedure allows us to access sizes significantly larger than procedures based on studying twisted boundary conditions. Our numerical results indicate the existence of a metallic phase in the presence of scattering between up and down spin components, while there is a sharp transition when the system decouples into two copies of the quantum Hall effect. In addition to the Z_2 invariant calculation in the case when up and down components are coupled, we also present a simple method of evaluating the integer invariant in the quantum Hall case where they are decoupled.Comment: Added detail regarding the mapping of almost commuting unitary matrices to almost commuting Hermitian matrices that form an approximate representation of the sphere. 6 pages, 6 figure

Classification of the phases of 1D spin chains with commuting Hamiltonians

We consider the class of spin Hamiltonians on a 1D chain with periodic boundary conditions that are (i) translational invariant, (ii) commuting and (iii) scale invariant, where by the latter we mean that the ground state degeneracy is independent of the system size. We correspond a directed graph to a Hamiltonian of this form and show that the structure of its ground space can be read from the cycles of the graph. We show that the ground state degeneracy is the only parameter that distinguishes the phases of these Hamiltonians. Our main tool in this paper is the idea of Bravyi and Vyalyi (2005) in using the representation theory of finite dimensional C^*-algebras to study commuting Hamiltonians.Comment: 8 pages, improved readability, added exampl

Solving Gapped Hamiltonians Locally

We show that any short-range Hamiltonian with a gap between the ground and excited states can be written as a sum of local operators, such that the ground state is an approximate eigenvector of each operator separately. We then show that the ground state of any such Hamiltonian is close to a generalized matrix product state. The range of the given operators needed to obtain a good approximation to the ground state is proportional to the square of the logarithm of the system size times a characteristic "factorization length". Applications to many-body quantum simulation are discussed. We also consider density matrices of systems at non-zero temperature.Comment: 13 pages, 2 figures; minor changes to references, additional discussion of numerics; additional explanation of nonzero temperature matrix product for

An analytical and experimental evaluation of a Fresnel lens solar concentrator

An analytical and experimental evaluation of line focusing Fresnel lenses with application potential in the 200 to 370 C range was studied. Analytical techniques were formulated to assess the solar transmission and imaging properties of a grooves down lens. Experimentation was based on a 56 cm wide, f/1.0 lens. A Sun tracking heliostat provided a nonmoving solar source. Measured data indicated more spreading at the profile base than analytically predicted, resulting in a peak concentration 18 percent lower than the computed peak of 57. The measured and computed transmittances were 85 and 87 percent, respectively. Preliminary testing with a subsequent lens indicated that modified manufacturing techniques corrected the profile spreading problem and should enable improved analytical experimental correlation