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- W1966554285 abstract "The electron-lattice interaction term of the Bloch-FrOhlich Hamiltonian, written in the occupation number representation, is bilinear in the electron creation and annihilation operators but linear in the phonon raising and lowering operators. This asymmetry leads to the non-commutability of the phonon number operator and the interaction term of the Hamiltonian. It is shown that by introducing a bilinear form for each phonon operator the commutability of these two terms can be achieved. Formally, the new lattice operators arise from the quantum field-theoretical treatment of the normal modes. Specifically, in the harmonic approximation and coordinate representation of the lattice Hamiltonian in phonon space, this is achieved by the replacement of wave functions by a coordinate-dependent operator field. One obtains then such a field for every normal mode of the lattice. The operator field expansion coefficients are the lattice vibrational mode creation and annihilation operators which appear only in a bilinear combination throughout the theory. To obtain an equivalence relation between the field-theoretical and wave-mechanical formulations, one requires that only one lattice quasiparticle per lattice vibrational mode be allowed. For this case, the relation between the lattice field operators and the conventional phonon operators assumes a simple form. Finally, the entire Bloch-FrOhlich Hamiltonian is rewritten in terms of the new set of lattice operators and the conservation of the new lattice quasiparticles is demonstrated. Thus, both the number of electrons and the number of lattice quasiparticles are shown to be constants of motion of an interacting electron-lattice system." @default.
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- W1966554285 date "2009-06-18" @default.
- W1966554285 modified "2023-09-26" @default.
- W1966554285 title "Constants of motion in an interacting electron-lattice system" @default.
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- W1966554285 doi "https://doi.org/10.1002/qua.560020733" @default.
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