The approximated density matrix of the polaron system obtained in our previous paper for deriving the Feynman effective mass ${m}_{F}$ and the Krivoglaz-Pekar mass ${m}_{\mathrm{KP}}$ is reconsidered. It is shown that to obtain a consistent definition of the polaron effective mass one must impose the condition ${m}_{F}{=m}_{\mathrm{KP}}.$ This consistent definition is based on the fact that the wave functions derived from the density matrix corresponding to each excited state must be normalized and orthogonal. This condition leads to a consistent definition of the effective mass and a different variation principle for treating excited states. Numerical results are presented.The approximated density matrix of the polaron system obtained in our previous paper for deriving the Feynman effective mass ${m}_{F}$ and the Krivoglaz-Pekar mass ${m}_{\mathrm{KP}}$ is reconsidered. It is shown that to obtain a consistent definition of the polaron effective mass one must impose the condition ${m}_{F}{=m}_{\mathrm{KP}}.$ This consistent definition is based on the fact that the wave functions derived from the density matrix corresponding to each excited state must be normalized and orthogonal. This condition leads to a consistent definition of the effective mass and a different variation principle for treating excited states. Numerical results are presented.

Physical review. B, Condensed matterApr 15, 19985 citations

Effective mass of the polaron: A functional integral approach

Herbert E. Spohn

Annals of PhysicsMay 1, 198789 citations

Feynman Path-Integral Calculation of the Polaron Effective Mass

John T. Marshall, M. S. Chawla

In the expansion of the ground-state energy of a polaron in a weak magnetic field, the zeroth-order term is the polaron self-energy, while the first-order term is inversely proportional to the polaron effective mass. The effective mass so obtained is exactly equivalent to the freepolaron effective mass as defined by Fr\"ohlich. This equivalence principle is used to approximate the polaron effective mass by employing an approximate expression for the ground-state energy of a polaron in a weak magnetic field obtained by applying Feynman's path-integral variational method. The resultant polaron effective mass is found to be higher than Feynman's result by less than 1%.In the expansion of the ground-state energy of a polaron in a weak magnetic field, the zeroth-order term is the polaron self-energy, while the first-order term is inversely proportional to the polaron effective mass. The effective mass so obtained is exactly equivalent to the freepolaron effective mass as defined by Fr\"ohlich. This equivalence principle is used to approximate the polaron effective mass by employing an approximate expression for the ground-state energy of a polaron in a weak magnetic field obtained by applying Feynman's path-integral variational method. The resultant polaron effective mass is found to be higher than Feynman's result by less than 1%.

Physical review. B, Solid stateNov 15, 197024 citations

Alternative derivation of the effective mass of the polaron

K. Tayanasanti, Virulh Sa-Yakanit

The polaron effective mass using the path integral approach was first introduced by Feynman. He has shown that from the partition function, he obtained the ground state energy and the effective mass mF of the polaron. By using the partition function, Krivoglaz and Pekar proposed another definition of the effective mass mKP. Sa-yakanit has shown that using the density matrix Feynmam's path integral representation, it is possible to obtain both Feynman's and Krivoglaz and Pekar's results. In this thesis we propose a consistent definition of effective mass that mF and mKP should be equal. We have shown that the wave functions obtained from the density matrix should be normalized. We have also shown that the dynamic mass of the polaron can be obtained from the density matrix. The comparison of our results with recent work by Wang et.al.are given.The polaron effective mass using the path integral approach was first introduced by Feynman. He has shown that from the partition function, he obtained the ground state energy and the effective mass mF of the polaron. By using the partition function, Krivoglaz and Pekar proposed another definition of the effective mass mKP. Sa-yakanit has shown that using the density matrix Feynmam's path integral representation, it is possible to obtain both Feynman's and Krivoglaz and Pekar's results. In this thesis we propose a consistent definition of effective mass that mF and mKP should be equal. We have shown that the wave functions obtained from the density matrix should be normalized. We have also shown that the dynamic mass of the polaron can be obtained from the density matrix. The comparison of our results with recent work by Wang et.al.are given.

Jan 1, 19960 citations

Static and Dynamic Effective Mass of the Polaron

Virulh Sa‐Yakanit, K. Tayanasanti

Jan 1, 19980 citations

The approximated density matrix of the polaron system obtained in our previous paper for deriving the Feynman effective mass

{m}_{F}

and the Krivoglaz-Pekar mass

{m}_{\mathrm{KP}}

is reconsidered. It is shown that to obtain a consistent definition of the polaron effective mass one must impose the condition

{m}_{F}{=m}_{\mathrm{KP}}.

This consistent definition is based on the fact that the wave functions derived from the density matrix corresponding to each excited state must be normalized and orthogonal. This condition leads to a consistent definition of the effective mass and a different variation principle for treating excited states. Numerical results are presented.