L. F. Lemmens

The energy loss function of the polaron gas

Abstract The energy loss function Im 1/ K (π, ω) of a gas of polarons is calculated in the RPA approximation. For typical densities of degenerate polar semiconductors, the energy loss function has pronounced structure. Up to three resonances appear. The coupled phonon-plasmon resonance, with frequency between ω TO and ω LO , leads to an extremely sharp peak in Im 1/ K (π, ω), for appropriate values of wavevector and densities.

Condensation and interaction range in harmonic boson traps: A variational approach

For a gas of N bosons interacting through a two-body Morse potential a variational bound of the free energy of a confined system is obtained. The calculation method is based on the Feynman-Kac functional projected on the symmetric representation. Within the harmonic approximation a variational estimate of the effect of the interaction range on the existence of many-particle bound states, and on the N-T phase diagram is obtained.

Many Body Diffusion and Interacting Electrons in a Harmonic Confinement

We present numerically exact energy estimates for two-dimensional electrons in a parabolic confinement. By application of an extension of the recently introduced many-body diffusion algorithm, the ground-state energies are simulated very efficiently. The new algorithm relies on partial antisymmetrization under permutation of particle coordinates. A comparison is made with earlier theoretical results for that system.

Use of the chemical potential for a limited number of fermions with a degenerate groundstate

Abstract:For fermions with degenerate single-particle energy levels, the usual relation between the total number of particles and the chemical potential μ is only satisfied for a specific number of particles, i.e. those leading to closed shells. The treatment of an arbitrary number of fermions requires a modification of the chemical potential, similar to the one proposed by Landsberg for Bose-condensed systems. We study the implications of the required modification for fermions in a potential, by calculating the ground state energy, the free energy, the density, the partition function and the dynamic two-point correlation function. It turns out that the modified relation between the fugacity and the number of particles leads to the correct ground state energy and density. But for other quantities like the entropy and the two-point correlation functions, an additional correction is required and derived. These calculations indicate that many-body perturbation theories based on H - μN with Lagrange multiplier μ, are not applicable in unmodified form for a fixed number of fermions at low temperature.

The polarization function of a finite number of confined spin polarized fermions

Abstract The Fourier transform of an inhomogeneous two-point correlation function, in space and Euclidean time, is derived for a limited number of spin polarized fermions in an external potential. The formulation is based on the many-body generalization of the Feynman–Kac functional. Special attention is given to the finite number aspects and the implications thereof for the fugacity. An analysis of the correlation function in terms of single-particle propagators is obtained, leading to an occupation function representation. For the harmonic model, the temporal Fourier components of the two-point correlation matrix are worked out in the low-temperature limit.

Many interacting electrons in a quantum dot

The propagator of N interacting identical particles in d spatial dimensions can be written as a Feynman-Kac functional over a symmetrized process, i.e. as a Euclidean-time path integral over the diffusion process of N identical free particles with superimposed potential-dependent exponential weights. Recently a many-body diffusion formalism [“MBDF”] was developed, which allows, for coordinate-symmetric potentials and for certain irreducible symmetry representations, to separate the total propagator into a sum of stochastically independent sub-propagators. This method was applied to calculate “numerically exactly” the ground state energy for electrons in a parabolic confinement. In particular the example of a 2D closed shell system with six, twelve and twenty unpolarised interacting electrons in a quantum dot with parabolic confinement was treated. The results obtained by the MBDF method are compared with earlier theoretical approximations for this system.

Path Integrals and Statistics of Identical Particles

We summarize the essential ingredients, which enabled us to derive the path-integral for a system of harmonically interacting spin-polarized identical particles in a parabolic confining potential, including both the statistics (Bose–Einstein or Fermi–Dirac) and the harmonic interaction between the particles. This quadratic model, giving rise to repetitive Gaussian integrals, allows to derive an analytical expression for the generating function of the partition function. The calculation of this generating function circumvents the constraints on the summation over the cycles of the permutation group. Moreover, it allows one to calculate the canonical partition function recursively for the system with harmonic two-body interactions. Also, static one-point and two-point correlation functions can be obtained using the same technique, which make the model a powerful trial system for further variational treatments of realistic interactions.

An ideal mixture of N confined S=1-bosons

Using a new method – Path integral approach to Many Body theory – we obtain the free energy for a finite number of bosons, confined in a harmonic potential and having spin states with a different energy characterised by a magnetic quantum number. It is seen that all internal states prefer a unique condensate attributed to the (high temperature) maximum in the specific heat, the second (very low temperature) maximum is identified as the Schottky anomaly, coming from lifting the degeneracy of the internal degrees of freedom. The susceptibility clearly demonstrates the dependence of the condensation temperature on the energies of the internal degrees of freedom.