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Title: A QMC study of the 3D & 2D electron-hole gas and a new method for solving the Schrödinger equation
Author: Brown, G. J.
Awarding Body: University of Cambridge
Current Institution: University of Cambridge
Date of Award: 2003
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This dissertation is divided into two parts. In the first half we study the electron-hole gas with the quantum Monte Carlo method. In the three-dimensional system we find that the paramagnetic excitonic insulator is energetically favourable for all densities and mass ratios studied. Increasing the hole mass was found to make the ferromagnetic state more competitive, though never lower in energy than the paramagnetic state. A transition to a Wigner crystal state, as the hole mass increased, was indicated but never found in the mass range we considered. The two-dimensional layered system exhibits phase transitions from an excitonic insulator to a two component plasma at high density, and to a Wigner crystal state at low density. This occurs when the layer separation becomes comparable to the in-layer particle spacing. The second half of the dissertation is devoted to the development of a new technique for solving the Schrödinger equation. We propose a new equation whose Green's function is used to evolve the wavefunction in time exactly, assuming the small time step approximation. There is no need for the fixed-mode constraint or artificial enforcement of the anti-symmetry of the wavefunction due to the Pauli-exclusion principle.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available