Addendum to "Classical and Quantum Evolutions of the de Sitter and the anti-de Sitter Universes in 2+1 dimensions"

The previous discussion \cite{ezawa} on reducing the phase space of the first order Einstein gravity in 2+1 dimensions is reconsidered. We construct a \lq\lq correct" physical phase space in the case of positive cosmological constant, taking into account the geometrical feature of SO(3,1) connections. A parametrization which unifies the two sectors of the physical phase space is also given.Comment: Latex 8 pages (Crucial and essential changes have been made.

Phase Transition in \nu=2 Bilayer Quantum Hall State

The Hall-plateau width and the activation energy were measured in the bilayer quantum Hall state at filling factor \nu=2, 1 and 2/3, by changing the total electron density and the density ratio in the two quantum wells. Their behavior are remarkably different from one to another. The \nu=1 state is found stable over all measured range of the density difference, while the \nu=2/3$ state is stable only around the balanced point. The \nu=2 state, on the other hand, shows a phase transition between these two types of the states as the electron density is changed.Comment: 5 pages including figures, RevTe

Conical Singular Solutions in (2+1)-Dimensional Gravity Employing the ADM Canonical Formalism

Topological solutions in the (2+1)-dimensional Einstein theory of gravity are studied within the ADM canonical formalism. It is found that a conical singularity appears in the closed de Sitter universe solution as a topological defect in the case of the Einstein theory with a cosmological constant. Quantum effects on the conical singularity are studied using the de Broglie-Bohm interpretation. Finite quantum tunneling effects are obtained for the closed de Sitter universe, while no quantum effects are obtained for an open universe.Comment: 15 pages, 3 figure

Collective modes of CP(3) Skyrmion crystals in quantum Hall ferromagnets

The two-dimensional electron gas in a bilayer quantum Hall system can sustain an interlayer coherence at filling factor nu=1 even in the absence of tunneling between the layers. This system has low-energy charged excitations which may carry textures in real spin or pseudospin. Away from filling factor nu =1 a finite density of these is present in the ground state of the 2DEG and forms a crystal. Depending on the relative size of the various energy scales, such as tunneling (Delta_SAS), Zeeman coupling (Delta_Z) or electrical bias (Delta_b), these textured crystal states can involve spin, pseudospin, or both intertwined. In this article, we present a comprehensive numerical study of the collective excitations of these textured crystals using the GRPA. For the pure spin case, at finite Zeeman coupling the state is a Skyrmion crystal with a gapless phonon mode, and a separate Goldstone mode that arises from a broken U(1) symmetry. At zero Zeeman coupling, we demonstrate that the constituent Skyrmions break up, and the resulting state is a meron crystal with 4 gapless modes. In contrast, a pure pseudospin Skyrme crystal at finite tunneling has only the phonon mode. For Delta_SAS=0, the state evolves into a meron crystal and supports an extra gapless U(1) mode in addition to the phonon. For a CP(3) Skyrmion crystal, we find a U(1) gapless mode in the presence of the symmetry-breaking fields. In addition, a second mode with a very small gap is present in the spectrum.Comment: 16 pages and 12 eps figure

The Study of Goldstone Modes in ν\nu=2 Bilayer Quantum Hall Systems

At the filling factor $\nu$=2, the bilayer quantum Hall system has three phases, the spin-ferromagnet phase, the spin singlet phase and the canted antiferromagnet (CAF) phase, depending on the relative strength between the Zeeman energy and interlayer tunneling energy. We present a systematic method to derive the effective Hamiltonian for the Goldstone modes in these three phases. We then investigate the dispersion relations and the coherence lengths of the Goldstone modes. To explore a possible emergence of the interlayer phase coherence, we analyze the dispersion relations in the zero tunneling energy limit. We find one gapless mode with the linear dispersion relation in the CAF phase.Comment: 13 pages, no figures. One reference is added. Typos correcte

Only hybrid anyons can exist in broken symmetry phase of nonrelativistic U(1)2U(1)^{2} Chern-Simons theory

We present two examples of parity-invariant $[U(1)]^{2}$ Chern-Simons-Higgs models with spontaneously broken symmetry. The models possess topological vortex excitations. It is argued that the smallest possible flux quanta are composites of one quantum of each type $(1,1)$. These hybrid anyons will dominate the statistical properties near the ground state. We analyse their statistical interactions and find out that unlike in the case of Jackiw-Pi solitons there is short range magnetic interaction which can lead to formation of bound states of hybrid anyons. In addition to mutual interactions they possess internal structure which can lead upon quantisation to discrete spectrum of energy levels.Comment: 10 pages in plain Latex (one argument added, version accepted for publication in Phys.Rev.D(Rapid Communications)

Einstein-Infeld-Hoffman method and soliton dynamics in a parity noninvariant system

We consider slow motion of a pointlike topological defect (vortex) in the nonlinear Schrodinger equation minimally coupled to Chern-Simons gauge field and subject to external uniform magnetic field. It turns out that a formal expansion of fields in powers of defect velocity yields only the trivial static solution. To obtain a nontrivial solution one has to treat velocities and accelerations as being of the same order. We assume that acceleration is a linear form of velocity. The field equations linearized in velocity uniquely determine the linear relation. It turns out that the only nontrivial solution is the cyclotron motion of the vortex together with the whole condensate. This solution is a perturbative approximation to the center of mass motion known from the theory of magnetic translations.Comment: 6 pages in Latex; shortened version to appear in Phys.Rev.