The Fröhlich Hamiltonian: mathematical results. III. Perturbation theory

1979 ◽  
Vol 57 (2) ◽  
pp. 114-119
Author(s):  
Bernard M. de Dormale
Keyword(s):  
Perturbation Theory ◽  
Effective Mass ◽  
Energy Shift ◽  
Simplified Model ◽  
Polaron Model ◽  
Exact Eigenvalue ◽  
Eigenvalue And Eigenvector

We prove the validity of perturbation theory for the polaron model. After obtaining the usual results for the Hamiltonian without cut-off, we derive the effective mass and energy shift for the Hamiltonian with cut-off. We also introduce a simplified model whose exact eigenvalue and eigenvector can be computed.

scholarly journals Capturing excitonic and polaronic effects in lead iodide perovskites from many-body perturbation theory

2021 ◽  
Author(s):  
Pooja Basera ◽  
Arunima Singh ◽  
Deepika Gill ◽  
Saswata Bhattacharya
Keyword(s):  
Optical Properties ◽  
Perturbation Theory ◽  
Binding Energy ◽  
Electronic Properties ◽  
Effective Mass ◽  
Exciton Binding Energy ◽  
Many Body ◽  
Energy Materials ◽  
Lead Iodide ◽  
Many Body Perturbation Theory

Lead iodide perovskites have attracted considerable interest as promising energy-materials. However, till date, several key electronic properties such as optical properties, effective mass, exciton binding energy and the radiative exciton...

Perturbation theory in the polaron model at finite temperature

1985 ◽  
Vol 65 (3) ◽  
pp. 1255-1263 ◽  
Author(s):  
N. N. Bologyubov ◽  
V. N. Plechko
Keyword(s):  
Perturbation Theory ◽  
Finite Temperature ◽  
Polaron Model

EFFECTIVE MASS OF STRONG-COUPLED BOUND POLARON IN AN ASYMMETRIC QUANTUM DOT INDUCED WITH RASHBA EFFECT

2011 ◽  
Vol 10 (03) ◽  
pp. 501-505 ◽  
Author(s):  
ZHIXIN LI ◽  
JUAN XIAO ◽  
AIYONG LIU ◽  
JINGLIN XIAO
Keyword(s):  
Quantum Dot ◽  
Effective Mass ◽  
Operator Method ◽  
Transformation Method ◽  
Rashba Effect ◽  
Linear Combination Operator ◽  
Polaron Model ◽  
Bound Polaron ◽  
Asymmetric Quantum Dot ◽  
Asymmetric Quantum

In this paper, on the basis of Huybrechs' strong-coupled polaron model, the Tokuda-modified linear-combination operator method and the unitary transformation method are used to study the properties of the strong-coupled bound polaron considering the influence of Rashba effect, which is brought by the spin-orbit (SO) interaction, in an asymmetric quantum dot (QD). The expression for the effective mass of the polaron as functions of the transverse and longitudinal bound strengths, velocity, vibration frequency, and the bound potential has been derived. After a simple numerical calculation on the RbCl crystal, we found that the total effective mass of the bound polaron is composed of three parts. The interaction between the orbit and the spin with different directions has different effects on the effective mass of the bound polaron.

THEORETICAL ASPECTS OF THE POLARIZABILITY OF THE NUCLEON

1993 ◽  
Vol 08 (30) ◽  
pp. 5267-5303 ◽  
Author(s):  
A.I. L’VOV
Keyword(s):  
Perturbation Theory ◽  
Chiral Perturbation Theory ◽  
Gauge Invariance ◽  
Degrees Of Freedom ◽  
Dominant Role ◽  
Energy Shift ◽  
Chiral Perturbation ◽  
Polarization Effects ◽  
Consistent Treatment

Two aspects of the nucleon electromagnetic polarizabilities, αN and βN, are discussed. The first one is the interrelation between static and Compton polarizabilities. Relativistically consistent treatment of the polarization effects based on effective Lagrangians results in the conclusion that the Compton polarizabilities, rather than the static ones, drive the energy shift of the nucleon in external fields. The cluster substructure of the static polarizabilities is shown to be crucial for consistent calculations of the polarizabilities. The second aspect concerns the dominant role of pion degrees of freedom in αN as seen through dispersion relations, chiral perturbation theory, and constituent models. The reported calculations of αN within soliton models are shown to be inconsistent with gauge invariance. The difficulties in explaining the observed large diamagnetic component of βN are emphasized.

The Klein–Gordon equation with the Kratzer potential in the noncommutative space

2018 ◽  
Vol 33 (35) ◽  
pp. 1850203 ◽  
Author(s):  
M. Darroodi ◽  
H. Mehraban ◽  
S. Hassanabadi
Keyword(s):  
Perturbation Theory ◽  
Phase Space ◽  
Gordon Equation ◽  
Energy Shift ◽  
Laboratory Frame ◽  
Noncommutative Space ◽  
Noncommutative Phase Space ◽  
Polar Coordinate ◽  
Klein Gordon ◽  
Klein Gordon Equation

The Klein–Gordon equation is considered for the Kratzer potential in the spherical polar coordinate in laboratory frame in noncommutative space. The energy shift due to noncommutativity is obtained via the perturbation theory. After rather cumbersome algebra, we found the eigenfunctions and eigenvalues of the system for a noncommutative phase space.

GROUND STATE PERTURBATION OF N-ANYON IN A MAGNETIC FIELD

1993 ◽  
Vol 08 (04) ◽  
pp. 341-348 ◽  
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.

THE EFFECTIVE MASS OF STRONG-COUPLED POLARON IN AN ASYMMETRIC QUANTUM DOT INDUCED WITH RASHBA EFFECT

2010 ◽  
Vol 24 (23) ◽  
pp. 2423-2430 ◽  
Author(s):  
ZHI-XIN LI ◽  
JING-LIN XIAO ◽  
HONG-YAN WANG
Keyword(s):  
Quantum Dot ◽  
Effective Mass ◽  
Unitary Transformation ◽  
Spin Orbit ◽  
Rashba Effect ◽  
Linear Combination Operator ◽  
Polaron Model ◽  
Asymmetric Quantum Dot ◽  
Asymmetric Quantum ◽  
Transformation Methods

In this paper, on the basis of Huybrechs' strong-coupled polaron model, Tokuda modified linear-combination operator and the unitary transformation methods are used to study the properties of the strong-coupled polaron considering the influence of Rashba effect, which is brought by the spin-orbit (SO) interaction, in the asymmetric quantum dot (QD). The expressions of the effective mass as a function of the transverse and longitudinal confinement strengths, the velocity and the vibration frequency were derived. Numerical calculation on the RbCl QD, as an example, is performed and the results show that the total effective mass of the polaron is composed of three parts. The interaction between the orbit and the spin with different directions has different effects on the effective mass of the polaron.

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