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Luttinger's Theorem
In condensed matter physics, Luttinger's theorem is a result derived by J. M. Luttinger and J. C. Ward in 1960 that has broad implications in the field of electron transport. It arises frequently in theoretical models of correlated electrons, such as the high-temperature superconductors, and in photoemission, where a metal's Fermi surface can be directly observed. Definition Luttinger's theorem states that the volume enclosed by a material's Fermi surface is directly proportional to the particle density. While the theorem is an immediate result of the Pauli exclusion principle in the case of noninteracting particles, it remains true even as interactions between particles are taken into consideration provided that the appropriate definitions of Fermi surface and particle density are adopted. Specifically, in the interacting case the Fermi surface must be defined according to the criteria that :G(\omega=0,\,p) \to 0 or \infty, where G is the single-particle Green function in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fermi Surface
In condensed matter physics, the Fermi surface is the surface in reciprocal space which separates occupied electron states from unoccupied electron states at zero temperature. The shape of the Fermi surface is derived from the periodicity and symmetry of the crystalline lattice and from the occupation of electronic band structure, electronic energy bands. The existence of a Fermi surface is a direct consequence of the Pauli exclusion principle, which allows a maximum of one electron per quantum state. The study of the Fermi surfaces of materials is called fermiology. Theory Consider a Spin (physics), spin-less ideal Fermi gas of N particles. According to Fermi–Dirac statistics, the mean occupation number of a state with energy \epsilon_i is given by : \langle n_i\rangle =\frac, where * \left\langle n_i\right\rangle is the mean occupation number of the ith state * \epsilon_i is the kinetic energy of the ith state * \mu is the chemical potential (at zero temperature, this is th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Green's Function
In mathematics, a Green's function (or Green function) is the impulse response of an inhomogeneous linear differential operator defined on a domain with specified initial conditions or boundary conditions. This means that if L is a linear differential operator, then * the Green's function G is the solution of the equation where \delta is Dirac's delta function; * the solution of the initial-value problem L y = f is the convolution Through the superposition principle, given a linear ordinary differential equation (ODE), one can first solve for each , and realizing that, since the source is a sum of delta functions, the solution is a sum of Green's functions as well, by linearity of . Green's functions are named after the British mathematician George Green, who first developed the concept in the 1820s. In the modern study of linear partial differential equations, Green's functions are studied largely from the point of view of fundamental solutions instead. Under many ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Condensed Matter Physics
Condensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter, especially the solid and liquid State of matter, phases, that arise from electromagnetic forces between atoms and electrons. More generally, the subject deals with condensed phases of matter: systems of many constituents with strong interactions among them. More exotic condensed phases include the superconductivity, superconducting phase exhibited by certain materials at extremely low cryogenic temperatures, the ferromagnetic and antiferromagnetic phases of Spin (physics), spins on crystal lattices of atoms, the Bose–Einstein condensates found in ultracold atomic systems, and liquid crystals. Condensed matter physicists seek to understand the behavior of these phases by experiments to measure various material properties, and by applying the physical laws of quantum mechanics, electromagnetism, statistical mechanics, and other theoretical physics, physic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
North-Holland Publishing Company
Elsevier ( ) is a Dutch academic publishing company specializing in scientific, technical, and medical content. Its products include journals such as ''The Lancet'', '' Cell'', the ScienceDirect collection of electronic journals, '' Trends'', the '' Current Opinion'' series, the online citation database Scopus, the SciVal tool for measuring research performance, the ClinicalKey search engine for clinicians, and the ClinicalPath evidence-based cancer care service. Elsevier's products and services include digital tools for data management, instruction, research analytics, and assessment. Elsevier is part of the RELX Group, known until 2015 as Reed Elsevier, a publicly traded company. According to RELX reports, in 2022 Elsevier published more than 600,000 articles annually in over 2,800 journals. As of 2018, its archives contained over 17 million documents and 40,000 e-books, with over one billion annual downloads. Researchers have criticized Elsevier for its high profit margins an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physical Review Letters
''Physical Review Letters'' (''PRL''), established in 1958, is a peer-reviewed, scientific journal that is published 52 times per year by the American Physical Society. The journal is considered one of the most prestigious in the field of physics. Over a quarter of Physics Nobel Prize-winning papers between 1995 and 2017 were published in it. ''PRL'' is published both online and as a print journal. Its focus is on short articles ("letters") intended for quick publication. The Lead Editor is Hugues Chaté. The Managing Editor is Robert Garisto. History The journal was created in 1958. Samuel Goudsmit, who was then the editor of '' Physical Review'', the American Physical Society's flagship journal, organized and published ''Letters to the Editor of Physical Review'' into a new standalone journal'','' which became ''Physical Review Letters''. It was the first journal intended for the rapid publication of short articles, a format that eventually became popular in many other fiel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Luttinger–Ward Functional
