Lower Spectral Branches of a Spin-Boson Model
نویسندگان
چکیده
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.
منابع مشابه
Dynamics of a large spin with weak dissipation q
We investigate the generalization of the spin-boson model to arbitrary spin size. The Born–Markov approximation is employed to derive a master equation in the regime of small coupling strengths to the environment. For spin one half, the master equation transforms into a set of Bloch equations, the solution of which is in good agreement with results of the spin-boson model for weak ohmic dissipa...
متن کامل3 Dynamics of a large spin with weak dissipation ⋆
We investigate the generalization of the spin-boson model to arbitrary spin size. The Born-Markov approximation is employed to derive a master equation in the regime of small coupling strengths to the environment. For spin one half, the master equation transforms into a set of Bloch equations, the solution of which is in good agreement with results of the spin-boson model for weak ohmic dissipa...
متن کاملSparse polynomial space approach to dissipative quantum systems: application to the sub-ohmic spin-boson model.
We propose a general numerical approach to open quantum systems with a coupling to bath degrees of freedom. The technique combines the methodology of polynomial expansions of spectral functions with the sparse grid concept from interpolation theory. Thereby we construct a Hilbert space of moderate dimension to represent the bath degrees of freedom, which allows us to perform highly accurate and...
متن کاملروش انتگرال مسیر برای مدل هابارد تک نواره
We review various ways to express the partition function of the single-band Hubard model as a path integral. The emphasis is made on the derivation of the action in the integrand of the path integral and the results obtained from this approach are discussed only briefly. Since the single-band Hubbard model is a pure fermionic model on the lattice and its Hamiltonian is a polynomial in creat...
متن کاملDecoherent Dynamics of a Two-Level System Coupled to a Sea of Spins
The dynamics of a two-level system which is coupled to an environmental sea of infinitely many spin-1y2 particles is investigated by use of the resolvent operator approach. Only at zero temperature does this spin-spin-bath model exhibit identical behavior as the more familiar spin-boson model. It is found that increasing temperature favors coherent dynamics. At high temperatures, the spin-spin-...
متن کامل