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physica status solidi (b)

On the Ground State Energy of a Gas of Interacting Polarons

L. F. Lemmens, F. Brosens, J. T. Devreese

Published Aug 1, 1977• 57 citations
Publisher

Abstract

Abstract Using a canonical transformation the Hamiltonian of a gas of interacting polarons is studied. After elimination of the phonons the reduced Hamiltonian describes a system of charged particles interacting through an effective interparticle potential. The Hartree‐Fock ground state of the reduced system is analysed.
DOI
10.1002/pssb.2220820204

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Quantum statistics for a finite number of polarons in a neutralizing background

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The ground-state energy of an N-polaron system, confined to a spherical quantum dot with a neutralizing background charge, is investigated within an all-coupling many-body path-integral variational principle, taking into account both the Fermi statistics of the polarons and the electron-electron interaction. The treatment of the ground-state energy is performed for both closed-shell and open-shell systems. The av. fermion d. in the neutral spherical dot is characterized by the Wigner-Seitz parameter rs. For a sufficiently large but finite no. of polarons, the dependence of the ground-state energy on rs is very similar to that for a polarons, gas in bulk. Hence, we can conclude that the ground-state properties of a polaron gas in bulk can be qual. described using a model of a finite no. of polarons in a confinement potential provided by a neutralizing background charge. [on SciFinder (R)]

Journal of Physics Condensed Matter•May 30, 2007•1 citation
An effective interaction potential for a pair of polarons is derived in a Landau-Pekar adiabatic approximation.The possibility of formation of bound states of two polarons is discussed.The lowlying energy states of a system of Landau-Pekar polarons interacting with the derived effective potential are investigated by employing approximation models including a body-centered cubic lattice of polarons, a Hartree-Fock gas of polarons, and a Hartree-Fock gas of polarons weakly coupled to a polaron plasma.The low-lying energy states based on these models are examined numerically for a specific test case intended to describe polarons in an ionic crystal with a polaron coupling constant large enough that the Landau-Pekar approximation may be expected to be appropriate.It is found that, for a wide range of polaron densities, the plasma-coupled gas model yields the best results among the models treated.
The ground-state energy of an NNN-polaron system confined to a quantum dot with a neutralizing background charge is investigated within an all-coupling many-body path-integral variational principle taking into account both Fermi statistics of polarons and the electron-electron interaction. The treatment of the ground-state energy is performed for both closed- and open-shell systems. The average fermion density in the neutral spherical dot is characterized by the Wigner-Seitz parameter rs{r}_{s}rs​. For a sufficiently large but finite number of polarons, the dependency of the ground-state energy on rs{r}_{s}rs​ is very similar to that for a polaron gas in bulk. From this, we can conclude that the ground-state energy of a polaron gas in bulk can be qualitatively described using a model of a finite number of polarons in a confinement potential provided by a neutralizing background charge.
A simplified version of a Bose gas with negative scattering length is studied with a model Hamiltonian similar to that used in the case of repulsive interactions. A new transformation is used which takes into account the attractive interactions in the system, and the ground-state energy is calculated from experimental values of the sound velocity in the system. Real values for the phonon energy spectrum are obtained, and the ratio of the effective mass to ordinary mass is deduced using experimental values of interparticle separation and core radius. A justification for using this modified Hamiltonian is attempted in the Appendix.
The ground-state energy of an N-polaron system, confined to a spherical quantum dot with a neutralizing background charge, is investigated within an all-coupling many-body path-integral variational principle, taking into account both the Fermi statistics of the polarons and the electron-electron interaction. The treatment of the ground-state energy is performed for both closed-shell and open-shell systems. The av. fermion d. in the neutral spherical dot is characterized by the Wigner-Seitz parameter rs. For a sufficiently large but finite no. of polarons, the dependence of the ground-state energy on rs is very similar to that for a polarons, gas in bulk. Hence, we can conclude that the ground-state properties of a polaron gas in bulk can be qual. described using a model of a finite no. of polarons in a confinement potential provided by a neutralizing background charge. [on SciFinder (R)]