Related papers: Homolumo Gap and Matrix Model
We introduce a dynamical matrix model where the matrix $X$ is interpreted as a Hamiltonian representing interaction of a bosonic system with a single fermion. We show how a system of second-quantized fermions influences the ground state of…
We consider a rather general type of matrix model, where the matrix M represents a Hamiltonian of the interaction of a bosonic system with a single fermion. The fluctuations of the matrix are partly given by some fundamental randomness and…
We study a new class of matrix models, formulated on a lattice. On each site are $N$ states with random energies governed by a Gaussian random matrix Hamiltonian. The states on different sites are coupled randomly. We calculate the density…
We consider a random matrix model of interaction between a small $n$-level system, $S$, and its environment, a $N$-level heat reservoir, $R$. The interaction between $S$ and $R$ is modeled by a tensor product of a fixed $% n\times n$ matrix…
We analyze several ground state related properties of mesoscopic systems using the random interaction matrix model EGOE(1+2)-$\cs$ (or RIMM) for many fermion systems with spin degree of freedom and the Hamiltonian containing pairing and…
Effects of randomness on interacting fermionic systems in one dimension are investigated by quantum Monte-Carlo techniques. At first, interacting spinless fermions are studied whose ground state shows charge ordering. Quantum phase…
We present some arguments showing spectrum doubling of matrix models in the limit $N\to\infty$ which is connected with fermionic determinant behaviour. The problems are similar to ones encountered in the lattice gauge theories with chiral…
We introduce a random interaction matrix model (RIMM) for finite-size strongly interacting fermionic systems whose single-particle dynamics is chaotic. The model is applied to Coulomb blockade quantum dots with irregular shape to describe…
Inspired by the algorithm of Barnsley's chaos game, we construct an open quantum system model based on the repeated interaction process. We shown that the quantum dynamics of the appropriate fermionic/bosonic system (in interaction with an…
We present novel approaches to the dynamics of an open quantum system coupled linearly to a non-Markovian fermionic or bosonic environment. In the first approach, we obtain a hierarchy of stochastic evolution equations of the diffusion…
We review a class of matrix models whose degrees of freedom are matrices with anticommuting elements. We discuss the properties of the adjoint fermion one-, two- and gauge invariant D-dimensional matrix models at large-N and compare them…
The system of two interacting bosons in a two-dimensional harmonic trap is compared with the system consisting of two noninteracting fermions in the same potential. In particular, we discuss how the properties of the ground state of the…
There can exist topological obstructions to continuously deforming a gapped Hamiltonian for free fermions into a trivial form without closing the gap. These topological obstructions are closely related to obstructions to the existence of…
Gaussian fermionic matrix product states (GfMPS) form a class of ansatz quantum states for 1d systems of noninteracting fermions. We show, for a simple critical model of free hopping fermions, that: (i) any GfMPS approximation to its ground…
We show that the quantum Hamilton Jacobi approach to a class of quantum mechanical bound state problems and the Gaussian orthogonal ensemble of random matrix theory are equivalent. The Berry connection for both problems is identical to…
There is a newly emerging understanding that in the chaotic domain of isolated finite interacting many particle systems smoothed densities define the statistical description of these systems and these densities follow from embedded…
In the last decade there has been increasing interest in the fields of random matrices, interacting particle systems, stochastic growth models, and the connections between these areas. For instance, several objects appearing in the limit of…
Embedded random matrix ensembles are generic models for describing statistical properties of finite isolated quantum many-particle systems. For the simplest spinless fermion (or boson) systems with say $m$ fermions (or bosons) in $N$ single…
We study time evolution of a subsystem's density matrix under unitary evolution, generated by a sufficiently complex, say quantum chaotic, Hamiltonian, modeled by a random matrix. We exactly calculate all coherences, purity and…
We discuss probabilistic models of random covariance structures defined by distributions over sparse eigenmatrices. The decomposition of orthogonal matrices in terms of Givens rotations defines a natural, interpretable framework for…