SOME PROBLEMS IN MANY BODY PROBLEM

Thesis/Dissertation · Mon Jan 01 04:00:00 EST 1962

OSTI ID:4701529

Kitamura, M

Two models for systems of many interacting fermions are studied. The model for the ground state suggested by Overhauser is studied for more general spin-dependent finite short- and long-range potential. It is found that for short-range potential almost all important features of the model are given by zero-range approximation, unless the interaction is so strong that the approximation used is no longer valid. For long-range potential, it is shown that the Overhauser ground state does not exist unless there is a strong spin flip negative potential between particles. The statistical perturbation theory is extended so that it can be applied to the theory of superconductivity. In connection with this, a new simple proof of the applicability of Wick's theorem to statistical mechanics on which the statistical perturbation theory is based, is given. Application of the theory to the ground state and calculation of the effective scattering matrix (the T-matrix) are also studied. The analytic properties of the T-matrix in a complex energy plane is studied in detail in one- dimension for a simple separable potentlal. It is found that the T-matrix has 2 poles besides 2 cuts along the imaginary axis. The nonlinear integral equation for an energy gap is also studied. (Dissertation Abstr.)

• Research Organization: Originating Research Org. not identified
• NSA Number: NSA-17-026747
• OSTI ID: 4701529
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

DIFFERENTIAL EQUATIONS
ENERGY
ENERGY LEVELS
FERMIONS
FIELD THEORY
INTEGRALS
INTERACTIONS
MANY BODY PROBLEM
MATHEMATICS
MATRICES
MECHANICS
PARTICLES
PERTURBATION THEORY
PHYSICS
QUANTUM MECHANICS
S- MATRIX
SCATTERING
SPIN
STATISTICS
SUPERCONDUCTIVITY
WICK THEOREM