In solid state physics, the Luttinger–Ward functional, proposed by Joaquin Mazdak Luttinger and John Clive Ward in 1960, is a scalar functional of the bare electron-electron interaction and the renormalized one-particle propagator. In terms of Feynman diagrams, the Luttinger–Ward functional is the sum of all closed, bold, two-particle irreducible diagrams, i.e., all diagrams without particles going in or out that do not fall apart if one removes two propagator lines. It is usually written as \Phi /math> or \Phi ,U/math>, where G is the one-particle Green's function and U is the bare interaction. The Luttinger–Ward functional has no direct physical meaning, but it is useful in proving conservation laws. The functional is closely related to the Baym–Kadanoff functional constructed independently by Gordon Baym and Leo Kadanoff in 1961. Some authors use the terms interchangeably; if a distinction is made, then the Baym–Kadanoff functional is identical to the two-particle ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fermi Liquid
Fermi liquid theory (also known as Landau's Fermi-liquid theory) is a theoretical model of interacting fermions that describes the normal state of the conduction electrons in most metals at sufficiently low temperatures. The theory describes the behavior of Many-body problem, many-body systems of particles in which the interactions between particles may be strong. The phenomenological model, phenomenological theory of Fermi liquids was introduced by the Soviet physicist Lev Davidovich Landau in 1956, and later developed by Alexei Alexeyevich Abrikosov, Alexei Abrikosov and Isaak Markovich Khalatnikov, Isaak Khalatnikov using Feynman diagrams, diagrammatic perturbation theory. The theory explains why some of the properties of an interacting fermion system are very similar to those of the ideal Fermi gas (collection of non-interacting fermions), and why other properties differ. Fermi liquid theory applies most notably to conduction electrons in normal (non-superconductivity, superco ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Momentum
In Newtonian mechanics, momentum (: momenta or momentums; more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass and is its velocity (also a vector quantity), then the object's momentum (from Latin '' pellere'' "push, drive") is: \mathbf = m \mathbf. In the International System of Units (SI), the unit of measurement of momentum is the kilogram metre per second (kg⋅m/s), which is dimensionally equivalent to the newton-second. Newton's second law of motion states that the rate of change of a body's momentum is equal to the net force acting on it. Momentum depends on the frame of reference, but in any inertial frame of reference, it is a ''conserved'' quantity, meaning that if a closed system is not affected by external forces, its total momentum does not change. Momentum is also conserved in special relativity (with a mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frequency
Frequency is the number of occurrences of a repeating event per unit of time. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio signals (sound), radio waves, and light. The interval of time between events is called the period. It is the reciprocal of the frequency. For example, if a heart beats at a frequency of 120 times per minute (2 hertz), its period is one half of a second. Special definitions of frequency are used in certain contexts, such as the angular frequency in rotational or cyclical properties, when the rate of angular progress is measured. Spatial frequency is defined for properties that vary or cccur repeatedly in geometry or space. The unit of measurement of frequency in the International System of Units (SI) is the hertz, having the symbol Hz. Definitions and units For cyclical phenomena such as oscillations, waves, or for examp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pauli Exclusion Principle
In quantum mechanics, the Pauli exclusion principle (German: Pauli-Ausschlussprinzip) states that two or more identical particles with half-integer spins (i.e. fermions) cannot simultaneously occupy the same quantum state within a system that obeys the laws of quantum mechanics. This principle was formulated by Austrian physicist Wolfgang Pauli in 1925 for electrons, and later extended to all fermions with his spin–statistics theorem of 1940. In the case of electrons in atoms, the exclusion principle can be stated as follows: in a poly-electron atom it is impossible for any two electrons to have the same two values of ''all'' four of their quantum numbers, which are: ''n'', the principal quantum number; ', the azimuthal quantum number; ''m'', the magnetic quantum number; and ''ms'', the spin quantum number. For example, if two electrons reside in the same orbital, then their values of ''n'', ', and ''m'' are equal. In that case, the two values of ''m''s (spin) pair must be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Condensed Matter Physics
Condensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter, especially the solid and liquid State of matter, phases, that arise from electromagnetic forces between atoms and electrons. More generally, the subject deals with condensed phases of matter: systems of many constituents with strong interactions among them. More exotic condensed phases include the superconductivity, superconducting phase exhibited by certain materials at extremely low cryogenic temperatures, the ferromagnetic and antiferromagnetic phases of Spin (physics), spins on crystal lattices of atoms, the Bose–Einstein condensates found in ultracold atomic systems, and liquid crystals. Condensed matter physicists seek to understand the behavior of these phases by experiments to measure various material properties, and by applying the physical laws of quantum mechanics, electromagnetism, statistical mechanics, and other theoretical physics, physic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fermi Surface
In condensed matter physics, the Fermi surface is the surface in reciprocal space which separates occupied electron states from unoccupied electron states at zero temperature. The shape of the Fermi surface is derived from the periodicity and symmetry of the crystalline lattice and from the occupation of electronic band structure, electronic energy bands. The existence of a Fermi surface is a direct consequence of the Pauli exclusion principle, which allows a maximum of one electron per quantum state. The study of the Fermi surfaces of materials is called fermiology. Theory Consider a Spin (physics), spin-less ideal Fermi gas of N particles. According to Fermi–Dirac statistics, the mean occupation number of a state with energy \epsilon_i is given by : \langle n_i\rangle =\frac, where * \left\langle n_i\right\rangle is the mean occupation number of the ith state * \epsilon_i is the kinetic energy of the ith state * \mu is the chemical potential (at zero temperature, this is th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
