Capacity Scaling in MIMO Systems with General Unitarily Invariant Random Matrices

We investigate the capacity scaling of MIMO systems with the system dimensions. To that end, we quantify how the mutual information varies when the number of antennas (at either the receiver or transmitter side) is altered. For a system comprising $R$ receive and $T$ transmit antennas with $R>T$, we find the following: By removing as many receive antennas as needed to obtain a square system (provided the channel matrices before and after the removal have full rank) the maximum resulting loss of mutual information over all signal-to-noise ratios (SNRs) depends only on $R$, $T$ and the matrix of left-singular vectors of the initial channel matrix, but not on its singular values. In particular, if the latter matrix is Haar distributed the ergodic rate loss is given by $\sum_{t=1}^{T}\sum_{r=T+1}^{R}\frac{1}{r-t}$ nats. Under the same assumption, if $T,R\to \infty$ with the ratio $\phi\triangleq T/R$ fixed, the rate loss normalized by $R$ converges almost surely to $H(\phi)$ bits with $H(\cdot)$ denoting the binary entropy function. We also quantify and study how the mutual information as a function of the system dimensions deviates from the traditionally assumed linear growth in the minimum of the system dimensions at high SNR.Comment: Accepted for publication in the IEEE Transactions on Information Theor

Renormalization-group analysis of the validity of staggered-fermion QCD with the fourth-root recipe

I develop a renormalization-group blocking framework for lattice QCD with staggered fermions. Under plausible, and testable, assumptions, I then argue that the fourth-root recipe used in numerical simulations is valid in the continuum limit. The taste-symmetry violating terms, which give rise to non-local effects in the fourth-root theory when the lattice spacing is non-zero, vanish in the continuum limit. A key role is played by reweighted theories that are local and renormalizable on the one hand, and that approximate the fourth-root theory better and better as the continuum limit is approached on the other hand.Comment: Minor corrections. Revtex, 58 page

Momentum Dependent Vertices σγγ\sigma \gamma \gamma, σργ\sigma \rho \gamma and σρρ\sigma \rho \rho : The NJL Scalar Hidden by Chiral Symmetry

We calculate the momentum dependence of three particle vertices $\sigma \gamma \gamma$, $\sigma \rho \gamma$ and $\sigma \rho \rho$ in the context of a Nambu Jona Lasinio type model. We show how they influence the processes $\gamma \gamma \rightarrow \sigma \rightarrow \pi \pi$, $\rho \rightarrow \gamma \sigma$ and $\gamma \gamma \rightarrow \rho \rho$ and how chiral symmetry shadows the presence of the $\sigma$.Comment: 9 pages (latex), 5 figures available from the authors, preprint Coimbra 940506, IJS-TP-94/10, accepted for publication in Zeit. f. Physik

Exact Dynamics of Multicomponent Bose-Einstein Condensates in Optical Lattices in One, Two and Three Dimensions

Numerous exact solutions to the nonlinear mean-field equations of motion are constructed for multicomponent Bose-Einstein condensates on one, two, and three dimensional optical lattices. We find both stationary and nonstationary solutions, which are given in closed form. Among these solutions are a vortex-anti-vortex array on the square optical lattice and modes in which two or more components slosh back and forth between neighboring potential wells. We obtain a variety of solutions for multicomponent condensates on the simple cubic lattice, including a solution in which one condensate is at rest and the other flows in a complex three-dimensional array of intersecting vortex lines. A number of physically important solutions are stable for a range of parameter values, as we show by direct numerical integration of the equations of motion.Comment: 22 pages, 9 figure

Spin Polarizabilities of the Nucleon from Polarized Low Energy Compton Scattering

As guideline for forthcoming experiments, we present predictions from Chiral Effective Field Theory for polarized cross sections in low energy Compton scattering for photon energies below 170 MeV, both on the proton and on the neutron. Special interest is put on the role of the nucleon spin polarizabilities which can be examined especially well in polarized Compton scattering. We present a model-independent way to extract their energy dependence and static values from experiment, interpreting our findings also in terms of the low energy effective degrees of freedom inside the nucleon: The polarizabilities are dominated by chiral dynamics from the pion cloud, except for resonant multipoles, where contributions of the Delta(1232) resonance turn out to be crucial. We therefore include it as an explicit degree of freedom. We also identify some experimental settings which are particularly sensitive to the spin polarizabilities.Comment: 30 pages, 19 figure

Scaling studies of QCD with the dynamical HISQ action

We study the lattice spacing dependence, or scaling, of physical quantities using the highly improved staggered quark (HISQ) action introduced by the HPQCD/UKQCD collaboration, comparing our results to similar simulations with the asqtad fermion action. Results are based on calculations with lattice spacings approximately 0.15, 0.12 and 0.09 fm, using four flavors of dynamical HISQ quarks. The strange and charm quark masses are near their physical values, and the light-quark mass is set to 0.2 times the strange-quark mass. We look at the lattice spacing dependence of hadron masses, pseudoscalar meson decay constants, and the topological susceptibility. In addition to the commonly used determination of the lattice spacing through the static quark potential, we examine a determination proposed by the HPQCD collaboration that uses the decay constant of a fictitious "unmixed s bar s" pseudoscalar meson. We find that the lattice artifacts in the HISQ simulations are much smaller than those in the asqtad simulations at the same lattice spacings and quark masses.Comment: 36 pages, 11 figures, revised version to be published. Revisions include discussion of autocorrelations and several clarification

Chiral corrections to the axial charges of the octet baryons from quenched QCD

We calculate one-loop correction to the axial charges of the octet baryons using quenched chiral perturbation theory, in order to understand chiral behavior of the axial charges in quenched approximation to quantum chromodynamics (QCD). In contrast to regular behavior of the full QCD chiral perturbation theory result, $c_0+c_{l2}m_\pi^2\,\ln{m_\pi^2}+\cdots$, we find that the quenched chiral perturbation theory result, $c_0^Q+(c_{l0}^Q+c_{l2}^Qm_\pi^2)\ln{m_\pi^2}+c_2^Q m_\pi^2+\cdots$, is singular in the chiral limit.Comment: standard LaTeX, 16 pages, 4 epsf figure

A new kind of Lax-Oleinik type operator with parameters for time-periodic positive definite Lagrangian systems

In this paper we introduce a new kind of Lax-Oleinik type operator with parameters associated with positive definite Lagrangian systems for both the time-periodic case and the time-independent case. On one hand, the new family of Lax-Oleinik type operators with an arbitrary $u\in C(M,\mathbb{R}^1)$ as initial condition converges to a backward weak KAM solution in the time-periodic case, while it was shown by Fathi and Mather that there is no such convergence of the Lax-Oleinik semigroup. On the other hand, the new family of Lax-Oleinik type operators with an arbitrary $u\in C(M,\mathbb{R}^1)$ as initial condition converges to a backward weak KAM solution faster than the Lax-Oleinik semigroup in the time-independent case.Comment: We give a new definition of Lax-Oleinik type operator; add some reference