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Relaxation rates of the linearized Uehling-Uhlenbeck equation for bosons
We linearize the Uehling-Uhlenbeck equation for bosonic gases close to thermal equilibrium under the assumption of a contact interaction characterized by a scattering length a. We show that the spectrum of relaxation rates is similar to that of a classical hard-sphere gas. However, the relaxation rates show a significant dependence on the fugacity z of the gas, increasing by as much as 60% of their classical value for z approaching 1. The relaxation modes are also significantly altered at higher values of z. The relaxation rates and modes are determined by the eigenvalues and eigenvectors of a Fredholm integral operator of the second kind. We derive an analytical form for the kernel of this operator and present numerical results for the first few eigenvalues and eigenvectors.Robert A. Welch Foundation F-1051Physic
"Light from chaos" in two dimensions
We perform a Monte-Carlo study of the lattice two-dimensional gauged
XY-model. Our results confirm the strong-coupling expansion arguments that for
sufficiently small values of the spin-spin coupling the ``gauge symmetry
breaking" terms decouple and the long-distance physics is that of the unbroken
pure gauge theory. We find no evidence for the existence, conjectured earlier,
of massless states near a critical value of the spin-spin coupling. We comment
on recent remarks in the literature on the use of gauged XY-models in proposed
constructions of chiral lattice gauge theories.Comment: 6 pages, 7 figure
Two-body recombination in a quantum mechanical lattice gas: Entropy generation and probing of short-range magnetic correlations
We study entropy generation in a one-dimensional (1D) model of bosons in an
optical lattice experiencing two-particle losses. Such heating is a major
impediment to observing exotic low temperature states, and "simulating"
condensed matter systems. Developing intuition through numerical simulations,
we present a simple empirical model for the entropy produced in this 1D
setting. We also explore the time evolution of one and two particle correlation
functions, showing that they are robust against two-particle loss. Because of
this robustness, induced two-body losses can be used as a probe of short range
magnetic correlations.Comment: 6 pages, 3 figures - v4, published versio
AdS/CFT and large-N volume independence
We study the Eguchi-Kawai reduction in the strong-coupling domain of gauge
theories via the gravity dual of N=4 super-Yang-Mills on R^3xS^1. We show that
D-branes geometrize volume independence in the center-symmetric vacuum and give
supergravity predictions for the range of validity of reduced large-N models at
strong coupling.Comment: 4 pages, 2 figures; references and comments adde
H.F. Hauff Pruner Housing & Ergonomics
The technology of electric tree pruners in the current agricultural market has many engineering problems, including; a deficit in power output, excessive overheating, and ergonomics. The 3-man pruner team has coordinated with H.F. Hauff Co. Inc., an agricultural equipment company owned by Neil Hauff, to produce an electric pruner prototype which addresses these problems. The methods used to design the optimal pruner prototype includes traditional engineering stress analysis, force flow analysis, finite element software, and Solidworks modeling software. The construction of the pruner involved manual machining methods and C.N.C. (Computerized Numerical Control) mill technology. During the design process, the team learned advanced analysis practices, the relationships between torque and linear output, work fixture design, product design practices, and found that slight modifications to geometry caused a force amplification effect. With the help of Neil, and his staff, the pruner team gained an appreciation and insight into the professional design process and the relationship between part complexity and fabrication time. The finished prototype was able to meet the initially established design requirements of the pruner. However, the design is still limited with regards power output and operation temperature. The design and analysis performed for this project has made it possible for further optimization of the current prototype and some engineering problems of current electric pruners were addressed and fixed. Weaknesses of the design include a high weight and non-optimal center of gravity
Domestic Outsourcing and Imported Inputs in the U.s. Economy: Insights from Integrated Economic Accounts
Pairing, Ferromagnetism, and Condensation of a normal spin-1 Bose gas
We theoretically study the stability of a normal, spin disordered, homogenous
spin-1 Bose gas against ferromagnetism, pairing, and condensation through a
Random Phase Approximation which includes exchange (RPA-X). Repulsive
spin-independent interactions stabilize the normal state against both
ferromagnetism and pairing, and for typical interaction strengths leads to a
direct transition from an unordered normal state to a fully ordered single
particle condensate. Atoms with much larger spin-dependent interaction may
experience a transition to a ferromagnetic normal state or a paired superfluid,
but, within the RPA-X, there is no instability towards a normal state with
spontaneous nematic order. We analyze the role of the quadratic Zeeman effect
and finite system size.Comment: 4 pages, 3 figures, 1 table. Supplementary materials attache
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