DERIVATION OF LAUGHLIN'S WAVEFUNCTION IN ANYON SYSTEM

1992 ◽  
Vol 06 (12) ◽  
pp. 737-745 ◽  
Author(s):  
Z. F. EZAWA ◽  
A. IWAZAKI
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Excitation Spectrum ◽  
Coulomb Interaction ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Semiclassical Approximation ◽  
Ground State Wavefunction ◽  
Statistical Interactions

In a semiclassical approximation we derive the ground-state wavefunction of the system of anyons in an external magnetic field, where anyons are interacting via the Coulomb interaction. The statistical interactions are treated in perturbation around the boson limit. The wavefunction coincides with the Laughlin wavefunction except for small corrections due to the Coulomb interaction. We also calculate the ground-state energy and the excitation spectrum.

ORBITAL PARAMAGNETISM IN TWO-DIMENSIONAL LATTICES

1991 ◽  
Vol 05 (08) ◽  
pp. 571-579 ◽  
Author(s):  
F.V. KUSMARTSEV
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Phase State ◽  
Two Dimensional ◽  
Absolute Minimum ◽  
Dimensional Lattice ◽  
The Absolute

We calculate the ground state energy and the magnetization of spinless fermions on a two-dimensional lattice in an external magnetic field. We prove that the absolute minimum of the energy corresponds to a flux value equal to the filling, i.e. the “commensurate flux phase” state is preferable. The magnetization of these fermions has a paramagnetic character of special orbital type.

TIGHT-BINDING MODEL FOR THE QUANTUM LADDER IN A MAGNETIC FIELD

1996 ◽  
Vol 10 (28) ◽  
pp. 3827-3856 ◽  
Author(s):  
KAZUMOTO IGUCHI
Keyword(s):  
Magnetic Field ◽  
Magnetic Flux ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Tight Binding ◽  
Critical Value ◽  
Tight Binding Model ◽  
Binding Model ◽  
First Case

A tight-binding model is formulated for the calculation of the electronic structure and the ground state energy of the quantum ladder under a magnetic field, where the magnetic flux at the nth plaquette is given by ϕn. First, the theory is applied to obtain the electronic spectra of the quantum ladder models with particular magnetic fluxes such as uniform magnetic fluxes, ϕn=0 and 1/2, and the staggered magnetic flux, ϕn= (−1)n+1ϕ0. From these, it is found that as the effect of electron hopping between two chains—the anisotropy parameter r=ty/tx—is increased, there are a metal-semimetal transition at r=0 and a semimetal–semiconductor transition at r=2 in the first case, and metal-semiconductor transitions at r=0 in the second and third cases. These transitions are thought of as a new category of metal-insulator transition due to the hopping anisotropy of the system. Second, using the spectrum, the ground state energy is calculated in terms of the parameter r. It is found that the ground state energy in the first case diverges as r becomes arbitrarily large, while that in the second and third cases can have the single or double well structure with respect to r, where the system is stable at some critical value of r=rc and the transition between the single and double well structures is associated with whether tx is less than a critical value of txc. The latter cases are very reminiscent of physics in polyacetylene studied by Su, Schrieffer and Heeger.

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.

UPPER BOUND ON THE GROUND-STATE ENERGY FOR THE FRÖHLICH POLARON IN A MAGNETIC FIELD

1994 ◽  
Vol 08 (10) ◽  
pp. 629-639 ◽  
Author(s):  
A. V. SOLDATOV
Keyword(s):  
Magnetic Field ◽  
Ground State Energy ◽  
Upper Bound ◽  
Ground State ◽  
Coupling Strength ◽  
State Energy ◽  
Polaron Model

The ground-state energy of the Fröhlich polaron model in a magnetic field is investigated by means of the Wick symbols formalism. The upper bound on the ground-state energy is derived which is valid for all values of magnetic field and coupling strength.

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.

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