Exact Density Matrix Elements for a Driven Dissipative Bosonic Mode in a Kerr-Like Medium

For a prototype Hamiltonian describing a driven, dissipative bosonic mode in a Kerr-like medium, the exact matrix elements of the reduced density matrix are obtained from a generating function in terms of the normal characteristic functions. The approach is based on the Heisenberg equations and operator calculus. The special and limiting cases are discussed.

Exact matrix treatment of the statistical mechanics of adsorption of large aromatic molecules on graphene

Theoretical adsorption isotherms show plateaus reflecting the types of conformer on the graphene surface. Both catechol and phenyl hydroquinone adsorption can be described by our interconvertible statistical mechanical monomer–dimer–trimer model.

Two-species hardcore reversible cellular automaton: matrix ansatz for dynamics and nonequilibrium stationary state

In this paper we study the statistical properties of a reversible cellular automaton in two out-of-equilibrium settings. In the first part we consider two instances of the initial value problem, corresponding to the inhomogeneous quench and the local quench. Our main result is an exact matrix product expression of the time evolution of the probability distribution, which we use to determine the time evolution of the density profiles analytically. In the second part we study the model on a finite lattice coupled with stochastic boundaries. Once again we derive an exact matrix product expression of the stationary distribution, as well as the particle current and density profiles in the stationary state. The exact expressions reveal the existence of different phases with either ballistic or diffusive transport depending on the boundary parameters.