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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Fermi liquid theory ： ウィキペディア英語版 Fermi liquid theory Fermi liquid theory (also known as Landau–Fermi liquid theory) is a theoretical model of interacting fermions that describes the normal state of most metals at sufficiently low temperatures. The interaction between the particles of the many-body system does not need to be small. The phenomenological theory of Fermi liquids was introduced by the Soviet physicist Lev Davidovich Landau in 1956, and later developed by Alexei Abrikosov and Isaak Khalatnikov using diagrammatic perturbation theory. The theory explains why some of the properties of an interacting fermion system are very similar to those of the Fermi gas (i.e. non-interacting fermions), and why other properties differ. Important examples of where Fermi liquid theory has been successfully applied are most notably electrons in most metals and Liquid He-3. Liquid He-3 is a Fermi liquid at low temperatures (but not low enough to be in its superfluid phase.) He-3 is an isotope of helium, with 2 protons, 1 neutron and 2 electrons per atom. Because there is an odd number of fermions inside the atom, the atom itself is also a fermion. The electrons in a normal (non-superconducting) metal also form a Fermi liquid, as do the nucleons (protons and neutrons) in an atomic nucleus. Strontium ruthenate displays some key properties of Fermi liquids, despite being a strongly correlated material, and is compared with high temperature superconductors like cuprates. ==Description== The key ideas behind Landau's theory are the notion of ''adiabaticity'' and the exclusion principle.〔 (draft copy)〕 Consider a non-interacting fermion system (a Fermi gas), and suppose we "turn on" the interaction slowly. Landau argued that in this situation, the ground state of the Fermi gas would adiabatically transform into the ground state of the interacting system. By Pauli's exclusion principle, the ground state $\backslash Psi\_0$ of a Fermi gas consists of fermions occupying all momentum states corresponding to momentum Landau quasiparticles are long-lived excitations with a lifetime $\backslash tau$ that satisfies $\backslash frac\backslash ll\backslash epsilon\_p$ where $\backslash epsilon\_p$ is the Fermi energy. For this system, the Green's function can be written (near its poles) in the form $G(\backslash omega,p)\backslash approx\backslash frac$ where $\backslash mu$ is the chemical potential and $\backslash epsilon(p)$ is the energy corresponding to the given momentum state. The value $Z$ is called the ''quasiparticle residue'' and is very characteristic of Fermi liquid theory. The spectral function for the system can be directly observed via ARPES experiment, and can be written (in the limit of low-lying excitations) in the form: $A(\backslash vec,\backslash omega)=Z\backslash delta(\backslash omega-v\_Fk\_)$ where $v\_F$ is the Fermi velocity. Physically, we can say that a propagating fermion interacts with its surrounding in such a way that the net effect of the interactions is to make the fermion behave as a "dressed" fermion, altering its effective mass and other dynamical properties. These "dressed" fermions are what we think of as "quasiparticles".〔 Another important property of Fermi liquids is related to the scattering cross section for electrons. Suppose we have an electron with energy $\backslash epsilon\_1$ above the Fermi surface, and suppose it scatters with a particle in the Fermi sea with energy $\backslash epsilon\_2$. By Pauli's exclusion principle, both the particles after scattering have to lie above the Fermi surface, with energies $\backslash epsilon\_3,\backslash epsilon\_4>\backslash epsilon\_F$ Now, suppose the initial electron has energy very close to the Fermi surface $\backslash epsilon\backslash approx\backslash epsilon\_F$ Then, we have that $\backslash epsilon\_2,\backslash epsilon\_3,\backslash epsilon\_4$ also have to be very close to the Fermi surface. This reduces the phase space volume of the possible states after scattering, and hence, by Fermi's golden rule, the scattering cross section goes to zero. Thus we can say that the lifetime of particles at the Fermi surface goes to infinity.〔 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Fermi liquid theory」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.