The Height of a Giraffe

A minor modification of the arguments of Press and Lightman leads to an estimate of the height of the tallest running, breathing organism on a habitable planet as the Bohr radius multiplied by the three-tenths power of the ratio of the electrical to gravitational forces between two protons (rather than the one-quarter power that Press got for the largest animal that would not break in falling over, after making an assumption of unreasonable brittleness). My new estimate gives a height of about 3.6 meters rather than Press's original estimate of about 2.6 cm. It also implies that the number of atoms in the tallest runner is very roughly of the order of the nine-tenths power of the ratio of the electrical to gravitational forces between two protons, which is about 3 x 10^32.Comment: 12 pages, LaTe

Evaporation of a Kerr black hole by emission of scalar and higher spin particles

We study the evolution of an evaporating rotating black hole, described by the Kerr metric, which is emitting either solely massless scalar particles or a mixture of massless scalar and nonzero spin particles. Allowing the hole to radiate scalar particles increases the mass loss rate and decreases the angular momentum loss rate relative to a black hole which is radiating nonzero spin particles. The presence of scalar radiation can cause the evaporating hole to asymptotically approach a state which is described by a nonzero value of $a_* \equiv a / M$. This is contrary to the conventional view of black hole evaporation, wherein all black holes spin down more rapidly than they lose mass. A hole emitting solely scalar radiation will approach a final asymptotic state described by $a_* \simeq 0.555$. A black hole that is emitting scalar particles and a canonical set of nonzero spin particles (3 species of neutrinos, a single photon species, and a single graviton species) will asymptotically approach a nonzero value of $a_*$ only if there are at least 32 massless scalar fields. We also calculate the lifetime of a primordial black hole that formed with a value of the rotation parameter $a_{*}$, the minimum initial mass of a primordial black hole that is seen today with a rotation parameter $a_{*}$, and the entropy of a black hole that is emitting scalar or higher spin particles.Comment: 22 pages, 13 figures, RevTeX format; added clearer descriptions for variables, added journal referenc

Nonuniqueness in spin-density-functional theory on lattices

In electronic many-particle systems, the mapping between densities and spin magnetizations, {n(r), m(r)}, and potentials and magnetic fields, {v(r), B(r)}, is known to be nonunique, which has fundamental and practical implications for spin-density-functional theory (SDFT). This paper studies the nonuniqueness (NU) in SDFT on arbitrary lattices. Two new, non-trivial cases are discovered, here called local saturation and global noncollinear NU, and their properties are discussed and illustrated. In the continuum limit, only some well-known special cases of NU survive.Comment: 4 pages, 1 figur

A New Superintegrable Hamiltonian

We identify a new superintegrable Hamiltonian in 3 degrees of freedom, obtained as a reduction of pure Keplerian motion in 6 dimensions. The new Hamiltonian is a generalization of the Keplerian one, and has the familiar 1/r potential with three barrier terms preventing the particle crossing the principal planes. In 3 degrees of freedom, there are 5 functionally independent integrals of motion, and all bound, classical trajectories are closed and strictly periodic. The generalisation of the Laplace-Runge-Lenz vector is identified and shown to provide functionally independent isolating integrals. They are quartic in the momenta and do not arise from separability of the Hamilton-Jacobi equation. A formulation of the system in action-angle variables is presented.Comment: 11 pages, 4 figures, submitted to The Journal of Mathematical Physic

A variance-minimization scheme for optimizing Jastrow factors

We describe a new scheme for optimizing many-electron trial wave functions by minimizing the unreweighted variance of the energy using stochastic integration and correlated-sampling techniques. The scheme is restricted to parameters that are linear in the exponent of a Jastrow correlation factor, which are the most important parameters in the wave functions we use. The scheme is highly efficient and allows us to investigate the parameter space more closely than has been possible before. We search for multiple minima of the variance in the parameter space and compare the wave functions obtained using reweighted and unreweighted variance minimization.Comment: 19 pages; 12 figure

Baby Skyrme models without a potential term

We develop a one-parameter family of static baby Skyrme models that do not require a potential term to admit topological solitons. This is a novel property as the standard baby Skyrme model must contain a potential term in order to have stable soliton solutions, though the Skyrme model does not require this. Our new models satisfy an energy bound that is linear in terms of the topological charge and can be saturated in an extreme limit. They also satisfy a virial theorem that is shared by the Skyrme model. We calculate the solitons of our new models numerically and observe that their form depends significantly on the choice of parameter. In one extreme, we find compactons while at the other there is a scale invariant model in which solitons can be obtained exactly as solutions to a Bogomolny equation. We provide an initial investigation into these solitons and compare them with the baby Skyrmions of other models

Critical scaling of jammed system after quench of temperature

Critical behavior of soft repulsive particles after quench of temperature near the jamming trasition is numerically investigated. It is found that the plateau of the mean square displacement of tracer particles and the pressure satisfy critical scaling laws. The critical density for the jamming transition depends on the protocol to prepare the system, while the values of the critical exponents which are consistent with the prediction of a phenomenology are independent of the protocol.Comment: 7 pages, 9 figures, to appear in Phys. Rev.

Dynamics of the Number of Trades of Financial Securities

We perform a parallel analysis of the spectral density of (i) the logarithm of price and (ii) the daily number of trades of a set of stocks traded in the New York Stock Exchange. The stocks are selected to be representative of a wide range of stock capitalization. The observed spectral densities show a different power-law behavior. We confirm the $1/f^2$ behavior for the spectral density of the logarithm of stock price whereas we detect a $1/f$-like behavior for the spectral density of the daily number of trades.Comment: 3 pages, 3 figures, submitted to Physica