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Preprint Series of Department of Mathematics, Hokkaido University

A scaling limit for a general class of quantum field models and its application to nuclear physics and condensed matter physics

Akito Suzuki

Published Oct 3, 2005• 0 citations
Publisher

Abstract

A scaling limit for the generalized spin-boson (GSB) model is considered. We derive a scaling limit of the Hamiltonian of the GSB model independently of whether or not the quantum scalareld has a mass. Applying it to a model for the eld of the nuclear force with isospin, we obtain an effective potential of the interaction between nucleons. Also, we get some applications to condensed matter physics.

DOI
10.14943/83896

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A scaling limit for the generalized spin-boson (GSB) model is considered. We derive a scaling limit of the Hamiltonian of the GSB model independently of whether or not the quantum scalareld has a mass. Applying it to a model for the eld of the nuclear force with isospin, we obtain an effective potential of the interaction between nucleons. Also, we get some applications to condensed matter physics.
We consider a scaling limit of the Hamiltonian of the generalized spin-boson (GSB) model which is an abstract quantum field theoretical model of particles interacting with a Bose field. Applying it to a Hamiltonian of the field of the nuclear force with isospin, we obtain an effective potential of the interaction between nucleons. Also, we discuss an application to a Hamiltonian of a lattice spin system interacting with a Bose field and obtain a spin–spin interaction in the vacuum of the Bose field. An interaction model between a Fermi field and a Bose field yields an interaction in the vacuum of the Bose field.
Generalized spin-boson (GSB) models describe the interaction between a quantum mechanical system and a structured boson environment, mediated by a family of coupling functions known as form factors. We propose an extension of the class of GSB models, which can accommodate non-normalizable form factors provided that they satisfy a weaker growth constraint, thus accounting for a rigorous description of a wider range of physical scenarios; we also show that such “singular” GSB models can be rigorously approximated by GSB models with normalizable form factors. Furthermore, we discuss in greater detail the structure of the spin-boson model with a rotating wave approximation: for this model, the result is improved via a nonperturbative approach that enables us to further extend the class of admissible form factors as well as to compute its resolvent and characterize its self-adjointness domain.
Conventional many-body quantum theory considers, as a rule, a system of particles in the mean field interacting through two-body forces. Recently it was suggested that in nuclear physics many-body forces, first of all three-body ones, are important for saturation of nuclear matter and for many details of nuclear structure. We consider possible influence of three-body forces, regardless of their origin (bare nucleon interactions or effective medium phenomena), on many-body dynamics. The new effects include, but are not limited to, renormalization of pairing and other two-body forces, enhancement of anharmonicity for collective modes, and special features of shell model calculations.
The shell model provides a powerful framework for nuclear structure calculations. The nucleons beyond an inert magic core are confined in a valence shell and interact through an effective two-body potential generally determined from the G-matrix method. However, the applicability of the shell model remains limited by the exponential growth of the many-body space with the number of valence nucleons and with the size of the one-body space. The quantum Monte Carlo (QMC) methods may thus be considered as a potentially attractive alternative to the direct diagonalization of the Hamiltonian matrix. The many-body problem is indeed reduced to a set of stochastic one-body problems describing independent particles in a fluctuating external field. Up to date, the QMC approaches of the shell model lead to the ground-state and the thermodynamic properties, but a detailed spectroscopy of nuclei is not reachable. Furthermore, they suffer from a common pathology of fermionic QMC methods, namely the sign/phase problem, which strongly contaminates the convergence of the calculation. In this context, we will present a new QMC method, providing the "yrast spectroscopy" of nuclei, and in which the sign/phase problem is managed through the constrained path approximation that is widely used in the ab initio nuclear calculations and in condensed matter physics.