How to construct a coordinate representation of a Hamiltonian operator on a torus

The dynamical system of a point particle constrained on a torus is quantized \`a la Dirac with two kinds of coordinate systems respectively; the Cartesian and toric coordinate systems. In the Cartesian coordinate system, it is difficult to express momentum operators in coordinate representation owing to the complication in structure of the commutation relations between canonical variables. In the toric coordinate system, the commutation relations have a simple form and their solutions in coordinate representation are easily obtained with, furthermore, two quantum Hamiltonians turning up. A problem comes out when the coordinate system is transformed, after quantization, from the Cartesian to the toric coordinate system.Comment: 17 pages, LaTeX, 1 Figure included as a compressed uuencoded postscript fil

Suppression of negative-energy propagation in the Dirac phenomenology due to the structure of a nucleon

The relativistic impulse optical model is investigated using derivative coupling potential. We found the suppression of the negative-energy propagation compared to the usual t-rho potential. However, it can be taken into account by the renormalized potential in the Dirac equation. Thus, the Dirac phenomenology is still valid

Resolution of Gordon Ambiguity of Nucleon Current in Relativistic Nuclear Matter

We investigate the electromagnetic vertex function for a nucleon in relativistic nuclear medium. The effect of mean fields on the internal nucleon lines (propagators) connected to external lines in the corresponding Feynman diagram offsets the difference between the familiar CC2 current and the so-called CC1 or CC3 current. It is therefore found that the CC2 current is physically reasonable. Consequently, the famous Gordon ambiguity of the nuclear current has been resolved

Effect of Meson Cloud of Nucleon on Nuclear Matter Saturation

We investigate the effect of the meson cloud of nucleon on saturation properties of nuclear matter. Quantum correction to the scalar and vector potentials in the Walecka model is taken into account. It leads to the renormalized wave function of a nucleon in the medium, or the dressed nucleon by the meson cloud. Consequently, the NN-sigma and NN-omega coupling constants are renormalized. The renormalization constant can be related to the anomalous magnetic moment. The resultant renormalized Walecka model is able to reproduce nuclear matter saturation properties well

Inverse versus Normal NiAs Structure as High-Pressure Phase of FeO and MnO

The high-pressure phases of FeO and MnO were studied by the first principles calculations. The present theoretical study predicts that the high-pressure phase of MnO is a metallic normal B8 structure (nB8), while that of FeO should take the inverse B8 structure (iB8). The novel feature of the unique high-pressure phase of stoichiometric FeO is that the system should be a band insulator in the ordered antiferromagnetic (AF) state and that the existence of a band gap leads to special stability of the phase. The observed metallicity of the high-pressure and high-temperature phase of FeO may be caused by the loss of AF order and also by the itinerant carriers created by non-stoichiometry. Analysis of x-ray diffraction experiments provides a further support to the present theoretical prediction for both FeO and MnO. Strong stability of the high-pressure phase of FeO will imply possible important roles in Earth's core.Comment: 7 pages, 3 figures and 1 table; submitted to "Nature

Equivalence between Schwinger and Dirac schemes of quantization

This paper introduces the modified version of Schwinger's quantization method, in which the information on constraints and the choice of gauge conditions are included implicitly in the choice of variations used in quantization scheme. A proof of equivalence between Schwinger- and Dirac-methods for constraint systems is given.Comment: 12pages, No figures, Latex, The proof is improved and one reference is adde

Numerical and Theoretical Study of a Monodisperse Hard-Sphere Glass Former

There exists a variety of theories of the glass transition and many more numerical models. But because the models need built-in complexity to prevent crystallization, comparisons with theory can be difficult. We study the dynamics of a deeply supersaturated \emph{monodisperse} four-dimensional (4D) hard-sphere fluid, which has no such complexity, but whose strong intrinsic geometrical frustration inhibits crystallization, even when deeply supersaturated. As an application, we compare its behavior to the mode-coupling theory (MCT) of glass formation. We find MCT to describe this system better than any other structural glass formers in lower dimensions. The reduction in dynamical heterogeneity in 4D suggested by a milder violation of the Stokes-Einstein relation could explain the agreement. These results are consistent with a mean-field scenario of the glass transition.Comment: 5 pages, 3 figure

Stable Marriage with Multi-Modal Preferences

We introduce a generalized version of the famous Stable Marriage problem, now based on multi-modal preference lists. The central twist herein is to allow each agent to rank its potentially matching counterparts based on more than one "evaluation mode" (e.g., more than one criterion); thus, each agent is equipped with multiple preference lists, each ranking the counterparts in a possibly different way. We introduce and study three natural concepts of stability, investigate their mutual relations and focus on computational complexity aspects with respect to computing stable matchings in these new scenarios. Mostly encountering computational hardness (NP-hardness), we can also spot few islands of tractability and make a surprising connection to the \textsc{Graph Isomorphism} problem