Microscopic Calculations for Quantum Many-Body Systems.

Irving E. Segal, D. J. Thouless

Frank V. Kowalski

Abstract Correlated interference is calculated for a microscopic particle retro‐reflecting from two spatially separated scatterers that are free to move, all three of which are treated as quantum bodies: the positions of the particle traversing this 1D interferometer and those of the interferometer components are all uncertain. Interference in a measurement of only the particle is shown to disappear for microscopic yet appear for mesoscopic scatterers, contrary to that of a quantum‐classical transition. A measurement of this threshold can verify quantum correlations in many‐body systems by measuring only the retro‐reflected microscopic particle. The decoherence of a mesoscopic scatterer is determined by this threshold without it having to traverse slits or beamsplitters.

Hao Fu

This thesis summarizes work on the theory of many-body effects in atomic systems. The modification of emission rates and spectra for a single impurity atom embedded in a many-body system is studied. In addition, the physics of two, cold atom systems is investigated. We first study the spontaneous decay of a source atom inside a dielectric. In a microscopic picture, the photon radiated by the source atom is scattered by the medium atoms. This scattered photon is absorbed by the source atom, which results in a modification of the atom's decay rate. The calculation is carried out to second order in the medium density and we find a result that differs from the one obtained in macroscopic calculations. Using the same microscopic model, we carry out a microscopic calculation for the recoil momentum acquired by a radiating atom in a medium. In our microscopic calculation, the average value of the photon momentum is modified by its scattering with the source atoms. This gives a modification to the recoil momentum of the source atom. The calculated correction agrees with the experimental observations. In the second part of the thesis, we study two, ultra-cold atomic systems. An exactly solvable model, a Tonks-Girardeau gas with a local potential, is explain first. Such a one dimensional quantum gas has been realized recently. The spectrum of the single particle density matrix is evaluated exactly. We find the "condensate density" as a function of the potential strength. We also propose to use time-of-flight imaging to detect experimental observables. The possibility of modulating the interaction strength in space using a Feshbach resonance in a degenerate Fermi gas is examined in the last part of the thesis. Using a periodic modulation, we find that the ground state of the system contains Cooper pairs with non-zero center-of-mass momenta. The resultant single particle spectrum is found to have an additional gap along particular directions. We propose experimental schemes to detect properties of both the ground state and the quasi-particle excitations.

Jesús Navarro, A. Polls

Vedene H. Smith

Cheng-Li Wu, D.H. Feng, Jin-Quan Chen +1 more

An effective boson Hamiltonian is derived from the original Hamiltonian of a many-fermion system. The results show that when the intrinsic motion of bosons is collective and the excitation energies of the system are small, the effective boson-boson interaction can be reduced to a two-body interaction while for odd systems or systems with uncorrelated fermions, there is an additional two-body boson-fermion interaction. Both these interactions can be calculated from the original fermion-fermion ones. Thus, the microscopic foundation of the interacting boson model is established without recourse to mapping procedures.NUCLEAR STRUCTURE Interacting boson model, boson fermion hybrid representation, microscopic foundation.