arXiv subjects

Nicolae Angelescu

Publications and source records attributed to Nicolae Angelescu.

2 recordsLinked to original sources

arXiv2008

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.

cond-mat.stat-mech↗

arXiv2005

Lower Spectral Branches of a Particle Coupled to a Bose Field

The structure of the lower part (i.e. $ε$-away below the two-boson threshold) spectrum of Fröhlich'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.

math-ph↗