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A simple solution of Fröhlich polarons

Hanyou Chu

Solid State CommunicationsOct 1, 19924 citations

Self-Consistent Hartree-Fock-Bogoliubov approach to the Frohlich Polaron Problem

Hong Yuan Ling, Ben Kain

Bulletin of the American Physical SocietyMar 16, 20170 citations

Weak and Intermediate Coupling Solutions of the Fröhlich Hamiltonian

Ashok Chatterjee, Soma Mukhopadhyay

After deriving the quantum mechanical model polaron Hamiltonian, Frohlich, Pelzar and Zineau presented a perturbative solution to the problem. This chapter examines the perturbation theory from Frohlich et al. and presents other important weak and intermediate coupling polaron theories. It discusses several polaronic properties like average number of virtual phonons in the polaron cloud, electron life-time, lattice polarization potential using the first-order perturbative wave function and obtained the polaron energy and the polaron mass using the second-order Rayleigh-Schrodinger perturbation theory (RSPT). The second-order RSPT is known to have a limited range of validity. In the one-phonon Tamm-Dancoff approximation, the exact ground state energy appears in the denominator instead of the unperturbed energy that appears in RSPT. The chapter also discusses the work of Lee and Pines who have used the Tomonaga's approximation made in the formulation of the meson-theoretic problem to the case of polaron.After deriving the quantum mechanical model polaron Hamiltonian, Frohlich, Pelzar and Zineau presented a perturbative solution to the problem. This chapter examines the perturbation theory from Frohlich et al. and presents other important weak and intermediate coupling polaron theories. It discusses several polaronic properties like average number of virtual phonons in the polaron cloud, electron life-time, lattice polarization potential using the first-order perturbative wave function and obtained the polaron energy and the polaron mass using the second-order Rayleigh-Schrodinger perturbation theory (RSPT). The second-order RSPT is known to have a limited range of validity. In the one-phonon Tamm-Dancoff approximation, the exact ground state energy appears in the denominator instead of the unperturbed energy that appears in RSPT. The chapter also discusses the work of Lee and Pines who have used the Tomonaga's approximation made in the formulation of the meson-theoretic problem to the case of polaron.

CRC Press eBooksOct 9, 20180 citations

Strong-Coupling Solutions of the Fröhlich Hamiltonian

Ashok Chatterjee, Soma Mukhopadhyay

This chapter describes some of the most important theories of the strong-coupling polaron. The nature of polarons in the strong-coupling limit is in some sense qualitatively different from the weak or intermediate-coupling polaron—the localization of a polaron being a case in point. Though a qualitative picture of a strong-coupling polaron is easy to visualize as opposed to the weak-coupling polaron, the mathematical formulation of a strongly coupled polaron is rather a difficult problem from the quantum mechanical point of view. In fact, the exact polaron energy in the weak-coupling limit can be obtained from the Frohlich Hamiltonian analytically, while the same is not possible in the strong-coupling limit. In the strong-coupling case, the electron velocity is much larger than the phonon frequency and therefore electron can follow the ion motion adiabatically. The adiabatic expansion of the polaron energy in the strong-coupling regime was reported by Bogoliubov and Tiablikov.This chapter describes some of the most important theories of the strong-coupling polaron. The nature of polarons in the strong-coupling limit is in some sense qualitatively different from the weak or intermediate-coupling polaron—the localization of a polaron being a case in point. Though a qualitative picture of a strong-coupling polaron is easy to visualize as opposed to the weak-coupling polaron, the mathematical formulation of a strongly coupled polaron is rather a difficult problem from the quantum mechanical point of view. In fact, the exact polaron energy in the weak-coupling limit can be obtained from the Frohlich Hamiltonian analytically, while the same is not possible in the strong-coupling limit. In the strong-coupling case, the electron velocity is much larger than the phonon frequency and therefore electron can follow the ion motion adiabatically. The adiabatic expansion of the polaron energy in the strong-coupling regime was reported by Bogoliubov and Tiablikov.

CRC Press eBooksOct 9, 20180 citations

Intermediate coupling theory for the multidimensional polaron

Shreekantha Sil, Ashok Chatterjee

Physics Letters ASep 1, 198910 citations

New solution for the polaron problem

И. Д. Феранчук, L I Komarov

New variational ansatz for the large-radius Fröhlich polaron is considered. The corresponding operator estimation for the energy of polaron proves to be very similar to the result found by Feynman on the basis of the variational principle for the functional integral of the system. It allows us to make clear the problem of ``phase transition'' and to anylize the structure of the localized state of the polaron in the intermediate coupling regime. It is shown that the analogous state exists also for the model of particle-field interaction with the divergent perturbation theory.New variational ansatz for the large-radius Fröhlich polaron is considered. The corresponding operator estimation for the energy of polaron proves to be very similar to the result found by Feynman on the basis of the variational principle for the functional integral of the system. It allows us to make clear the problem of ``phase transition'' and to anylize the structure of the localized state of the polaron in the intermediate coupling regime. It is shown that the analogous state exists also for the model of particle-field interaction with the divergent perturbation theory.

arXiv:cond-mat/0510510Oct 19, 20052 citations

Solution of the Fr\"ohlich polaron problem at intermediate couplings

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