Numerical solving of the 2D-eigenvalue problem in a self-consistent basis

2005 ◽  
Author(s):  
S. I. Vinitsky ◽  
D. N. Pak ◽  
V. A. Rostovtsev ◽  
N. A. Chekanov ◽  
Yu. A. Ukolov
Keyword(s):  
Eigenvalue Problem ◽  
Self Consistent ◽  
Consistent Basis

A MAPLE Symbolic-Numeric Program for Solving the 2D-Eigenvalue Problem by a Self-consistent Basis Method

2005 ◽  
pp. 32-39
Author(s):  
I. N. Belyaeva ◽  
N. A. Chekanov ◽  
A. A. Gusev ◽  
V. A. Rostovtsev ◽  
Yu. A. Ukolov ◽  
...  
Keyword(s):  
Eigenvalue Problem ◽  
Self Consistent ◽  
Consistent Basis ◽  
Basis Method

A SELF-CONSISTENT ANALYTIC THEORY OF THE SPIN BIPOLARON IN THE t–J MODEL

2000 ◽  
Vol 14 (08) ◽  
pp. 809-835
Author(s):  
HEINZ BARENTZEN ◽  
VIKTOR OUDOVENKO
Keyword(s):  
Integral Equation ◽  
Eigenvalue Problem ◽  
Bound States ◽  
Numerical Solutions ◽  
P Wave ◽  
Linear Integral Equation ◽  
Soluble Form ◽  
Coupled Equations ◽  
Self Consistent ◽  
D Wave

The spin bipolaron in the t–J model, i.e., two holes interacting with an antiferromagnetic spin background, is treated by an extension of the self-consistent Born approximation (SCBA), which has proved to be very accurate in the single-hole (spin polaron) problem. One of the main ingredients of our approach is the exact form of the bipolaron eigenstates in terms of a complete set of two-hole basis vectors. This enables us to eliminate the hole operators and to obtain the eigenvalue problem solely in terms of the boson (magnon) operators. The eigenvalue equation is then solved by a procedure similar to Reiter's construction of the single-polaron wave function in the SCBA. As in the latter case, the eigenvalue problem comprises a hierarchy of infinitely many coupled equations. These are brought into a soluble form by means of the SCBA and an additional decoupling approximation, whereupon the eigenvalue problem reduces to a linear integral equation involving the bipolaron self-energy. The numerical solutions of the integral equation are in quantitative agreement with the results of previous numerical studies of the problem. The d-wave bound state is found to have the lowest energy with a critical value J/t| c ≈ 0.4. In contrast to recent claims, we find no indication for a crossover between the d-wave and p-wave bound states.

The evolution of the Kuiper belt during the formation of the outer planets

1999 ◽  
Vol 173 ◽  
pp. 37-44
Author(s):  
M.D. Melita ◽  
A. Brunini
Keyword(s):  
Kuiper Belt ◽  
Outer Planets ◽  
Self Consistent ◽  
Planetary Bodies ◽  
Mass Depletion

AbstractA self-consistent study of the formation of planetary bodies beyond the orbit of Saturn and the evolution of Kuiper disks is carried out by means of an N-body code where accretion and gravitational encounters are considered. This investigation is focused on the aggregation of massive bodies in the outer planetary region and on the consequences of such process in the corresponding cometary belt. We study the link between the bombardment of massive bodies and mass depletion and eccentricity excitation.

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