3,271 research outputs found
Quantum Fluctuations of Black Hole Geometry
By using the minisuperspace model for the interior metric ofstatic black
holes, we solve the Wheeler-DeWitt equation to study quantum mechanics of the
horizon geometry. Our basic idea is to introduce the gravitational mass and the
expansions of null rays as quantum operators. Then, the exact wave function is
found as a mass eigenstate, and the radius of the apparent horizon is
quantum-mechanically defined. In the evolution of the metric variables, the
wave function changes from a WKB solution giving the classical trajectories to
a tunneling solution. By virtue of the quantum fluctuations of the metric
evolution beyond the WKB approximation, we can observe a static black hole
state with the apparent horizon separating from the event horizon.Comment: 18 pages, DPNU-93-3
The Vertex-Face Correspondence and the Elliptic 6j-symbols
A new formula connecting the elliptic -symbols and the fusion of the
vertex-face intertwining vectors is given. This is based on the identification
of the fusion intertwining vectors with the change of base matrix elements
from Sklyanin's standard base to Rosengren's natural base in the space of even
theta functions of order . The new formula allows us to derive various
properties of the elliptic -symbols, such as the addition formula, the
biorthogonality property, the fusion formula and the Yang-Baxter relation. We
also discuss a connection with the Sklyanin algebra based on the factorised
formula for the -operator.Comment: 23 page
Free Field Approach to the Dilute A_L Models
We construct a free field realization of vertex operators of the dilute A_L
models along with the Felder complex. For L=3, we also study an E_8 structure
in terms of the deformed Virasoro currents.Comment: (AMS-)LaTeX(2e), 43page
Continuous-time quantum walk on integer lattices and homogeneous trees
This paper is concerned with the continuous-time quantum walk on Z, Z^d, and
infinite homogeneous trees. By using the generating function method, we compute
the limit of the average probability distribution for the general isotropic
walk on Z, and for nearest-neighbor walks on Z^d and infinite homogeneous
trees. In addition, we compute the asymptotic approximation for the probability
of the return to zero at time t in all these cases.Comment: The journal version (save for formatting); 19 page
Localization of the Grover walks on spidernets and free Meixner laws
A spidernet is a graph obtained by adding large cycles to an almost regular
tree and considered as an example having intermediate properties of lattices
and trees in the study of discrete-time quantum walks on graphs. We introduce
the Grover walk on a spidernet and its one-dimensional reduction. We derive an
integral representation of the -step transition amplitude in terms of the
free Meixner law which appears as the spectral distribution. As an application
we determine the class of spidernets which exhibit localization. Our method is
based on quantum probabilistic spectral analysis of graphs.Comment: 32 page
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