QUANTUM THEORY OF THE ENERGY SPECTRUM OF SUPERFLUIDS

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

OSTI ID:4162925

Jackson, H W

An explicit formula for the energy eigenvalues for the low states of a superfluid is developed in a free phonon'' approximation; this formula exhibits clearly the quasiparticle nature of the excited states. Initially, a certain basis of correlated wave functions is assumed and used to construct an orthonormal basis. In the representation of the latter basis, the Hamiltonian has a particularly simple form, which is then diagonalized by a Bogoliubov-type frainsformation. The method and results can be applied to a system of strongly interacting particles, such as real system of He-4, as well as to a model system of weakly interacting particles. The energy formula yields the results obtained by Feynman and by Bogoliubov as special cases. Next the free phonon'' results are taken as a zerothorder approximation and used to calculate the correction to the dispersion curve for elementary excitations in the approximation of the Brillouin-Wigner second-order energy formula. The computed elementary energy spectrum is compared with the dispersion curve constracted from the single inelastic scattering of neutrons by Henshaw and Woods, andd with the theoretical curve obtained from a variational calculation by Feynman and Cohen. Approximations involved in the present calculation are discussed, and a discrepancy between theoretical and experimental energy values for excitations with small momentum is studied. A method for examining the stability of elementary excitations corresponding to both experimental and theoretical dispersion curves is presented and applied to the curves mentioned above. Finally criteria are developed which indicate the accuracy of approximations to the 3particle distribution function generated by the ground state of a quantum fluid. One criterion is applied to the Kirkwood superposition form for a system of He-4 in order to study the errors involved in the approximation; a related criterion is used to investigate the accuracy of approximations occurring in the second-order perturbation calculation described above. (Dissertation Abstr.)

• Research Organization: Originating Research Org. not identified
• NSA Number: NSA-18-000944
• OSTI ID: 4162925
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

CRYOGENICS
DIFFERENTIAL EQUATIONS
DISTRIBUTION
EIGENVALUES
ENERGY
ENERGY LEVELS
ERRORS
EXCITATION
EXPLOSIVES
FLUIDS
FREQUENCY
GAMMA RADIATION
HAMILTONIAN
HELIUM 4
HIGH TEMPERATURE
INELASTIC SCATTERING
INTERACTIONS
MANY BODY PROBLEM
MATHEMATICS
MEASURED VALUES
MEDICINE
MOMENTUM
NEUTRON BEAMS
NUCLEAR EXPLOSIONS
NUMERICALS
PARTICLE MODELS
PARTICLES
PERTURBATION THEORY
PHONONS
PHYSICS
QUANTUM MECHANICS
QUASI PARTICLES
RADIATION EFFECTS
RADIATION PROTECTION
SAFETY
SCATTERING
SHOCK WAVES
SOUND
SPECTRA
STABILITY
SUPERFLUIDITY
VARIATIONS
VELOCITY
VISCOSITY