The statistical properties of dynamically triangulated manifolds (DT mfds) in terms of the geodesic distance have been studied numerically. The string susceptibility exponents for the boundary surfaces in three-dimensional DT mfds were measured numer
ically. For spherical boundary surfaces, we obtained a result consistent with the case of a two-dimensional spherical DT surface described by the matrix model. This gives a correct method to reconstruct two-dimensional random surfaces from three-dimensional DT mfds. Furthermore, a scaling property of the volume distribution of minimum neck baby universes was investigated numerically in the case of three and four dimensions, and we obtain a common scaling structure near to the critical points belonging to the strong coupling phase in both dimensions. We have evidence for the existence of a common fractal structure in three- and four-dimensional simplicial quantum gravity.
Quantum mechanical behavior of coupled N-kicked rotators is studied. In the large N limit each rotator evolves under influence of the mean-field generated by surrounding rotators. It is found that the system spontaneously generates classical chaos in
the large N limit when the system parameter exceeds a critical value. Numerical simulation of a quantum rotator coupled to a classical rotator supports this idea.
The string susceptibility exponents of dynamically triangulated two dimensional surfaces with sphere and torus topology were calculated using the grand-canonical Monte Carlo method. We also simulated the model coupled to d-Ising spins (d=1,2,3,5).
A model of simplicial quantum gravity in three dimensions(3D) was investigated numerically based on the technique of dynamical triangulation (DT). We are concerned with the genus of surfaces appearing on boundaries (i.e., sections) of a 3D DT manifol
d with $S^{3}$ topology. Evidence of a scaling behavior of the genus distributions of boundary surfaces has been found.
The string susceptibility exponents of dynamically triangulated 2-dimensional surfaces with various topologies, such as a sphere, torus and double-torus, were calculated by the grand-canonical Monte Carlo method. These simulations were made for surfa
ces coupled to $d$-Ising spins ($d$=0,1,2,3,5). In each simulation the area of surface was constrained to within 1000 to 3000 of triangles, while maintaining the detailed-balance condition. The numerical results show excellent agreement with theoretical predictions as long as $d leq 2$.
A model of simplicial quantum gravity in three dimensions is investigated numerically based on the technique of the dynamical triangulation (DT). We are concerned with the surfaces appearing on boundaries (i.e., sections) of three-dimensional DT mani
fold with $S^{3}$ topology. A new scaling behavior of genus distributions of boundary surfaces is found.Furthermore, these surfaces are compared with the random surfaces generated by the two-dimensional DT method which are well known as a correct discretized method of the two-dimensional quantum gravity.
Complex structures are determined for surfaces with $S^2$ and $T^2$ topologies generated by the dynamical triangulation method. For a surface with $S^2$ topology the spacial distribution of the conformal mode is obtained, while for the case of $T^2$
topology the distribution of the moduli parameter is calculated. It is also shown that the network of Feynman diagrams of massive $phi^3$ scalar theory has a unique complex structure. This gives a numerical justification of the hadronic string model for explaining the n-particle dual amplitude.
Two-dimensional random surfaces are studied numerically by the dynamical triangulation method. In order to generate various kinds of random surfaces, two higher derivative terms are added to the action. The phases of surfaces in the two-dimensional p
arameter space are classified into three states: flat, crumpled surface, and branched polymer. In addition, there exists a special point (pure gravity) corresponding to the universal fractal surface. A new probe to detect branched polymers is proposed, which makes use of the minbu(minimum neck baby universe) analysis. This method can clearly distinguish the branched polymer phase from another according to the sizes and arrangements of baby universes. The size distribution of baby universes changes drastically at the transition point between the branched polymer and other kind of surface. The phases of surfaces coupled with multi-Ising spins are studied in a similar manner.
The complex structure of a surface generated by the two-dimensional dynamical triangulation(DT) is determined by measuring the resistivity of the surface. It is found that surfaces coupled to matter fields have well-defined complex structures for cas
es when the matter central charges are less than or equal to one, while they become unstable beyond c=1. A natural conjecture that fine planar random network of resistors behave as a continuous sheet of constant resistivity is justified numerically for c<1.
