Extension to the case of a magnetic field of Feynman’s path-integral upper bound on the ground-state energy: Application to the Fröhlich polaron

1992 ◽  
Vol 45 (12) ◽  
pp. 6459-6478 ◽  
Author(s):  
J. T. Devreese ◽  
F. Brosens
Keyword(s):  
Magnetic Field ◽  
Path Integral ◽  
Ground State Energy ◽  
Upper Bound ◽  
Ground State ◽  
State Energy ◽  
Energy Application

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.

AN UPPER BOUND FOR THE GROUND STATE ENERGY OF BIPOLARON: A PATH INTEGRAL TREATMENT

1990 ◽  
Vol 04 (19) ◽  
pp. 1201-1209
Author(s):  
D.C. KHANDEKAR
Keyword(s):  
Path Integral ◽  
Ground State Energy ◽  
Upper Bound ◽  
Ground State ◽  
State Energy ◽  
Integral Formulation ◽  
Path Integral Formulation ◽  
Integral Treatment ◽  
The Stability

A path integral formulation to study the properties of bipolaron is presented. The formulation is subsequently used to derive an upper bound for the ground state energy of the bipolaron. The estimate is used to discuss the stability of bipolaron.

CONTINUOUS UPPER BOUND ON THE GROUND-STATE ENERGY OF THE FRÖHLICH POLARON

1994 ◽  
Vol 08 (08n09) ◽  
pp. 553-560 ◽  
Author(s):  
A. V. SOLDATOV
Keyword(s):  
Magnetic Field ◽  
Asymptotic Behavior ◽  
Ground State Energy ◽  
Upper Bound ◽  
Ground State ◽  
Coherent States ◽  
Weak Coupling ◽  
State Energy ◽  
Coupling Parameter ◽  
Weak Coupling Limit

The upper bound on the ground-state energy for the Fröhlich polaron is derived by means of a new version of variational principle based on the Wick symbols formalism and the coherent states theory. The bound is continuous in some respect, i.e. it is valid for all values of coupling parameter including the intermediate regions. Asymptotic behavior of the bound for the weak coupling limit and for the strong coupling limit provides, in general, lower values than well-known existing bounds. The bound can be readily generalized for the case of nonzero magnetic field.

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.

Bounds on the ground state energy: Application of the variational principle

2009 ◽  
Vol 77 (1) ◽  
pp. 44-47 ◽  
Author(s):  
Bibhas Bhattacharyya
Keyword(s):  
Variational Principle ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Energy Application

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.

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