THE GROUND-STATE ENERGY OF STRONG-COUPLING POLARON IN QUANTUM ROD

2009 ◽  
Vol 08 (04n05) ◽  
pp. 439-442 ◽  
Author(s):  
CUI TAO WANG ◽  
CUI LAN ZHAO ◽  
JING LIN XIAO
Keyword(s):  
Strong Coupling ◽  
Ground State Energy ◽  
Ground State ◽  
Vibrational Frequency ◽  
State Energy ◽  
Longitudinal Optical ◽  
Parabolic Potential ◽  
Quantum Rod ◽  
Transformation Methods ◽  
Methods Numerical

The vibrational frequency and the ground-state energy of strong-coupling polaron in quantum rod (QR), bounded in parabolic potential with ellipsoidal boundary condition, are respectively, obtained using the linear-combination operator and unitary transformation methods. Numerical results illustrate that the vibrational frequency will increase with decreasing the effective radii R0 of ellipsoidal parabolic potential and the aspect ratio e' of ellipsoid while with increasing electron-bulk longitudinal-optical (LO)-phonon coupling strength α, and that the ground-state energy will increase with decreasing R0 and α. Besides, the ground-state energy will decrease with e' increasing in 0 < e' < 1 area, get to minimum when e' = 1, and then increase with e' increasing in e' > 1 area.

POLARON IN A QUANTUM DOT UNDER AN ELECTRIC FIELD

2007 ◽  
Vol 21 (24) ◽  
pp. 1635-1642
Author(s):  
MIAN LIU ◽  
WENDONG MA ◽  
ZIJUN LI
Keyword(s):  
Quantum Dot ◽  
Electric Field ◽  
Field Intensity ◽  
Ground State Energy ◽  
Ground State ◽  
Electric Field Intensity ◽  
State Energy ◽  
Theoretical Study ◽  
The Moment ◽  
Transformation Methods

We conducted a theoretical study on the properties of a polaron with electron-LO phonon strong-coupling in a cylindrical quantum dot under an electric field using linear combination operator and unitary transformation methods. The changing relations between the ground state energy of the polaron in the quantum dot and the electric field intensity, restricted intensity, and cylindrical height were derived. The numerical results show that the polar of the quantum dot is enlarged with increasing restricted intensity and decreasing cylindrical height, and with cylindrical height at 0 ~ 5 nm , the polar of the quantum dot is strongest. The ground state energy decreases with increasing electric field intensity, and at the moment of just adding electric field, quantum polarization is strongest.

The influences of parabolic potential and magnetism on strongly coupled polaron characteristics within asymmetric Gaussian quantum wells

2021 ◽  
Author(s):  
Saren Gaowa ◽  
Yan-Bo Geng ◽  
Zhao-Hua Ding ◽  
Jing-Lin Xiao
Keyword(s):  
Magnetic Field ◽  
Quantum Wells ◽  
Barrier Height ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Cyclotron Frequency ◽  
Strongly Coupled ◽  
Parabolic Potential ◽  
Do So

In this research, the effects of magnetism and parabolic potential on strongly coupled polaron characteristics within asymmetric Gaussian quantum wells (AGQWs) were investigated. To do so, the following six parameters were studied, temperature, AGQW barrier height, Gaussian confinement potential (GCP) width, confinement strengths along the directions of [Formula: see text] and [Formula: see text], as well as magnetic field cyclotron frequency. The relationships among frequency oscillation, AGQW parameters and polaron ground state energy in RbCl crystal were studied based on linear combination operator and Lee–Low–Pines unitary transformation. It was concluded that ground state energy absolute value was decreased by increasing GCP width and temperature, and increased with the increase of confinement strength along [Formula: see text] and [Formula: see text] directions, cyclotron frequency of magnetic field and barrier height of AGQW. It was also found that vibrational frequency was increased by enhancing confinement strengths along the directions of [Formula: see text] and [Formula: see text], magnetic field cyclotron frequencies, barrier height AGQW and temperature and decreased with the increase of GCP width.

