A Modular Invariant Quantum Theory From the Connection Formulation of (2+1)-Gravity on the Torus

By choosing an unconventional polarization of the connection phase space in (2+1)-gravity on the torus, a modular invariant quantum theory is constructed. Unitary equivalence to the ADM-quantization is shown.Comment: Latex, 4 page

Conductivity landscape of highly oriented pyrolytic graphite surface containing ribbons and edges

We present an extensive study on electrical spectroscopy of graphene ribbons and edges of highly oriented pyrolytic graphite (HOPG) using atomic force microscope (AFM). We have addressed in the present study two main issues, (1) How does the electrical property of the graphite (graphene) sheet change when the graphite layer is displaced by shear forces? and (2) How does the electrical property of the graphite sheet change across a step edge? While addressing these two issues we observed, (1) variation of conductance among the graphite ribbons on the surface of HOPG. The top layer always exhibits more conductance than the lower layers, (2) two different monolayer ribbons on the same sheet of graphite shows different conductance, (3) certain ribbon/sheet edges show sharp rise in current, (4) certain ribbons/sheets on the same edge shows both presence and absense of the sharp rise in the current, (5) some lower layers at the interface near a step edge shows a strange dip in the current/conductance (depletion of charge). We discuss possible reasons for such rich conducting landscape on the surface of graphite.Comment: 13 pages, 9 figures. For better quality figures please contact autho

Optimal Covariant Measurement of Momentum on a Half Line in Quantum Mechanics

We cannot perform the projective measurement of a momentum on a half line since it is not an observable. Nevertheless, we would like to obtain some physical information of the momentum on a half line. We define an optimality for measurement as minimizing the variance between an inferred outcome of the measured system before a measuring process and a measurement outcome of the probe system after the measuring process, restricting our attention to the covariant measurement studied by Holevo. Extending the domain of the momentum operator on a half line by introducing a two dimensional Hilbert space to be tensored, we make it self-adjoint and explicitly construct a model Hamiltonian for the measured and probe systems. By taking the partial trace over the newly introduced Hilbert space, the optimal covariant positive operator valued measure (POVM) of a momentum on a half line is reproduced. We physically describe the measuring process to optimally evaluate the momentum of a particle on a half line.Comment: 12 pages, 3 figure

A catalytic combustion-type CO gas sensor incorporating aluminum nitride as an intermediate heat transfer layer for accelerated response time

A catalytic combustion-type carbon monoxide gas sensor exhibiting good sensing performance even at moderate temperatures was previously developed by employing a Pt loaded CeO2–ZrO2–SnO2 solid solution as the CO oxidizing catalyst. The addition of aluminum nitride as an intermediate heat transfer layer between the Pt coil and the CO oxidizing catalyst drastically accelerated the response of this device to CO at temperatures as low as 70 °C

63/65^{63/65}Cu- and 35/37^{35/37}Cl-NMR Studies of Triplet Localization in the Quantum Spin System NH4_4CuCl3_3

$^{63/65}$Cu- and $^{35/37}$Cl-NMR experiments were performed to investigate triplet localization in the $S=1/2$ dimer compound NH$_4$CuCl$_3$, which shows magnetization plateaus at one-quarter and three-quarters of the saturation magnetization. In $^{63/65}$Cu-NMR experiments, signal from only the singlet Cu site was observed, because that from the triplet Cu site was invisible due to the strong spin fluctuation of onsite 3$d$-spins. We found that the temperature dependence of the shift of $^{63/65}$Cu-NMR spectra at the singlet Cu site deviated from that of macroscopic magnetization below T=6 K. This deviation is interpreted as the triplet localization in this system. From the $^{35/37}$Cl-NMR experiments at the 1/4-plateau phase, we found the two different temperature dependences of Cl-shift, namely the temperature dependence of one deviates below T=6 K from that of the macroscopic magnetization as observed in the $^{63/65}$Cu-NMR experiments, whereas the other corresponds well with that of the macroscopic magnetization in the entire experimental temperature region. We interpreted these dependences as reflecting the transferred hyperfine field at the Cl site located at a singlet site and at a triplet site, respectively. This result also indicates that the triplets are localized at low temperatures. $^{63/65}$Cu-NMR experiments performed at high magnetic fields between the one-quarter and three-quarters magnetization plateaus have revealed that the two differently oriented dimers in the unit cell are equally occupied by triplets, the fact of which limits the theoretical model on the periodic structure of the localized triplets.Comment: 19 pages, 9 figures, submitted to PRB (in press

