Jeffrey R. Schmidt

Direct experimental test of scalar confinement

The concept of Lorentz scalar quark confinement has a long history and is still widely used despite its well-known theoretical faults. We point out here that the predictions of scalar confinement also conflict directly with experiment. We investigate the dependence of heavy-light meson mass differences on the mass of the light quark. In particular, we examine the strange and nonstrange D mesons. We find that the predictions of scalar confinement are in considerable conflict with measured values.

From Coalgebra to Bialgebra for the Six-Vertex Model: The Star-Triangle Relation as a Necessary Condition for Commuting Transfer Matrices

Using the most elementary methods and considerations, the solution of the star-triangle condition (a2+b2-c2)/2ab = ((a’)^2+(b’)^2-(c’))^2/2a’b’ is shown to be a necessary condition for the extension of the operator coalgebra of the six-vertex model to a bialgebra. A portion of the bialgebra acts as a spectrum-generating algebra for the algebraic Bethe ansatz, with which higher-dimensional representations of the bialgebra can be constructed. The star-triangle relation is proved to be necessary for the commutativity of the transfer matrices T(a, b, c) and T(a’, b’, c’).

Maxwellian relaxation of elastic particles in one dimension

The statistical mechanics of one-dimensional binary mixtures is discussed from both a theoretical and simulation point of view at a level suitable for senior and introductory graduate level courses in statistical mechanics. By using a simple mathematical technique, the nonlinear Boltzmann equation is solved exactly in Fourier space. An efficient simulation algorithm is presented which yields results that are in excellent agreement with theory. We show that the velocity distribution of each type of particle relaxes to a Maxwellian for all mass ratios other than unity and infinity, and the relaxation time is a minimum for the mass ratio of 3+22.

Spectrum-generating bialgebra of the hexagonal-lattice dimer model

The method of constructing a complete set of “zero-operator” identities preserved by the matrix coproduct is shown to be general, and is used to build the operator bialgebra for the hexagonal-lattice dimer model. This technique is complementary to the RTT-equation, and does not require a solution to the Yang–Baxter equation. The resulting bialgebra in the case of hexagonal lattice dimers has a distinctly Yangian structure, but has no R-matrix or antipode.

QCD strings with spinning quarks

We construct a consistent action for a massive spinning quark on the end of a QCD string that leads to a pure Thomas precession of the quarks spin. The string action is modified by the addition of Grassmann degrees of freedom to the string such that the equations of motion for the quark spin follow from boundary conditions, just as do those for the quarks position.

Remark on the computation of mode sums

The computation of mode sums of the types encountered in basic quantum field theoretic applications is addressed with an emphasis on their expansions into functions of distance that can be interpreted as potentials. We show how to regularize and calculate the Casimir energy for the continuum Nambu-Goto string with massive ends as well as for the discrete Isgur-Paton non-relativistic string with massive ends. As an additional example, we examine the effect on the interquark potential of a constant Kalb-Ramond field strength interacting with a QCD string. (c) 2000 The American Physical Society.

A Rodriguez formula and integration measure for the quantum deformed Legendre functions

Quantum deformed analogs of the Legendre functions are constructed from shift operator representations of the quantum deformed orbital angular momentum operators. A Rodriguez formula is found as well as the measure used to orthonormalize the functions.

Puiseux Series Expansions for the Eigenvalues of Transfer Matrices and Partition Functions from the Newton Polygon Method for Nanotubes and Ribbons

For certain classes of lattice models of nanosystems the eigenvalues of the row-to-row transfer matrix and the components of the corner transfer matrix truncations are algebraic functions of the fugacity and of Boltzmann weights. Such functions can be expanded in Puiseux series using techniques from algebraic geometry. Each successive term in the expansions in powers a Boltzmann weight is obtained exactly without modifying previous terms. We are able to obtain useful analytical expressions for any thermodynamic function for these systems from the series in circumstances in which no exact solutions can be found.

Analytic solution of a set of discrete Boltzmann equations

An analytical solution to the discrete Boltzmann equations corresponding to a hexagonal lattice gas cell automata are derived and the information entropy is computed and compared to that of a numerical simulation of the gas.