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| lecturenotes:bestof [2025/08/22 16:46] – pbloechl | lecturenotes:bestof [2025/08/22 17:00] (current) – pbloechl |
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| - Consistent framework to divide the system into **phonons**, electronic excitations, electron-phonon coupling, phonon scattering etc. (Introduction to Solid State Theory) | - Consistent framework to divide the system into **phonons**, electronic excitations, electron-phonon coupling, phonon scattering etc. (Introduction to Solid State Theory) |
| - **Average Phase Approximation (APA)**: The APA Hamiltonian discards the off-diagonal elements of the many-particle Hamiltonian in a basis of Slater determinants built from natural orbitals. While it is based on Slater determinants, it goes beyond the mean-field approximation and demonstrates correlation effects on the spectra such as lifetime broadening and satellites. (Advanced Solid-State Theory) | - **Average Phase Approximation (APA)**: The APA Hamiltonian discards the off-diagonal elements of the many-particle Hamiltonian in a basis of Slater determinants built from natural orbitals. While it is based on Slater determinants, it goes beyond the mean-field approximation and demonstrates correlation effects on the spectra such as lifetime broadening and satellites. (Advanced Solid-State Theory) |
| - **Lehmann amplitudes**: Lehmann amplitudes are introduced as time-dependent objects along with their "Lehmann" occupations. The resulting expressions resemble closely those for non-interacting particles, while they nevertheless capture rigorously the interacting many-body problem. The conventional time-independent Lehmann amplitudes are what I call the stationary Lehmann amplitudes and their energies. The common term quasi-particle wave functions is avoided because of the ambiguity with the quasi-particle concept from Landau's Fermi-liquid theory. (Advanced Solid-State Theory) | - **Lehmann amplitudes**: Lehmann amplitudes are introduced as time-dependent objects along with their "Lehmann occupations". The resulting expressions using "Lehmann occupations" resemble closely those for non-interacting particles, while they nevertheless capture rigorously the interacting many-body problem. The conventional time-independent Lehmann amplitudes are what I call the stationary Lehmann amplitudes. The common term "quasi-particle wave functions" is avoided in this context because of the ambiguity with the quasi-particle concept from Landau's Fermi-liquid theory. (Advanced Solid-State Theory) |
| | - **Diagrammatic expansion of grand potential**: Rather than expanding the Green's function in the interaction strength, I expand the grand potential, which is a functional of the non-interacting Green's function. The Green's function diagrams are then derived from the grand potential. |
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