Lower Spectral Branches of a Particle Coupled to a Bose Field

The structure of the lower part (i.e. $\epsilon$-away below the two-boson threshold) spectrum of Fr\"ohlich's polaron Hamiltonian in the weak coupling regime is obtained in spatial dimension $d\geq 3$. It contains a single polaron branch defined for total momentum $p\in G^{(0)}$, where $G^{(0)}\subset {\mathbb R}^d$ is a bounded domain, and, for any $p\in {\mathbb R}^d$, a manifold of polaron + one-boson states with boson momentum $q$ in a bounded domain depending on $p$. The polaron becomes unstable and dissolves into the one boson manifold at the boundary of $G^{(0)}$. The dispersion laws and generalized eigenfunctions are calculated

Lower Spectral Branches of a Spin-Boson Model

We study the structure of the spectrum of a two-level quantum system weakly coupled to a boson field (spin-boson model). Our analysis allows to avoid the cutoff in the number of bosons, if their spectrum is bounded below by a positive constant. We show that, for small coupling constant, the lower part of the spectrum of the spin-boson Hamiltonian contains (one or two) isolated eigenvalues and (respectively, one or two) manifolds of atom $+ 1$-boson states indexed by the boson momentum $q$. The dispersion laws and generalized eigenfunctions of the latter are calculated

Spectral properties of stochastic dynamics on compact manifolds

Minlos RA, Zhizhina ZV, Kondratiev Y. Spectral properties of stochastic dynamics on compact manifolds. Transactions of the Moscow Mathematical Society. 1998;59

Spectral properties of stochastic dynamics on compact manifolds

Minlos RA, Zhizhina ZV, Kondratiev Y. Spectral properties of stochastic dynamics on compact manifolds. Transactions of the Moscow Mathematical Society. 1998;59

Small mass behaviour in quantum lattice models

Minlos RA, Rebenko AL, Albeverio S, Kondratiev Y. Small mass behaviour in quantum lattice models. Journal of Statistical Physics . 1998;92(5-6):1153-1172