A study of the factors of mimicry.

Thesis (Ed.M.)--Boston Universit

Ground state entanglement and geometric entropy in the Kitaev's model

We study the entanglement properties of the ground state in Kitaev's model. This is a two-dimensional spin system with a torus topology and nontrivial four-body interactions between its spins. For a generic partition $(A,B)$ of the lattice we calculate analytically the von Neumann entropy of the reduced density matrix $\rho_A$ in the ground state. We prove that the geometric entropy associated with a region $A$ is linear in the length of its boundary. Moreover, we argue that entanglement can probe the topology of the system and reveal topological order. Finally, no partition has zero entanglement and we find the partition that maximizes the entanglement in the given ground state.Comment: 4 pages, one fig, ReVTeX 4; updated to the published versio

Large Fourier transforms never exactly realized by braiding conformal blocks

Fourier transform is an essential ingredient in Shor's factoring algorithm. In the standard quantum circuit model with the gate set \{\U(2), \textrm{CNOT}\}, the discrete Fourier transforms $F_N=(\omega^{ij})_{N\times N},i,j=0,1,..., N-1, \omega=e^{\frac{2\pi i}{N}}$, can be realized exactly by quantum circuits of size $O(n^2), n=\textrm{log}N$, and so can the discrete sine/cosine transforms. In topological quantum computing, the simplest universal topological quantum computer is based on the Fibonacci (2+1)-topological quantum field theory (TQFT), where the standard quantum circuits are replaced by unitary transformations realized by braiding conformal blocks. We report here that the large Fourier transforms $F_N$ and the discrete sine/cosine transforms can never be realized exactly by braiding conformal blocks for a fixed TQFT. It follows that approximation is unavoidable to implement the Fourier transforms by braiding conformal blocks

Differential Renormalization of Massive Quantum Field Theories

We extend the method of differential renormalization to massive quantum field theories treating in particular \ph4-theory and QED. As in the massless case, the method proves to be simple and powerful, and we are able to find, in particular, compact explicit coordinate space expressions for the finite parts of two notably complicated diagrams, namely, the 2-loop 2-point function in \ph4 and the 1-loop vertex in QED.Comment: 8 pages(LaTex, no figures

Nonperturbative Formulas for Central Functions of Supersymmetric Gauge Theories

For quantum field theories that flow between ultraviolet and infrared fixed points, central functions, defined from two-point correlators of the stress tensor and conserved currents, interpolate between central charges of the UV and IR critical theories. We develop techniques that allow one to calculate the flows of the central charges and that of the Euler trace anomaly coefficient in a general N=1 supersymmetric gauge theory. Exact, explicit formulas for $SU(N_c)$ gauge theories in the conformal window are given and analysed. The Euler anomaly coefficient always satisfies the inequality $$. This is new evidence in strongly coupled theories that this quantity satisfies a four-dimensional analogue of the $c$-theorem, supporting the idea of irreversibility of the RG flow. Various other implications are discussed.Comment: latex, 27 page

Half-Life of 14^{14}O

We have measured the half-life of $^{14}$O, a superallowed $(0^{+} \to 0^{+})$ $\beta$ decay isotope. The $^{14}$O was produced by the $^{12}$C($^{3}$He,n)$^{14}$O reaction using a carbon aerogel target. A low-energy ion beam of $^{14}$O was mass separated and implanted in a thin beryllium foil. The beta particles were counted with plastic scintillator detectors. We find $t_{1/2} = 70.696\pm 0.052$ s. This result is $1.5\sigma$ higher than an average value from six earlier experiments, but agrees more closely with the most recent previous measurement.Comment: 10 pages, 5 figure