397 research outputs found
Numerical Study of TAP Metastable States in 3-body Ising Spin Glasses
The distribution of solutions of the Thouless-Anderson-Palmer equation is
studied by extensive numerical experiments for fully connected 3-body
interaction Ising spin glass models in a level of annealed calculation. A
recent study predicted that when the equilibrium state of the system is
characterized by one-step replica symmetry breaking, the distribution is
described by a Becchi-Rouet-Stora-Tyutin (BRST) supersymmetric solution in the
relatively low free energy region, whereas the BRST supersymmetry is broken for
higher values of free energy (Crisanti et al., Phys. Rev. B 71 (2005) 094202).
Our experiments qualitatively reproduce the discriminative behavior of
macroscopic variables predicted by the theoretical assessment.Comment: 13 pages, 4 figure
Phase Diagram of the ------ Model at Quarter Filling
We examine the ground-state properties of the one-dimensional Hubbard model
at quarter filling with Coulomb interactions between nearest-neighbors
and next-nearest neighbors . Using the density-matrix renormalization
group and exact diagonalization methods, we obtain an accurate ground-state
phase diagram in the - plane with three different phases: - and -charge-density-wave and a broad metallic phase
in-between. The metal is a Tomonaga-Luttinger-liquid whose critical exponent
is largest around , where and are frustrated,
and smallest, , at the boundaries between the metallic phase and
each of the two ordered phases.Comment: 4 pages, 5 figures, sumitted to PR
Anti-self-dual Maxwell solutions on hyperk\"ahler manifold and N=2 supersymmetric Ashtekar gravity
Anti-self-dual (ASD) Maxwell solutions on 4-dimensional hyperk\"ahler
manifolds are constructed. The N=2 supersymmetric half-flat equations are
derived in the context of the Ashtekar formulation of N=2 supergravity. These
equations show that the ASD Maxwell solutions have a direct connection with the
solutions of the reduced N=2 supersymmetric ASD Yang-Mills equations with a
special choice of gauge group. Two examples of the Maxwell solutions are
presented.Comment: 9 page
Dynamical Symmetry Breaking in Fractal Space
We formulate field theories in fractal space and show the phase diagrams of
the coupling versus the fractal dimension for the dynamical symmetry breaking.
We first consider the 4-dimensional Gross-Neveu (GN) model in the
(4-d)-dimensional randomized Cantor space where the fermions are restricted to
a fractal space by the high potential barrier of Cantor fractal shape. By the
statistical treatment of this potential, we obtain an effective action
depending on the fractal dimension. Solving the 1/N leading Schwinger-Dyson
(SD) equation, we get the phase diagram of dynamical symmetry breaking with a
critical line similar to that of the d-dimensional (2<d<4) GN model except for
the system-size dependence. We also consider QED4 with only the fermions
formally compactified to d dimensions. Solving the ladder SD equation, we
obtain the phase diagram of dynamical chiral symmetry breaking with a linear
critical line, which is consistent with the known results for d=4 (the
Maskawa-Nakajima case) and d=2 (the case with the external magnetic field).Comment: 28 pages, 5 figures, LaTeX with epsf macr
Compact Einstein Spaces based on Quaternionic K\"ahler Manifolds
We investigate the Einstein equation with a positive cosmological constant
for -dimensional metrics on bundles over Quaternionic K\"ahler base
manifolds whose fibers are 4-dimensional Bianchi IX manifolds. The Einstein
equations are reduced to a set of non-linear ordinary differential equations.
We numerically find inhomogeneous compact Einstein spaces with orbifold
singularity.Comment: LaTeX 28 pages, 5 eps figure
Effective Theoretical Approach to Back Reaction of the Dynamical Casimir Effect in 1+1 Dimensions
We present an approach to studying the Casimir effects by means of the
effective theory. An essential point of our approach is replacing the mirror
separation into the size of space S^1 in the adiabatic approximation. It is
natural to identify the size of space S^1 with the scale factor of the
Robertson-Walker-type metric. This replacement simplifies the construction of a
class of effective models to study the Casimir effects. To check the validity
of this replacement we construct a model for a scalar field coupling to the
two-dimensional gravity and calculate the Casimir effects by the effective
action for the variable scale factor. Our effective action consists of the
classical kinetic term of the mirror separation and the quantum correction
derived by the path-integral method. The quantum correction naturally contains
both the Casimir energy term and the back-reaction term of the dynamical
Casimir effect, the latter of which is expressed by the conformal anomaly. The
resultant effective action describes the dynamical vacuum pressure, i.e., the
dynamical Casimir force. We confirm that the force depends on the relative
velocity of the mirrors, and that it is always attractive and stronger than the
static Casimir force within the adiabatic approximation.Comment: Published Version, 16 pages, LaTeX2e with graphics package, 1 figur
A Deformation of Sasakian Structure in the Presence of Torsion and Supergravity Solutions
We discuss a deformation of Sasakian structure in the presence of totally
skew-symmetric torsion by introducing odd dimensional manifolds whose metric
cones are K\"ahler with torsion. It is shown that such a geometry inherits
similar properties to those of Sasakian geometry. As an example of them, we
present an explicit expression of local metrics and see how Sasakian structure
is deformed by the presence of torsion. We also demonstrate that our example of
the metrics admits the existence of hidden symmetries described by non-trivial
odd-rank generalized closed conformal Killing-Yano tensors. Furthermore, using
these metrics as an {\it ansatz}, we construct exact solutions in five
dimensional minimal (un-)gauged supergravity and eleven dimensional
supergravity. Finally, we discuss the global structures of the solutions and
obtain regular metrics on compact manifolds in five dimensions, which give
natural generalizations of Sasaki--Einstein manifolds and
. We also discuss regular metrics on non-compact manifolds in eleven
dimensions.Comment: 38 pages, 1 table, v2: version to appear in Class. Quant. Gra
Charged Rotating Kaluza-Klein Black Holes Generated by G2(2) Transformation
Applying the G_{2(2)} generating technique for minimal D=5 supergravity to
the Rasheed black hole solution, we present a new rotating charged Kaluza-Klein
black hole solution to the five-dimensional Einstein-Maxwell-Chern-Simons
equations. At infinity, our solution behaves as a four-dimensional flat
spacetime with a compact extra dimension and hence describes a Kaluza-Klein
black hole. In particlar, the extreme solution is non-supersymmetric, which is
contrast to a static case. Our solution has the limits to the asymptotically
flat charged rotating black hole solution and a new charged rotating black
string solution.Comment: 24 page
Macroscopic quantum tunneling of two-component Bose-Einstein condensates
We show theoretically the existence of a metastable state and the possibility
of decay to the ground state through macroscopic quantum tunneling in
two-component Bose-Einstein condensates with repulsive interactions. Numerical
analysis of the coupled Gross-Pitaevskii equations clarifies the metastable
states whose configuration preserves or breaks the symmetry of the trapping
potential, depending on the interspecies interaction and the particle number.
We calculate the tunneling decay rate of the metastable state by using the
collective coordinate method under the WKB approximation. Then the height of
the energy barrier is estimated by the saddle point solution. It is found that
macroscopic quantum tunneling is observable in a wide range of particle
numbers. Macroscopic quantum coherence between two distinct states is
discussed; this might give an additional coherent property of two-component
Bose condensed systems. Thermal effects on the decay rate are estimated.Comment: 11 pages, 10 figures, revtex
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