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A series of (oligo)phenthiazines, thiazolium salts and sulfonic acid functionalized organic/inorganic hybrid materials were synthesized. The organic groups were covalently bound on the inorganic surface through reactions of organosilane precursors with TEOS or with the silanol groups of material surface. These synthetic methods are called the co-condensation process and the post grafting. The structures and the textural parameters of the generated hybrid materials were characterized by XRD, N2 adsorption-desorption measurements, SEM and TEM. The incorporations of the organic groups were verified by elemental analysis, thermogravimetric analysis, FT-IR, UV-Vis, EPR, CV, as well as by 13C CP-MAS NMR and 29Si CP-MAS NMR spectroscopy. Introduction of various organic groups endow different phsysical, chemical properties to these hybrid materials. The (oligo)phenothiazines provide a group of novel redox acitive hybrid materials with special electronic and optic properties. The thiazolium salts modified materials were applied as heterogenized organo catalysts for the benzoin condensation and the cross-coupling of aldehydes with acylimines to yield a-amido ketones. The sulfonic acid containing materials can not only be used as Broensted acid catalysts, but also can serve as ion exchangable supports for further modifications and applications.

A new approach with BRST invariance is suggested to cure the degeneracy problem of ill defined path integrals in the path- integral calculation of quantum mechanical tunneling effects in which the problem arises due to the occurrence of zero modes. The Faddeev-Popov procedure is avoided and the integral over the zero mode is transformed in a systematic way into a well defined integral over instanton positions. No special procedure has to be adopted as in the Faddeev-Popov method in calculating the Jacobian of the transformation. The quantum mechanical tunneling for the Sine-Gordon potential is used as a test of the method and the width of the lowest energy band is obtained in exact agreement with that of WKB calculations.

A new look at the RST model
(1996)

The RST model is augmented by the addition of a scalar field and a boundary term so that it is well-posed and local. Expressing the RST action in terms of the ADM formulation, the constraint structure can be analysed completely. It is shown that from the view point of local field theories, there exists a hidden dynamical field 1 in the RST model. Thanks to the presence of this hidden dynamical field, we can reconstruct the closed algebra of the constraints which guarantee the general invariance of the RST action. The resulting stress tensors TSigma Sigma are recovered to be true tensor quantities. Especially, the part of the stress tensors for the hidden dynamical field 1 gives the precise expression for tSigma . At the quantum level, the cancellation condition for the total central charge is reexamined. Finally, with the help of the hidden dynamical field 1, the fact that the semi-classical static soluti on of the RST model has two independent parameters (P,M), whereas for the classical CGHS model there is only one, can be explained.

Significance of zero modes in path-integral quantization of solitonic theories with BRST invariance
(1996)

The significance of zero modes in the path-integral quantization of some solitonic models is investigated. In particular a Skyrme-like theory with topological vortices in (1 + 2) dimensions is studied, and with a BRST invariant gauge fixing a well defined transition amplitude is obtained in the one loop approximation. We also present an alternative method which does not necessitate evoking the time-dependence in the functional integral, but is equivalent to the original one in dealing with the quantization in the background of the static classical solution of the non-linear field equations. The considerations given here are particularly useful in - but also limited to -the one-loop approximation.

The constraint structure of the induced 2D-gravity with the Weyl and area-preserving diffeomorphism invariances is analysed in the ADM formulation. It is found that when the area-preserving diffeomorphism constraints are kept, the usual conformal gauge does not exist, whereas there is the possibility to choose the so-called "quasi-light-cone" gauge, in which besides the area-preserving diffeomorphism invariance, the reduced Lagrangian also possesses the SL(2,R) residual symmetry. This observation indicates that the claimed correspondence between the SL(2,R) residual symmetry and the area-preserving diffeomorphism invariance in both regularisation approaches does not hold. The string-like approach is then applied to quantise this model, but a fictitious non-zero central charge in the Virasoro algebra appears. When a set of gauge-independent SL(2,R) current-like fields is introduced instead of the string-like variables, a consistent quantum theory is obtained, which means that the area-preserving diffeomorphism invariance can be maintained at the quantum level.

Quantum tunneling between degenerate ground states through the central barrier of a potential is extended to excited states with the instanton method. This extension is achieved with the help of an LSZ reduction technique as in field theory and may be of importance in the study of macroscopic quantum phenomena in magnetic systems.

Starting from the coherent state representation of the evolution operator with the help of the path-integral, we derive a formula for the low-lying levels E = ffl0 Gamma 24ffl cos(s + ,)ss of a quantum spin system. The quenching of macroscopic quantum coherence is understood as the vanishing of cos(s + ,)ss in disagreement with the suppression of tunneling (i.e. 4ffl = 0) as claimed in the literature. A new configuration called the macroscopic Fermi-particle is suggested by the character of its wave function. The tunne- ling rate ( 24fflss ) does not vanish, not for integer spin s nor for a half-integer value of s, and is calculated explicitly (for the position dependent mass) up to the one-loop approximation.

A formula suitable for a quantitative evaluation of the tunneling effect in a ferromagnetic particle is derived with the help of the instanton method. The tunneling between n-th degenerate states of neighboring wells is dominated by a periodic pseudoparticle configuration. The low-lying level-splitting previously obtained with the LSZ method in field theory in which the tunneling is viewed as the transition of n bosons induced by the usual(vacuum) instanton is recovered.The observation made with our new result is that the tunneling effect increases at excited states. The results should be useful in analyzing results of experimental tests of macroscopic quantum coherence in ferromagnetic particles.

The greybody factors in BTZ black holes are evaluated from 2D CFT in the spirit of AdS3/CFT correspondence. The initial state of black holes in the usual calculation of greybody factors by effective CFT is described as Poincar'e vacuum state in 2D CFT. The normalization factor which cannot be fixed in the effective CFT without appealing to string theory is shown to be determined by the normalized bulk-to-boundary Green function. The relation among the greybody factors in different dimensional black holes is exhibited. Two kinds of (h; _h) = (1; 1) operators which couple with the boundary value of massless scalar field are discussed.

2D quantum dilaton gravitational Hamiltonian, boundary terms and new definition for total energy
(1995)

The ADM and Bondi mass for the RST model have been first discussed from Hawking and Horowitz's argument. Since there is a nonlocal term in the RST model, the RST lagrangian has to be localized so that Hawking and Horowitz's proposal can be carried out. Expressing the localized RST action in terms of the ADM formulation, the RST Hamiltonian can be derived, meanwhile keeping track of all boundary terms. Then the total boundary terms can be taken as the total energy for the RST model. Our result shows that the previous expression for the ADM and Bondi mass actually needs to be modified at quantum level, but at classical level, our mass formula can be reduced to that given by Bilal and Kogan [5] and de Alwis [6]. It has been found that there is a new contribution to the ADM and Bondi mass from the RST boundary due to the existence of the hidden dynamical field. The ADM and Bondi mass with and without the RST boundary for the static and dynamical solutions have been discussed respectively in detail, and some new properties have been found. The thunderpop of the RST model has also been encountered in our new Bondi mass formula.