Acoustical polaron in three dimensions: The ground-state energy and the self-trapping transition

1985 ◽  
Vol 32 (6) ◽  
pp. 3515-3521 ◽  
Author(s):  
F. M. Peeters ◽  
J. T. Devreese
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
The Self ◽  
Three Dimensions ◽  
Self Trapping

SELF-TRAPPING TRANSITION OF ACOUSTIC POLARON IN SLAB

2013 ◽  
Vol 27 (08) ◽  
pp. 1350050
Author(s):  
JUNHUA HOU ◽  
XIAOMING DONG ◽  
XIAOFENG DUAN
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Alkali Halides ◽  
2D Systems ◽  
Phonon Coupling ◽  
Length Unit ◽  
First Derivative ◽  
Electron Phonon Coupling ◽  
Self Trapping

Self-trapping transition of the acoustic polaron in slab is researched by calculating the polaron ground state energy and the first derivative of the ground state energy with respect to the electron–phonon coupling. It is indicated that the possibility of self-trapping transition for acoustic polaron in slab fall in between 3D and 2D systems. The electron may be self-trapped in slab systems of GaN , AlN and alkali halides, if the slab systems are thinner than one over ten of the length unit ℏ/mc.

scholarly journals Variational Principle Techniques and the Propertiesof a Cut-off and Anharmonic Wave Function

2009 ◽  
Vol 6 (1) ◽  
pp. 113-119 ◽  
Author(s):  
A. N. Ikot ◽  
L. E. Akpabio ◽  
K. Essien ◽  
E. E. Ituen ◽  
I. B. Obot
Keyword(s):  
Dynamical System ◽  
Wave Function ◽  
Variational Principle ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Variational Principles ◽  
Analytical Tool ◽  
Three Dimensions ◽  
Anharmonic Oscillators

The variational principles are very useful analytical tool for the study of the ground state energy of any dynamical system. In this work, we have evaluated the method and techniques of variational principle to derive the ground state energy for the harmonic, cut-off and anharmonic oscillators with a ground state wave function for a one-body Hamiltonian in three dimensions.

scholarly journals The Dilute Fermi Gas via Bogoliubov Theory

2021 ◽  
Author(s):  
Marco Falconi ◽  
Emanuela L. Giacomelli ◽  
Christian Hainzl ◽  
Marcello Porta
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Particle Density ◽  
Scattering Length ◽  
Three Dimensions ◽  
Positive Interaction ◽  
Interaction Potentials ◽  
Bogoliubov Theory ◽  
Regular Class

AbstractWe study the ground state properties of interacting Fermi gases in the dilute regime, in three dimensions. We compute the ground state energy of the system, for positive interaction potentials. We recover a well-known expression for the ground state energy at second order in the particle density, which depends on the interaction potential only via its scattering length. The first proof of this result has been given by Lieb, Seiringer and Solovej (Phys Rev A 71:053605, 2005). In this paper, we give a new derivation of this formula, using a different method; it is inspired by Bogoliubov theory, and it makes use of the almost-bosonic nature of the low-energy excitations of the systems. With respect to previous work, our result applies to a more regular class of interaction potentials, but it comes with improved error estimates on the ground state energy asymptotics in the density.

MULTI-DIMENSIONAL FRÖHLICH BIPOLARON AND DIMENSIONAL SCALING

1990 ◽  
Vol 04 (11n12) ◽  
pp. 1879-1888 ◽  
Author(s):  
SHREEKANTHA SIL ◽  
ASHOK CHATTERJEE
Keyword(s):  
Effective Mass ◽  
Strong Coupling ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Three Dimensions ◽  
Scaling Relations ◽  
Dimensional Scaling ◽  
Polar Crystal ◽  
Fröhlich Bipolaron

The formation and stability of the Fröhlich bipolaron in a multi-dimensional polar crystal is investigated within the framework of strong coupling Landau-Pekar theory. The ground state energy, the effective mass and the size of the bipolaron are calculated. It is shown that Fröhlich bipolarons can exist in both two and three dimensions, the bipolaronic binding being stronger in lower dimensions. The dimensional scaling relations satisfied by the ground state energy and the effective mass of the bipolaron are also obtained.

The ground state energy of the ±J spin glass from the genetic algorithm

1994 ◽  
Vol 4 (9) ◽  
pp. 1281-1285 ◽  
Author(s):  
P. Sutton ◽  
D. L. Hunter ◽  
N. Jan
Keyword(s):  
Genetic Algorithm ◽  
Spin Glass ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy

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.

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