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Radiation from a moving Scalar Source

Ren Hai, Weinberg Erick J.
05 Dec 1993 hep-th arxiv.org/abs/hep-th/9312038

We study classical radiation and quantum bremsstrahlung effect of a moving point scalar source. Our classical analysis provides another example of resolving a well-known apparent paradox, that of whether a constantly accelerating source radiates or not. Quantum mechanically, we show that for a scalar source with arbitrary motion, the tree level emission rate of scalar particles in the inertial frame equals the sum of emission and absorption rates of zero-energy Rindler particles in the Rindler frame. We then explicitly verify this result for a source undergoing constant proper acceleration.

Time-Dependent Open String Solutions in 2+1 Dimensional Gravity

Ren Hai
09 Dec 1993 gr-qc arxiv.org/abs/gr-qc/9312018

We find general, time-dependent solutions produced by open string sources carrying no momentum flow in 2+1 dimensional gravity. The local Poincar\'e group elements associated with these solutions and the coordinate transformations that transform these solutions into Minkowski metric are obtained. We also find the relation between these solutions and the planar wall solutions in 3+1 dimensions.

Fermions in a Global Monopole Background

Ren Hai
09 Dec 1993 hep-th arxiv.org/abs/hep-th/9312074

We study the scattering of fermions in a ``global monopole'' background metric. This is the four-dimensional analogue of the scattering on a cone in three dimensions. The scattering amplitude is exactly obtained. We then study massless fermion-dyon systems in such a background metric. The density of the $S$-wave fermion condensate is found to be given by a constant times the flat space value of Callan and Rubakov.

Noncompact Lattice Formulation of Gauge Theories

Friedberg R., Lee T. D., Pang Y., Ren H. C.
11 May 1995 hep-lat arxiv.org/abs/hep-lat/9505010

We expand the gauge field in terms of a suitably constructed complete set of Bloch wave functions, each labeled by a band designation $\,n\,$ and a wave number $\,\vec K\,$ restricted to the Brillouin zone. A noncompact formulation of lattice QCD (or QED) can be derived by restricting the expansion only to the $\,0^{th}$-band ($\,n = 0\,$) functions, which are simple continuum interpolations of discrete values associated with sites or links on a lattice. The exact continuum theory can be reached through the inclusion of all $\,n = 0\,$ and $\,n \ne 0\,$ bands, without requiring the lattice size $\,\ell \to 0\,$. This makes it possible, at a nonzero $\,\ell\,$, for the lattice coupling $\,g_\ell\,$ to act as the renormalized continuum coupling. All physical results in the continuum are, of course, independent of $\,\ell\,$.

WZW model based on the extended de Sitter group

Ren Hai
17 May 1995 hep-th arxiv.org/abs/hep-th/9505103

We study the WZW model based on the centrally extended 2D de Sitter algebra. We obtain the spacetime metric and its explicitly conformally flat expression. The symmetries of the spacetime are found by identifying the Killing vectors with the group generators. The energy-momentum tensor obtained from the affine-Sugawara construction agrees with that from the more conventional approach. The exact center charge agrees to one-loop order with the one-loop beta function equations. We have also studied the representations of the corresponding enveloping Virasoro algebra.

Superconducting state properties of a d-wave superconductor with mass anisotropy

Xu Ji-Hai, Ren Yong, Ting C. S.
27 Nov 1995 cond-mat arxiv.org/abs/cond-mat/9511130

