Path Integral Monte Carlo Simulations for Fermion Systems: Pairing in the Electron-Hole Plasma

We review the path integral method wherein quantum systems are mapped with Feynman's path integrals onto a classical system of "ring-polymers" and then simulated with the Monte Carlo technique. Bose or Fermi statistics correspond to possible "cross-linking" of polymers. As proposed by Feynman, superfluidity and Bose condensation result from macroscopic exchange of bosons. To map fermions onto a positive probability distribution, one must restrict the paths to lie in regions where the fermion density matrix is positive. We discuss a recent application to the two-component electron-hole plasma. At low temperature excitons and bi-excitons form. We have used nodal surfaces incorporating paired fermions and see evidence of a Bose condensation in the energy, specific heat and superfluid density. In the restricted path integral picture, pairing appears as intertwined electron-hole paths. Bose condensation occurs when these intertwined paths wind around the periodic boundaries.Comment: 14 pages, 7 figures Prepared for the 1999 International Conference on Strongly Coupled Coulomb Systems, Saint-Malo, Franc

Quantum Monte Carlo treatment of elastic exciton-exciton scattering

We calculate cross sections for low energy elastic exciton-exciton scattering within the effective mass approximation. Unlike previous theoretical approaches, we give a complete, non-perturbative treatment of the four-particle scattering problem. Diffusion Monte Carlo is used to calculate the essentially exact energies of scattering states, from which phase shifts are determined. For the case of equal-mass electrons and holes, which is equivalent to positronium-positronium scattering, we find a_s = 2.1 a_x for scattering of singlet-excitons and a_s= 1.5 a_x for triplet-excitons, where a_x is the excitonic radius. The spin dependence of the cross sections arises from the spatial exchange symmetry of the scattering wavefunctions. A significant triplet-triplet to singlet-singlet scattering process is found, which is similar to reported effects in recent experiments and theory for excitons in quantum wells. We also show that the scattering length can change sign and diverge for some values of the mass ratio m_h/m_e, an effect not seen in previous perturbative treatments.Comment: 6 pages, 6 figures. Revision has updated figures, improved paper structure, some minor correction

Path integral Monte Carlo simulation of charged particles in traps

This chapter is devoted to the computation of equilibrium (thermodynamic) properties of quantum systems. In particular, we will be interested in the situation where the interaction between particles is so strong that it cannot be treated as a small perturbation. For weakly coupled systems many efficient theoretical and computational techniques do exist. However, for strongly interacting systems such as nonideal gases or plasmas, strongly correlated electrons and so on, perturbation methods fail and alternative approaches are needed. Among them, an extremely successful one is the Monte Carlo (MC) method which we are going to consider in this chapter.Comment: 18 pages, based on talks on Hareaus school on computational methods, Greifswald, September 200

Models of coherent exciton condensation

That excitons in solids might condense into a phase-coherent ground state was proposed about 40 years ago, and has been attracting experimental and theoretical attention ever since. Although experimental confirmation has been hard to come by, the concepts released by this phenomenon have been widely influential. This tutorial review discusses general aspects of the theory of exciton and polariton condensates, focussing on the reasons for coherence in the ground state wavefunction, the BCS to Bose crossover(s) for excitons and for polaritons, and the relationship of the coherent condensates to standard lasers.Comment: 27 pages, 6 figures. Submitted for a special issue of J. Phys. Cond. Matt. associated with the EU network "Photon-mediated phenomena in semiconductor nanostructures