Coupled oscillators and Feynman's three papers

According to Richard Feynman, the adventure of our science of physics is a perpetual attempt to recognize that the different aspects of nature are really different aspects of the same thing. It is therefore interesting to combine some, if not all, of Feynman's papers into one. The first of his three papers is on the ``rest of the universe'' contained in his 1972 book on statistical mechanics. The second idea is Feynman's parton picture which he presented in 1969 at the Stony Brook conference on high-energy physics. The third idea is contained in the 1971 paper he published with his students, where they show that the hadronic spectra on Regge trajectories are manifestations of harmonic-oscillator degeneracies. In this report, we formulate these three ideas using the mathematics of two coupled oscillators. It is shown that the idea of entanglement is contained in his rest of the universe, and can be extended to a space-time entanglement. It is shown also that his parton model and the static quark model can be combined into one Lorentz-covariant entity. Furthermore, Einstein's special relativity, based on the Lorentz group, can also be formulated within the mathematical framework of two coupled oscillators.Comment: 31 pages, 6 figures, based on the concluding talk at the 3rd Feynman Festival (Collage Park, Maryland, U.S.A., August 2006), minor correction

Monte Carlo Study of the S=1/2 and S=1 Heisenberg Antiferromagnet on a Spatially Anisotropic Square Lattice

We present a quantum Monte Carlo study of a Heisenberg antiferromagnet on a spatially anisotropic square lattice, where the coupling strength in the x-direction ($J_x$) is different from that in the y-direction ($J_y$). By varying the anisotropy $\alpha$ from 0 to 1, we interpolate between the one-dimensional chain and the two-dimensional isotropic square lattice. Both $S=1/2$ and S=1 systems are considered separately in order to facilitate comparison. The temperature dependence of the uniform susceptibility and the spin-spin correlation length are computed down to very low temperatures for various values of $\alpha$. For S=1, the existence of a quantum critical point at $\alpha^{S=1}_c=0.040(5)$ as well as the scaling of the spin gap is confirmed. Universal quantities predicted from the ${\cal O}(3)$ nonlinear $\sigma$ model agree with our results at $\alpha=0.04$ without any adjustable parameters. On the other hand, the $S=1/2$ results are consistent with $\alpha^{S=1/2}_c=0$, as discussed by a number of previous theoretical studies. Experimental implications for $S=1/2$ compounds such as Sr$_2$CuO$_3$ are also discussed.Comment: 8 pages, 7 figures, to be published in Phys. Rev.

Feynman's Decoherence

Gell-Mann's quarks are coherent particles confined within a hadron at rest, but Feynman's partons are incoherent particles which constitute a hadron moving with a velocity close to that of light. It is widely believed that the quark model and the parton model are two different manifestations of the same covariant entity. If this is the case, the question arises whether the Lorentz boost destroys coherence. It is pointed out that this is not the case, and it is possible to resolve this puzzle without inventing new physics. It is shown that this decoherence is due to the measurement processes which are less than complete.Comment: RevTex 15 pages including 6 figs, presented at the 9th Int'l Conference on Quantum Optics (Raubichi, Belarus, May 2002), to be published in the proceeding

Incorporating labor supply responses into the estimated effects of an assured child support benefit

Assured child support benefits are an important component of many proposals to reform the child support system. The authors estimate the likely effects of assured benefits on poverty and welfare participation when (a) parents eligible for child support work the same number of hours as they currently work and (b) parents eligible for child support change the number of hours they work in order to maximize their income and leisure time. They find that in each situation assured benefits will reduce poverty rates and the poverty gap; welfare caseloads and expenditures will also fall. When parents are allowed to change the number of hours they work, the impact of assured benefits will be about the same, but the costs of the assured benefit program will increase.

Amplitude Variations in Pulsating Yellow Supergiants

It was recently discovered that the amplitudes of pulsating red giants and supergiants vary significantly on time scales of 20-30 pulsation periods. Here, we analyze the amplitude variability in 29 pulsating yellow supergiants (5 RVa, 4 RVb, 9 SRd, 7 long-period Cepheid, and 4 yellow hypergiant stars), using visual observations from the AAVSO International Database, and Fourier and wavelet analysis using the AAVSO's VSTAR package. We find that these stars vary in amplitude by factors of up to 10 or more (but more typically 3-5), on a mean time scale (L) of 33 +/- 4 pulsation periods (P). Each of the five sub-types shows this same behavior, which is very similar to that of the pulsating red giants, for which the median L/P was 31. For the RVb stars, the lengths of the cycles of amplitude variability are the same as the long secondary periods, to within the uncertainty of each.Comment: To be submitted to JAAVS

