Fermions in spherical field theory

We derive the spherical field formalism for fermions. We find that the spherical field method is free from certain difficulties which complicate lattice calculations, such as fermion doubling, missing axial anomalies, and computational problems regarding internal fermion loops.Comment: corrected journal inf

Nonpropagation of tachyon on the BTZ black hole in type 0B string theory

We obtain the BTZ black hole (AdS$_3 \times$S$^3$) as a non-dilatonic solution from type 0B string theory. Analyzing the perturbation around this black hole background, we show that the tachyon is not a propagating mode.Comment: some detailed explanations are added, modified version will be appeared in Physics Letters B, 11 pages in RevTeX, no figure

Stability of g-modes in rotating B-type stars

We have studied the stability of low degree $g$-modes in uniformly rotating B-type stars, taking into account the effects of the Coriolis force and the rotational deformation. From an analysis treating rotation frequency as a small parameter it is found that slow rotation tends to $destabilize$ high radial-order $retrograde$ $g$-modes, although the effect is very small or absent for relatively low order modes. Calculating eigenfrequencies at selected rotation rates, we find, on the other hand, that rapid rotation tends to $stabilize$ $retrograde$ $g$-modes. The stabilizing effect appears stronger for less massive B-type stars having low effective temperatures. If we change rotation rate continuously, the frequency of a $g$-mode belonging to ($l', m$) crosses frequencies of other $g$-modes belonging to ($l', m$). If the parity of the two encountering modes are the same, they interact each other and the stability (i.e., imaginary part of eigenfrequency) of each mode is modified. Using an asymptotic method we discuss the property of such mode crossings and couplings. For rapidly rotating stars mode couplings are important for the stability of low degree $g$-modes. In particular, we find that the stabilization of retrograde $g$-modes in rapidly rotating stars is due to many strong mode couplings, while %prograde sectoral% modes are exceptionally immune to the damping effects from the mode couplings.Comment: 13 pages, 15 figure

Some upper and lower bounds on PSD-rank

Positive semidefinite rank (PSD-rank) is a relatively new quantity with applications to combinatorial optimization and communication complexity. We first study several basic properties of PSD-rank, and then develop new techniques for showing lower bounds on the PSD-rank. All of these bounds are based on viewing a positive semidefinite factorization of a matrix $M$ as a quantum communication protocol. These lower bounds depend on the entries of the matrix and not only on its support (the zero/nonzero pattern), overcoming a limitation of some previous techniques. We compare these new lower bounds with known bounds, and give examples where the new ones are better. As an application we determine the PSD-rank of (approximations of) some common matrices.Comment: 21 page

Rotation of Cosmic Voids and Void-Spin Statistics

We present a theoretical study of void spins and their correlation properties. The concept of the spin angular momentum for an unbound void is introduced to quantify the effect of the tidal field on the distribution of matter that make up the void. Both the analytical and numerical approaches are used for our study. Analytically, we adopt the linear tidal torque model to evaluate the void spin-spin and spin-density correlations, assuming that a void forms in the initial region where the inertia momentum and the tidal shear tensors are maximally uncorrelated with each other. Numerically, we use the Millennium run galaxy catalog to find voids and calculate their spin statistics. The numerical results turn out to be in excellent agreement with the analytic predictions, both of which consistently show that there are strong spatial alignments between the spin axes of neighbor voids and strong anti-alignments between the void spin axes and the directions to the nearest voids. We expect that our work will provide a deeper insight into the origin and properties of voids and the large scale structure.Comment: accepted version, ApJ in press, the concept of void spins explained, typos correcte

The diagonalization of quantum field Hamiltonians

We introduce a new diagonalization method called quasi-sparse eigenvector diagonalization which finds the most important basis vectors of the low energy eigenstates of a quantum Hamiltonian. It can operate using any basis, either orthogonal or non-orthogonal, and any sparse Hamiltonian, either Hermitian, non-Hermitian, finite-dimensional, or infinite-dimensional. The method is part of a new computational approach which combines both diagonalization and Monte Carlo techniques.Comment: 12 pages, 8 figures, new material adde