Ground-state energy of an exciton-(LO) phonon system in two and three dimensions: General outline and three-dimensional case

1996 ◽  
Vol 54 (18) ◽  
pp. 12841-12851 ◽  
Author(s):  
B. Gerlach ◽  
F. Luczak
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Dimensional Case ◽  
General Outline

EFFECTS OF THE NEXT-NEAREST-NEIGHBOR HOPPING IN OPTICAL LATTICES

2008 ◽  
Vol 22 (01) ◽  
pp. 33-44 ◽  
Author(s):  
YUN'E GAO ◽  
FUXIANG HAN
Keyword(s):  
Phase Diagram ◽  
Hubbard Model ◽  
Ground State Energy ◽  
Ground State ◽  
Optical Lattices ◽  
State Energy ◽  
Nearest Neighbor ◽  
Three Dimensional ◽  
Dispersion Relations ◽  
Insulating Phase

Introducing the next-nearest-neighbor hopping t′ into the Bose–Hubbard model, we study its effects on the phase diagram, on the ground-state energy, and on the quasiparticle and quasihole dispersion relations of the Mott insulating phase in optical lattices. We have found that a negative value of t′ enlarges the Mott-insulating region on the phase diagram, while a positive value of t′ acts oppositely. We have also found that the effects of t′ are dependent on the dimensionality of optical lattices with its effects largest in three-dimensional optical lattices.

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.

THE ELECTRONIC CORRELATION EFFECT FROM WEAK TO STRONG IN THE THREE DIMENSIONAL ELECTRON GAS

2012 ◽  
Vol 26 (11) ◽  
pp. 1250065 ◽  
Author(s):  
ZHI-MING YU ◽  
QING-WEI WANG ◽  
YU-LIANG LIU
Keyword(s):  
Phase Transition ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Electron Gas ◽  
Three Dimensional ◽  
Positive Function ◽  
Correlation Effect ◽  
Electronic Correlation ◽  
The Difference

Based on the success of the eigenfunctional theory ( EFT) in the one-dimensional model,16,24,51 we apply it to the three-dimensional homogeneous electron gas. By EFT, we first present a rigorous expression of the pair distribution function g(r) of the electron gas. This expression effectively solves the negative problem of g(r) that when electronic correlation effect is strong, the previous theories give a negative g(r),9 while g(r) is strictly a positive function. From this reasonable g(r), we estimate and establish a newly effective fitting expression of the ground state energy of electron gas. The new fitting expression presents a similar result with present theories when rs is small, since only in the limit of rs is small, present theories estimate a exact ground state energy. When rs increases, the difference between EFT and other theories becomes more and more remarkable. The difference is expected as EFT estimates a reasonable g(r) and would effectively amend the overestimate of previous theories in the ground state energy. In addition, by the ground state energy, we estimate the phase transition derived by the strong correlation effect. When the density decreases, the electronic correlation effect changes from weak to strong and we observe a sudden phase transition from paramagnetic to full spin polarization occurring at rs = 31 ± 4.

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.

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