Related papers: Semiclassical Approach to Finite-N Matrix Models
We introduce the first random matrix model of a complex $\beta$-ensemble. The matrices are tridiagonal and can be thought of as the non-Hermitian analogue of the Hermite $\beta$-ensembles discovered by Dumitriu and Edelman (J. Math. Phys.,…
We consider a product of an arbitrary number of independent rectangular Gaussian random matrices. We derive the mean densities of its eigenvalues and singular values in the thermodynamic limit, eventually verified numerically. These…
We consider the noncommutative space $\mathbb{R}^3_\lambda$, a deformation of the algebra of functions on $\mathbb{R}^3$ which yields a "foliation" of $\mathbb{R}^3$ into fuzzy spheres. We first construct a natural matrix base adapted to…
In this article, a model of random hermitian matrices is considered, in which the measure $\exp(-S)$ contains a general U(N)-invariant potential and an external source term: $S=N\tr(V(M)+MA)$. The generalization of known determinant…
In this thesis, we describe some recent results obtained in the analysis of two-dimensional quantum field theories by means of semiclassical techniques. These achievements represent a natural development of the non-perturbative studies…
The supersymmetric collective field theory with the potential $v'(x)=\omega x-{\eta\over x}$ is studied, motivated by the matrix model proposed by Jevicki and Yoneya to describe two dimensional string theory in a black hole background.…
The class of three-diagonal Jacobi matrix with exponentially increasing elements is considered. Under some assumptions the matrix corresponds to unbounded self-adjoint operator in the weighted space. The weight depends on elements of the…
We address the question as to why, in the semiclassical limit, classically chaotic systems generically exhibit universal quantum spectral statistics coincident with those of Random Matrix Theory. To do so, we use a semiclassical resummation…
Semiclassical approximation based on extracting a c-number classical component from quantum field is widely used in the quantum field theory. Semiclassical states are considered then as Gaussian wave packets in the functional Schrodinger…
Certain time dependent configurations in the c=1 matrix model correspond to string theory backgrounds which have spacelike boundaries and appear geodesically incomplete. We investigate quantum mechanical properties of a class of such…
We construct normalizable, semi-classical states for the previously proposed model of quantum gravity which is formulated as a spectral triple over holonomy loops. The semi-classical limit of the spectral triple gives the Dirac Hamiltonian…
These expository notes are centered around the circular law theorem, which states that the empirical spectral distribution of a nxn random matrix with i.i.d. entries of variance 1/n tends to the uniform law on the unit disc of the complex…
We develop the formalism for the one-loop no-boundary state in a cosmological model with fermions. We use it to calculate the reduced density matrix for an inflaton field by tracing out the fermionic degrees of freedom, yielding both the…
Certain power-counting non-renormalizable theories, including the most general self-interacting scalar fields in four and three dimensions and fermions in two dimensions, have a simplified renormalization structure. For example, in…
Inspired by the theory of quantum information, I use two non-Hermitian random matrix models - a weighted sum of circular unitary ensembles and a product of rectangular Ginibre unitary ensembles - as building blocks of three new products of…
We study the dynamics of many-body Fermi systems, for a class of initial data which are close to quasi-free states exhibiting a nonvanishing pairing matrix. We focus on the mean-field scaling, which for fermionic systems is naturally…
The Wigner-von Neumann method, which was previously used for perturbing continuous Schr\"{o}dinger operators, is here applied to their discrete counterparts. In particular, we consider perturbations of arbitrary $T$-periodic Jacobi…
Eigenvalue distributions of properly regularized Wilson loop operators are used to study the transition from ultra-violet (UV) behavior to infra-red (IR) behavior in gauge theories coupled to matter that potentially have an IR fixed point…
We formulate the planar `large N limit' of matrix models with a continuously infinite number of matrices directly in terms of U(N) invariant variables. Non-commutative probability theory, is found to be a good language to describe this…
The solutions of Heisenberg equations and two-particles eigenvalue problems for nonrelativistic models of current-current fermion interaction and $N, \Theta $ model are obtained in the frameworks of dynamical mapping method. The equivalence…