Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1999-02-11
Nucl.Phys. B553 (1999) 583-600
Physics
High Energy Physics
High Energy Physics - Theory
20 pages, LaTeX. Typos and conflicts in notation resolved
Scientific paper
10.1016/S0550-3213(99)00250-3
We introduce a general method for transforming the equations of motion following from a Das-Jevicki-Sakita Hamiltonian, with boundary conditions, into a boundary value problem in one-dimensional quantum mechanics. For the particular case of a one-dimensional chain of interacting NxN Hermitean matrices, the corresponding large N boundary value problem is mapped into a linear Fredholm equation with Hilbert-Schmidt type kernel. The equivalence of this kernel, in special cases, to a second order differential operator allows us recover all previously known explicit solutions for the matrix eigenvalues. In the general case, the distribution of eigenvalues is formally derived through a series of saddle-point approximations. The critical behaviour of the system, including a previously observed Kosterlitz-Thouless transition, is interpreted in terms of the stationary points. In particular we show that a previously conjectured infinite series of sub-leading critical points are due to expansion about unstable stationary points and consequently not realized.
No associations
LandOfFree
Eigenvalue Dynamics and the Matrix Chain does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Eigenvalue Dynamics and the Matrix Chain, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Eigenvalue Dynamics and the Matrix Chain will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-228208