Nationbuilding 101: Reductionism in Property, Liberty, and Corporate Governance

In this Article, Professor Reed re-examines the importance of property as a formal legal institution. He continues by arguing that central to creating property is the right to exclude others from resources acquired without force, theft, or fraud. In countries where this right has been firmly established, per capita income far exceeds that of countries lacking a strong right to exclude. Professor Reed then asserts the importance to nation builders of appreciating the virtual semantic equivalence of the terms property and liberty. Finally, he argues that both the specific and broad senses of corporate governance can be reduced to property issues, making the understanding and implementation of a strong property system an important step toward prosperity, individual freedom, and sustainable peace

Independent electrons model for open quantum systems: Landauer-Buettiker formula and strict positivity of the entropy production

A general argument leading from the formula for currents through an open noninteracting mesoscopic system given by the theory of non-equilibrium steady states (NESS) to the Landauer-Buettiker formula is pointed out. Time reversal symmetry is not assumed. As a consequence it follows that, as far as the system has a nontrivial scattering theory and the reservoirs have different temperatures and/or chemical potentials, the entropy production is strictly positive.Comment: 12 pages. Submitted for publication in J. Math. Phys. on 2006-06-05. Revision and extension of: G. Nenciu, A general proof of Landauer-Buettiker formula, [math-ph/0603030

Lone Star Productions

Lone Star Productions (LSP) is a concert promotions business that was started in 1981 by Bill Oldman. Since 1986, this company has been the exclusive provider of concert promotion materials for 75% of the top grossing national tours. In 1997, Bill Oldman sold the company to a group of investors headed by Mike Sims. With a background in banking and investments, Sims took over a LSP’s president. Bill Oldman remained as the Chief Executive Officer of the company. Lone Star Productions’ business encompasses several segments, including concert promotions, audio and video production, production staffing, video editing, web site development, and equipment and suite rental. Currently, concert promotions account for 90% of the company’s revenue. Efforts to build business in the areas other than concert promotion have been mildly successful, but LSP considers the further development of these business areas to be critical to the long-term profitability and financial stability of the company, LSP is currently considering buying the largest video production company in the Dallas, Texas area.(Contact author for a copy of the complete report.)Small Busn. Mgmt

Noncommutative waves have infinite propagation speed

We prove the existence of global solutions to the Cauchy problem for noncommutative nonlinear wave equations in arbitrary even spatial dimensions where the noncommutativity is only in the spatial directions. We find that for existence there are no conditions on the degree of the nonlinearity provided the potential is positive. We furthermore prove that nonlinear noncommutative waves have infinite propagation speed, i.e., if the initial conditions at time 0 have a compact support then for any positive time the support of the solution can be arbitrarily large.Comment: 15 pages, references adde

Nonlinear Schroedinger equation with two symmetric point interactions in one dimension

We consider a time-dependent one-dimensional nonlinear Schroedinger equation with a symmetric potential double well represented by two delta interactions. Among our results we give an explicit formula for the integral kernel of the unitary semigroup associated with the linear part of the Hamiltonian. Then we establish the corresponding Strichartz-type estimate and we prove local existence and uniqueness of the solution to the original nonlinear problem

On the Mean-Field Limit of Bosons with Coulomb Two-Body Interaction

In the mean-field limit the dynamics of a quantum Bose gas is described by a Hartree equation. We present a simple method for proving the convergence of the microscopic quantum dynamics to the Hartree dynamics when the number of particles becomes large and the strength of the two-body potential tends to 0 like the inverse of the particle number. Our method is applicable for a class of singular interaction potentials including the Coulomb potential. We prove and state our main result for the Heisenberg-picture dynamics of "observables", thus avoiding the use of coherent states. Our formulation shows that the mean-field limit is a "semi-classical" limit.Comment: Corrected typos and included an elementary proof of the Kato smoothing estimate (Lemma 6.1

Linear vs. nonlinear effects for nonlinear Schrodinger equations with potential

We review some recent results on nonlinear Schrodinger equations with potential, with emphasis on the case where the potential is a second order polynomial, for which the interaction between the linear dynamics caused by the potential, and the nonlinear effects, can be described quite precisely. This includes semi-classical regimes, as well as finite time blow-up and scattering issues. We present the tools used for these problems, as well as their limitations, and outline the arguments of the proofs.Comment: 20 pages; survey of previous result

Decay of a Bound State under a Time-Periodic Perturbation: a Toy Case

We study the time evolution of a three dimensional quantum particle, initially in a bound state, under the action of a time-periodic zero range interaction with ``strength'' (\alpha(t)). Under very weak generic conditions on the Fourier coefficients of (\alpha(t)), we prove complete ionization as (t \to \infty). We prove also that, under the same conditions, all the states of the system are scattering states.Comment: LaTeX2e, 15 page