Unitary Equivalence of the Metric and Holonomy Formulations of 2+1 Dimensional Quantum Gravity on the Torus

Recent work on canonical transformations in quantum mechanics is applied to transform between the Moncrief metric formulation and the Witten-Carlip holonomy formulation of 2+1-dimensional quantum gravity on the torus. A non-polynomial factor ordering of the classical canonical transformation between the metric and holonomy variables is constructed which preserves their classical modular transformation properties. An extension of the definition of a unitary transformation is briefly discussed and is used to find the inner product in the holonomy variables which makes the canonical transformation unitary. This defines the Hilbert space in the Witten-Carlip formulation which is unitarily equivalent to the natural Hilbert space in the Moncrief formulation. In addition, gravitational theta-states arising from ``large'' diffeomorphisms are found in the theory.Comment: 31 pages LaTeX [Important Revision: a section is added constructing the inner product/Hilbert space for the Witten-Carlip holonomy formulation; the proof of unitary equivalence of the metric and holonomy formulations is then completed. Other additions include discussion of relation of canonical and unitary transformations. Title/abstract change.

Universe Reheating after Inflation

We study the problem of scalar particle production after inflation by a rapidly oscillating inflaton field. We use the framework of the chaotic inflation scenario with quartic and quadratic inflaton potentials. Particular attention is paid to parametric resonance phenomena which take place in the presence of the quickly oscillating inflaton field. We have found that in the region of applicability of perturbation theory the effects of parametric resonance are crucial, and estimates based on first order Born approximation often underestimate the particle production. In the case of the quartic inflaton potential $V(\varphi) = \lambda \varphi^4$, the particle production process is very efficient even for small values of coupling constants. The reheating temperature of the universe in this case is $\left[\lambda\, \log\, (1/\lambda) \right]^{- 1}$ times larger than the corresponding estimates based on first order Born approximation. In the case of the quadratic inflaton potential the reheating process depends crucially on the type of coupling between the inflaton and the other scalar field and on the magnitudes of the coupling constants. If the inflaton coupling to fermions and its linear (in inflaton field) coupling to scalar fields are suppressed, then, as previously discussed by Kofman, Linde and Starobinsky (see e.g. Ref. 13), the inflaton field will eventually decouple from the rest of the matter, and the residual inflaton oscillations may provide the (cold) dark matter of the universe. In the case of the quadratic inflaton potential we obtain the lowest and the highest possible bounds on the effective energy density of the inflaton field when it freezes out.Comment: 40 pages, Preprint BROWN-HET-957 (revised version, some mistakes corrected), uses phyzz

Cosmological Sphaleron from Real Tunneling and Its Fate

We show that the cosmological sphaleron of Einstein-Yang-Mills system can be produced from real tunneling geometries. The sphaleron will tend to roll down to the vacuum or pure gauge field configuration, when the universe evolves in the Lorentzian signature region with the sphaleron and the corresponding hypersurface being the initial data for the Yang-Mills field and the universe, respectively. However, we can also show that the sphaleron, although unstable, can be regarded as a pseudo-stable solution because its lifetime is even much greater than those of the universe.Comment: 20 pages, LaTex, article 12pt style, TIT/HEP-242/COSMO-3

Quantum three-body system in D dimensions

The independent eigenstates of the total orbital angular momentum operators for a three-body system in an arbitrary D-dimensional space are presented by the method of group theory. The Schr\"{o}dinger equation is reduced to the generalized radial equations satisfied by the generalized radial functions with a given total orbital angular momentum denoted by a Young diagram $[\mu,\nu,0,...,0]$ for the SO(D) group. Only three internal variables are involved in the functions and equations. The number of both the functions and the equations for the given angular momentum is finite and equal to $(\mu-\nu+1)$.Comment: 16 pages, no figure, RevTex, Accepted by J. Math. Phy