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Robert Minlos

Publications and source records attributed to Robert Minlos.

3 recordsLinked to original sources

On point-like interaction of three particles: two fermions and another particle. II

This work continues \cite{bib1} where the construction of Hamiltonian $H$ for the system of three quantum particles is considered. Namely the system consists of two fermions with mass $1$ and another particle with mass $m>0$. In the present paper, like in \cite{bib1}, we study the part $T_{l=1}$ of auxilliary operator $T = \oplus_{l=0}^{\infty} T_l$ involving the construction of the resolvent for the operator $H$. In this work together with the previous one two constants $0 m_0$ the operator $T_{l=1}$ is selfadjoint but for $m \leqslant m_0$ it has the deficiency indexes $(1,1)$; 2) for $m_1 n_0\}$ with the asymptotics \[ λ_n = λ_0 e^{δn} + O(1),\quad n\to\infty, \] where $λ_0 <0$, $δ>0$, $n_0>0$ and there is'nt other spectrum on the interval $λ< λ_{n_0}$.

math-ph

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

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