Thermodynamics and kinetics of the undercooled liquid and the glass transition of the Zr41.2Ti13.8Cu12.5Ni10.0Be22.5 alloy

Differential scanning calorimetry (DSC) was used to determine the thermodynamic functions of the undercooled liquid and the amorphous phase with respect to the crystalline state of the Zr41.2Ti13.8Cu12.5Ni10.0Be22.5bulk metallic glass forming alloy. The specific heat capacities of this alloy in the undercooled liquid, the amorphous state and the crystal were determined. The differences in enthalpy, ∆H, entropy, ∆S, and Gibbs free energy, ∆G, between crystal and the undercooled liquid were calculated using the measured specific heat capacity data as well as the heat of fusion. The results indicate that the Gibbs free energy difference between metastable undercooled liquid and crystalline solid, ∆G, stays small compared to conventional metallic glass forming alloys even for large undercoolings. Furthermore, the Kauzmann temperature, TK, where the entropy of the undercooled liquid equals to that of the crystal, was determined to be 560 K. The Kauzmann temperature is compared with the experimentally observed rate-dependent glass transition temperature, Tg. Both onset and end temperatures of the glass transition depend linearly on the logarithm of the heating rate based on the DSC experiments. Those characteristic temperatures for the kinetically observed glass transition become equal close to the Kauzmann temperature in this alloy, which suggests an underlying thermodynamic glass transition as a lower bound for the kinetically observed freezing process

The evolution of organizational niches : U.S. automobile manufacturers, 1885-1981.

Although the niche figures prominently in contemporary theories of organization, analysts often fail to tie micro processes within the niche to long-term changes in the broader environment. In this paper, we advance arguments about the relationship between an organization's niche and evolution in the structure of its organizational population over time. We focus on the technological niche and processes of positioning and crowding among firms in the niche space, relating them to the level of concentration among all firms in the market. Building on previous empirical studies in organizational ecology, we study the evolution of concentration in the American automobile industry from 1885 to 1981 and estimate models of the hazard of exit of individual producers from the market. The findings show that niche and concentration interact in complex ways, yielding a more unified depiction of organizational evolution than typically described or reported

Geometry and seismic properties of the subducting Cocos plate in central Mexico

The geometry and properties of the interface of the Cocos plate beneath central Mexico are determined from the receiver functions (RFs) utilizing data from the Meso America Subduction Experiment (MASE). The RF image shows that the subducting oceanic crust is shallowly dipping to the north at 15° for 80 km from Acapulco and then horizontally underplates the continental crust for approximately 200 km to the Trans-Mexican Volcanic Belt (TMVB). The crustal image also shows that there is no continental root associated with the TMVB. The migrated image of the RFs shows that the slab is steeply dipping into the mantle at about 75° beneath the TMVB. Both the continental and oceanic Moho are clearly seen in both images, and modeling of the RF conversion amplitudes and timings of the underplated features reveals a thin low-velocity zone between the plate and the continental crust that appears to absorb nearly all of the strain between the upper plate and the slab. By inverting RF amplitudes of the converted phases and their time separations, we produce detailed maps of the seismic properties of the upper and lower oceanic crust of the subducting Cocos plate and its thickness. High Poisson's and Vp/Vs ratios due to anomalously low S wave velocity at the upper oceanic crust in the flat slab region may indicate the presence of water and hydrous minerals or high pore pressure. The evidence of high water content within the oceanic crust explains the flat subduction geometry without strong coupling of two plates. This may also explain the nonvolcanic tremor activity and slow slip events occurring in the subducting plate and the overlying crust

Interaction effects of a child tax credit, national health insurance, and assured child support

If the government offered a refundable tax credit for children, national health insurance, and an assured child support benefit to all families with children - poor families as well as nonpoor families - what would happen to poverty, welfare dependency, and other related issues? The authors simulate the effects of each program operating on its own and of all three acting in concert. They find that the impacts of the programs interacting with one another would be much larger than the sum of the impacts produced by each program alone. With the three programs in place, the poverty rate would fall by 43 percent, the AFDC caseload would shrink by 22 percent, and the annual incomes of poor families would rise by $2500. In addition, AFDC recipients would work more hours. Data come from the 1987 Survey of Income and Program Participation.