INFLUENCE OF LATTICE VIBRATION ON THE GROUND STATE OF MAGNETOPOLARON IN A PARABOLIC QUANTUM DOT

2010 ◽  
Vol 24 (27) ◽  
pp. 2705-2712 ◽  
Author(s):  
EERDUNCHAOLU ◽  
WEI XIN ◽  
YUWEI ZHAO
Keyword(s):  
Magnetic Field ◽  
Strong Coupling ◽  
Ground State Energy ◽  
Vibration Frequency ◽  
Ground State ◽  
Weak Coupling ◽  
State Energy ◽  
Cyclotron Frequency ◽  
Lattice Vibration ◽  
The Magnetic Field

Influence of the lattice vibration on the properties of the magnetopolaron in the parabolic quantum dots (QDs) is studied by using the Huybrechts' linear combination operator and Lee–Low–Pines (LLP) transformation methods. The expressions for the vibration frequency and the ground-state energy of the magnetopolaron as functions of the confinement strength of the QDs, the magnetic field and temperature are derived under the strong and weak coupling, respectively. The results of the numerical calculations show that the changes of the vibration frequency and ground-state energy of the magnetopolaron with the confinement strength of the QDs, the magnetic field and temperature are different under different couplings. The vibration frequency and the ground-state energy of the weak-coupling magnetopolaron and the vibration frequency of the strong-coupling magnetopolaron will increase with increase of the confinement strength of the QDs and cyclotron frequency, the vibration frequency and ground-state energy of the strong-coupling magnetopolaron. However, the ground-state energy of the weak-coupling magnetopolaron will decrease with increase of the temperature. The dependence of the ground-state energy of the strong-coupling magnetopolaron on the confinement strength of the QDs and cyclotron frequency is strongly influenced by the temperature. The remarkable influence of the temperature on the ground-state energy of the magnetopolaron arises when the temperature is relatively higher.

SECOND ORDER APPROXIMATION FOR OPTICAL POLARON IN THE STRONG COUPLING CASE

1995 ◽  
Vol 09 (08) ◽  
pp. 485-498
Author(s):  
N. N. BOGOLUBOV
Keyword(s):  
Strong Coupling ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Order Approximation ◽  
Nonlinear Differential Equations ◽  
Second Order ◽  
Linear Type ◽  
Second Order Approximation ◽  
Coupling Case

Here we propose a method of constructing a second order approximation for ground state energy for a class of model Hamiltonian with linear type interaction on bose operators in the strong coupling case. For the application of the above method we have considered polaron model and propose constructing a set of nonlinear differential equations for definition ground state energy in the strong coupling case. We have considered also radial symmetry case.

Effects of Temperature and Hydrogen-Like Impurity on the Vibrational Frequency of the Polaron in RbCl Parabolic Quantum Dots

NANO ◽  
2016 ◽  
Vol 11 (03) ◽  
pp. 1650029 ◽  
Author(s):  
Wei Xiao ◽  
Jing-Lin Xiao
Keyword(s):  
Binding Energy ◽  
Ground State Energy ◽  
Ground State ◽  
Vibrational Frequency ◽  
State Energy ◽  
Impurity Potential ◽  
Ground State Binding Energy ◽  
Effects Of Temperature ◽  
Increasing Function ◽  
Coulombic Impurity Potential

The properties of an electron strongly coupled to longitudinal optical (LO) phonon in RbCl parabolic quantum dot (PQD) with a hydrogen-like impurity at the center were investigated at a finite temperature. We have obtained the vibrational frequency of a strong-coupling polaron in RbCl PQD by using linear combination operator method. We then calculate the effects of temperature, the Coulombic impurity potential and the effective confinement strength on the vibrational frequency by using unitary transformation and the quantum statistics theory methods. The influences of the temperature, the Coulombic impurity potential and the effective confinement strength on the ground state energy and the ground state binding energy are also analyzed. The strengths of these quantities increase with raising temperature. The vibrational frequency is an increasing function of the Coulombic impurity potential and the effective confinement strength. The ground state energy is an increasing function of the effective confinement strength, whereas it is a decreasing one of the Coulombic impurity potential. The ground state binding energy is an increasing function of the Coulombic impurity potential, whereas it is a decayed one of the effective confinement strength.

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