Asymptotic Level Spacing of the Laguerre Ensemble: A Coulomb Fluid Approach

We determine the asymptotic level spacing distribution for the Laguerre Ensemble in a single scaled interval, $(0,s)$, containing no levels, E_{\bt}(0,s), via Dyson's Coulomb Fluid approach. For the $\alpha=0$ Unitary-Laguerre Ensemble, we recover the exact spacing distribution found by both Edelman and Forrester, while for $\alpha\neq 0$, the leading terms of $E_{2}(0,s)$, found by Tracy and Widom, are reproduced without the use of the Bessel kernel and the associated Painlev\'e transcendent. In the same approximation, the next leading term, due to a ``finite temperature'' perturbation (\bt\neq 2), is found.Comment: 10pp, LaTe

Dirac monopole with Feynman brackets

We introduce the magnetic angular momentum as a consequence of the structure of the sO(3) Lie algebra defined by the Feynman brackets. The Poincare momentum and Dirac magnetic monopole appears as a direct result of this framework.Comment: 10 page

Does Inflation Provide Natural Initial Conditions for the Universe?

If our universe underwent inflation, its entropy during the inflationary phase was substantially lower than it is today. Because a low-entropy state is less likely to be chosen randomly than a high-entropy one, inflation is unlikely to arise through randomly-chosen initial conditions. To resolve this puzzle, we examine the notion of a natural state for the universe, and argue that it is a nearly-empty spacetime. If empty space has a small vacuum energy, however, inflation can begin spontaneously in this background. This scenario explains why a universe like ours is likely to have begun via a period of inflation, and also provides an origin for the cosmological arrow of time.Comment: Submitted to Gravity Research Foundation Essay Competition; based on hep-th/041027

Relativistic Dyson Rings and Their Black Hole Limit

In this Letter we investigate uniformly rotating, homogeneous and axisymmetric relativistic fluid bodies with a toroidal shape. The corresponding field equations are solved by means of a multi-domain spectral method, which yields highly accurate numerical solutions. For a prescribed, sufficiently large ratio of inner to outer coordinate radius, the toroids exhibit a continuous transition to the extreme Kerr black hole. Otherwise, the most relativistic configuration rotates at the mass-shedding limit. For a given mass-density, there seems to be no bound to the gravitational mass as one approaches the black-hole limit and a radius ratio of unity.Comment: 13 pages, 1 table, 5 figures, v2: some discussion and two references added, accepted for publication in Astrophys. J. Let

Phonon emission and arrival times of electrons from a single-electron source

In recent charge-pump experiments, single electrons are injected into quantum Hall edge channels at energies significantly above the Fermi level. We consider here the relaxation of these hot edge-channel electrons through longitudinal-optical-phonon emission. Our results show that the probability for an electron in the outermost edge channel to emit one or more phonons en route to a detector some microns distant along the edge channel suffers a double-exponential suppression with increasing magnetic field. This explains recent experimental observations. We also describe how the shape of the arrival-time distribution of electrons at the detector reflects the velocities of the electronic states post phonon emission. We show how this can give rise to pronounced oscillations in the arrival-time-distribution width as a function of magnetic field or electron energy

Anthropic tuning of the weak scale and of m_u/m_d in two-Higgs-doublet models

It is shown that in a model in which up-type and down-type fermions acquire mass from different Higgs doublets, the anthropic tuning of the Higgs mass parameters can explain the fact that the observed masses of the $d$ and $u$ quarks are nearly the same with $d$ slightly heavier. If Yukawa couplings are assumed not to "scan" (vary among domains), this would also help explain why the t quark is much heavier than the b quark. It is also pointed out that the existence of dark matter invalidates some earlier anthropic arguments against the viability of domains where the Standard Model Higgs has positive $\mu^2$, but makes other even stronger arguments possible.Comment: 31 pages, 7 figure

Singlets and reflection symmetric spin systems

We rigorously establish some exact properties of reflection symmetric spin systems with antiferromagnetic crossing bonds: At least one ground state has total spin zero and a positive semidefinite coefficient matrix. The crossing bonds obey an ice rule. This augments some previous results which were limited to bipartite spin systems and is of particular interest for frustrated spin systems.Comment: 11 pages, LaTeX 2

Heat Stability of Casein in the Presence of Calcium and Other Salts

Summary The extent of calcium binding and the heat stability of colloidal suspensions of freeze-dried casein in calcium hydroxide solution, with added phosphates, citrates, and chlorides in some tests, was studied. The calcium-binding power of freshly prepared freeze-dried casein was greater (pK 4.5) than that reported for other casein preparations. However, the pK value decreased during storage of the casein at room temperature and within 1 or 2 mo. attained a value (pK = 3.0 ± 0.3) in agreement with published values. The heat stability of simple casein caseinate suspensions was inversely related to the extent to which the casein was saturated with calcium, and this relation appeared to be linear at calcium levels sufficient to give over 80% saturation. The heat stability of more complex suspensions was inversely related to the ratio of soluble or ionic calcium to soluble phosphate in the suspension. Chlorides and phosphates of sodium, potassium, and ammonium displaced calcium from caseinate to about the same extent, but ammonium ion appeared to have a specific depressant effect on heat stability

Influence of κ-casein and β-lactoglobulin on the Heat Stability of Skimmilk

Abstract Milks from individual cows were classified according to their heat stability-pH relation as Type A (maximum and minimum heat stability) and Type B (no minimum heat stability). The heat stability responses of these milks could be changed from Type A to B and from B to A by adding κ -casein and β -lactoglobulin, respectively. Addition of either α s - or β -casein did not affect the heat stability of milk. The heat stability-pH relation of milk heated at 90C for 10min was no longer affected by the addition of κ -casein

Effect of Various Salts on the Coagulation of Casein

Summary Addition of potassium or sodium chloride (80 or 130m M ) to skimmilk increased the time the milk could be held in frozen storage without development of 4% precipitate by volume. Addition of phosphate or calcium (10m M ) had the opposite effect. Addition of large amounts of sodium chloride (up to 1.0 M ) offset the destabilizing effect of phosphate or calcium at 0, 10, and 20° F., but addition of similar amounts of potassium chloride stabilized the samples only at 10 and 20° F. Addition of potassium chloride (1.0 M or more) and of phosphate (100m M or more) induced gelation of milk at room temperature. Addition of sodium chloride and phosphate did not induce gelation. Addition of either potassium or sodium chloride (2.3 M ) shifted approximately 20% of the insoluble calcium and 7.5% of the insoluble phosphate to the soluble forms, displaced calcium from casein, and increased the dissociation of calcium citrate. A possible explanation of these effects, based on the interlinking of potassium-calcium-caseinate micelles by precipitating calcium phosphate, is presented