The perturbation theory approach to the ground state energy in an infinite fermion system

For the ground state energy of the spin-boson (SB) model, we give a new upper bound in the case with infrared singularity condition (i.e. without infrared cutoff), and a new lower bound in the case of massless bosons with infrared regularity condition. We first investigate spectral properties of the Wigner–Weisskopf (WW) model, and apply them to SB model to achieve our purpose. Then, as an extra result of the spectral analysis for WW model, we show that a non-perturbative ground state appears, and its ground state energy is so low that we cannot conjecture it by using the regular perturbation theory.

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Asymptotic estimate of large orders in perturbation theory for the many-fermion ground state energy

Annals of Physics ◽

10.1016/0003-4916(83)90044-1 ◽

1983 ◽

Vol 146 (2) ◽

pp. 473

Keyword(s):

Perturbation Theory ◽

Ground State Energy ◽

Ground State ◽

Asymptotic Estimate ◽

State Energy ◽

The Many

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A perturbation theory approach to the ground state exciton energy in the limit of a weak magnetic field in anomalous exciton Hall effect

Journal of Physics Conference Series ◽

10.1088/1742-6596/2015/1/012135 ◽

2021 ◽

Vol 2015 (1) ◽

pp. 012135

Author(s):

V A Shabashov ◽

V K Kozin ◽

A V Kavokin ◽

I A Shelykh

Keyword(s):

Magnetic Field ◽

Perturbation Theory ◽

Dipole Moment ◽

External Magnetic Field ◽

Hall Effect ◽

Ground State ◽

Weak Magnetic Field ◽

State Energy ◽

Theory Approach ◽

Exciton Energy

Abstract The anomalous exciton Hall effect is a phenomenon that occurs in a quantum well in the presence of an external magnetic field applied perpendicular to the surface due to the interaction of the exciton dipole moment with an electric field, formed by the charged impurities. The effect was fully described in [1] for different magnetic field regimes. In this paper, we focus on the way the perturbation method was used for finding the ground state energy of an exciton in the limit of a weak magnetic field.

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Study of the Perturbation Series for the Ground-State Energy of a Many-Fermion System

Physical Review ◽

10.1103/physrev.132.1373 ◽

1963 ◽

Vol 132 (3) ◽

pp. 1373-1387 ◽

Cited By ~ 29

Author(s):

George A. Baker ◽

J. L. Gammel ◽

B. J. Hill

Keyword(s):

Ground State Energy ◽

Ground State ◽

State Energy ◽

Perturbation Series ◽

Fermion System

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GROUND STATE PERTURBATION OF N-ANYON IN A MAGNETIC FIELD

Modern Physics Letters A ◽

10.1142/s0217732393000350 ◽

1993 ◽

Vol 08 (04) ◽

pp. 341-348 ◽

Cited By ~ 1

Author(s):

YUN SOO MYUNG ◽

J.M. CHOI ◽

M.J. UM ◽

C. JUE

Keyword(s):

Magnetic Field ◽

Perturbation Theory ◽

Ground State Energy ◽

Ground State ◽

Uniform Magnetic Field ◽

State Energy ◽

Energy Shift ◽

Landau Levels ◽

Fractional Statistics ◽

First Order

We study N-anyon of the α-statistics in a uniform magnetic field, to investigate certain properties of the ground state of a fractional statistics. Using the improved bosonic end-perturbation theory, we obtain the first order perturbative energy shift of the ground state energy. It is realized that there exists a second order perturbative energy with Landau levels.

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