Introduction to determinantal point processes from a quantum probability viewpoint

Determinantal point processes on a measure space X whose kernels represent trace class Hermitian operators on L^2(X) are associated to "quasifree" density operators on the Fock space over L^2(X).Comment: Contributed to the proceedings of the 26th Conference on Quantum Probability and Infinite Dimensional Analysi

Convergence of continuous-time quantum walks on the line

The position density of a "particle" performing a continuous-time quantum walk on the integer lattice, viewed on length scales inversely proportional to the time t, converges (as t tends to infinity) to a probability distribution that depends on the initial state of the particle. This convergence behavior has recently been demonstrated for the simplest continuous-time random walk [see quant-ph/0408140]. In this brief report, we use a different technique to establish the same convergence for a very large class of continuous-time quantum walks, and we identify the limit distribution in the general case.Comment: Version to appear in Phys. Rev.

Evidence for pronounced quark loop effects in QCD

We have measured the hadron spectrum in lattice QCD, using staggered fermions, for 0 (the quenched approximation), 2 and 4 light degenerate dynamical quarks. In addition to earlier results involving extrapolations in valence quark masses for fixed dynamical mass, we also report results where we extrapolate in the dynamical mass for 4 flavors. We see a marked difference in the hadron spectrum for 2 and 4 flavors; the hadron spectrum is nearly parity doubled for 4 flavors, indicating smaller effects of chiral symmetry breaking. This pronounced effect in the hadron spectrum cannot be removed by a simple change in scale as the number of light quark flavors is changed. Further simulations at larger volume are needed to rule out finite volume effects.Comment: 5 pages, 4 figures. Presented at Lattice QCD on Parallel Computers, Tsukuba, Japan, march 199

Generalized Du Fort-Frankel methods for parabolic initial boundary value problems

The Du Fort-Frankel difference scheme is generalized to difference operators of arbitrary high order accuracy in space and to arbitrary order of the parabolic differential operator. Spectral methods can also be used to approximate the spatial part of the differential operator. The scheme is explicit, and it is unconditionally stable for the initial value problem. Stable boundary conditions are given for two different fourth order accurate space approximations

On the Navier-Stokes equations with constant total temperature

For various applications in fluid dynamics, it is assumed that the total temperature is constant. Therefore, the energy equation can be replaced by an algebraic relation. The resulting set of equations in the inviscid case is analyzed. It is shown that the system is strictly hyperbolic and well posed for the initial value problems. Boundary conditions are described such that the linearized system is well posed. The Hopscotch method is investigated and numerical results are presented