YBa$_2$Cu$_3$O$_7$ (YBCO) exhibits a large anisotropy between the $a$ and $b$ axes in the CuO$_2$ planes because of the presence of CuO chains. In order to account for such an anisotropy we develop a Ginzburg-Landau (GL) theory for an anisotropic d-wave superconductor in an external magnetic field, based on an anisotropic effective mass approximation within CuO$_2$ planes. The anisotropic parameter $\lambda=m_x/m_y$, where $m_x$ ($m_y$) is the effective mass in the $x$ ($y$) direction, is found to have significant physical consequences: In the bulk case, there exist both the $s$- and $d$-wave order parameters with the same transition temperature, as long as $\lambda\ne 1$. The GL equations are also solved both analytically and numerically for the vortex state, and it is shown that both the $s$- and $d$-wave components show a two-fold symmetry, in contrast to the four-fold symmetry around the vortex, as expected for the purely $d$-wave vortex. With the deviation of $\lambda$ from unity, the opposite winding between the $s$- and $d$-wave components observed in the purely $d$-wave case is gradually taken over by the same winding number. The vortex lattice is found to have oblique structure in a wide temperature range with the precise shape depending on the anisotropy.

Isospin dependence of collective flow in heavy-ion collisions at intermediate energies

Li Bao-An, Ren Z. Z., Ko C. M., Yennello S. J.
09 May 1996 nucl-th nucl-ex arxiv.org/abs/nucl-th/9605015

Within the framework of an isospin-dependent Boltzmann-Uehling-Uhlenbeck (BUU) model using initial proton and neutron densities calculated from the nonlinear relativistic mean-field (RMF) theory, we compare the strength of transverse collective flow in reactions $^{48}Ca+^{58}Fe$ and $^{48}Cr+^{58}Ni$, which have the same mass number but different neutron/proton ratios. The neutron-rich system ($^{48}Ca+^{58}Fe$) is found to show significantly stronger negative deflection and consequently has a higher balance energy, especially in peripheral collisions. NOTE ADDED IN PROOF: The new phenomenon predicted in this work has just been confirmed by an experiment done by G.D. Westfall et al. using the NSCL/MSU radioactive beam facility and a spartan soccer. A paper by R. Pak et al. is submitted to PRL to report the experimental result.

Gleason's problem in weighted Bergman space on egg domains

Ren Guangbin, Shi Jihuai
05 Aug 1996 math.CV arxiv.org/abs/math/9608201

In the paper, we discuss on the egg domains: $$ \Omega_a=\left{\xi=(z,w)\in\bold C^{n+m}: \ z\in\bold C^n, \ w\in\bold C^m, |z|^2+|w|^{2/a}<1\right}, \qquad 0<a\le 2. $$ We show that Gleason's problem can be solved in the weight Bergman space on theegg domains. The proof will need the help of the recent work of the second named author on the weighted Bergman projections on this kind of domain. As an application, we obtain a multiplier theorem on the egg domains.

Extended bound states and resonances of two fermions on a periodic lattice

Blaer A. S., Ren H. C., Tchernyshyov O.
12 Aug 1996 supr-con cond-mat.supr-con arxiv.org/abs/supr-con/9608003

The high-$T_c$ cuprates are possible candidates for d-wave superconductivity, with the Cooper pair wave function belonging to a non-trivial irreducible representation of the lattice point group. We argue that this d-wave symmetry is related to a special form of the fermionic kinetic energy and does not require any novel pairing mechanism. In this context, we present a detailed study of the bound states and resonances formed by two lattice fermions interacting via a non-retarded potential that is attractive for nearest neighbors but repulsive for other relative positions. In the case of strong binding, a pair formed by fermions on adjacent lattice sites can have a small effective mass, thereby implying a high condensation temperature. For a weakly bound state, a pair with non-trivial symmetry tends to be smaller in size than an s-wave pair. These and other findings are discussed in connection with the properties of high-$T_c$ cuprate superconductors.

A Possible Mechanism for Pseudo-Gap in Cuprates

Ren Hai-cang
19 Dec 1996 cond-mat arxiv.org/abs/cond-mat/9612184

The electron spectrum in the normal phase of cuprates is analyzed in terms of the boson-fermion model. It is argued that the existence of the uncondensed pairs and the quasi-two-dimensional nature of the crystal structure are responsible for the pseudo-gap above T_C observed recently.