Many-particle theory
In statistical mechanics and theoretical solid state physics which is many-body theory (English many-body theory ) the quantum mechanical description of a very large number of interacting with each other microparticles ( bosons , fermions ) and their collective behavior.
Such a system differs significantly in its physical properties from an isolated (free) particle. The fundamental problem is not the number of particles involved, but the consideration of their interaction and dependencies.
In contrast to the multibody problem of classical mechanics , many-particle theory also takes into account quantum effects such as the indistinguishability of quantum particles and particle characterization via spin and uses methods of quantum field theory such as field quantization . Their transfer to problems of solid state physics in the 1950s ( David Pines , Philippe Nozières , Alexei Alexejewitsch Abrikossow , Lew Landau , Arkadi Migdal , David Bohm , Murray Gell-Mann , Julian Schwinger , Joaquin Mazdak Luttinger and others) led to the emergence of the many-particle theory.
The quantum mechanical description of the many-particle problem is made more difficult by the mathematical form of the sought-after many-body wave function or the many-particle field operator, which depends in some way on all particle positions and all spin states (i.e. contains any number of arbitrarily complex mixed terms). By decomposing into single-particle states, which are each characterized by a position or spin, but taking into account the indistinguishability of the particles by the Slater determinant , the construction of an antisymmetric multi-particle state, albeit a posteriori, from several single-particle states respectively. The single-particle states move as independent particles in an averaged potential, whereby the theory is also referred to as mean field theory . The Hartree-Fock method as a representative of this theory pursues precisely this approach, which leads to the occurrence of the exchange interaction , which cannot be classically explained . Higher-order many-body correction terms - quantum correlation - cannot be provided by the method. This is exactly where the methods of many-particle theory come into play. A possible physical description is done here by:
- elementary excitations or quasiparticles ,
- canonical transformations as in the reduction of the Kepler problem to an effective one-body problem,
- With the help of quantum statistics , the self-energy functional theory ,
- Methods of quantum field theory such as the so-called second quantization , the Green functions and the perturbative description with the help of Feynman diagrams .
Since with it not only solids (metals, semiconductors , dielectrics , magnetism and others), but also liquids, superfluids , superconductivity , plasmas and the like. a. are treated, i.e. matter in all possible phases , this development also stands for the transition from theoretical solid-state physics to the physics of condensed matter .
Many-body phenomena
Quantum liquids instead of ideal quantum gases
Superconductivity and superfluidity
literature
- Eberhard KU Gross , Erich Runge: Many-particle theory. 2nd Edition. Teubner, Stuttgart, ISBN 978-3-519-03086-7 .
- Alexander L. Fetter, John Dirk Walecka : Quantum theory of many particle systems. New York, McGraw Hill 1971, ISBN 0-07-020653-8 .
- Wolfgang Nolting: Basic Course Theoretical Physics 7th 6th edition. Springer, Berlin / Heidelberg ISBN 3-540-24117-5.
- David J. Thouless : The quantum mechanics of many-body systems. 2nd Edition. Academic Press, New York 1961, 1972, ISBN 0-12-691560-1 . German: quantum mechanics of many-body systems. BI university paperback, 1964.