Holographic mean-field theory for baryon many-body systems

Two widely used concepts in physics and the life sciences are combined: mean field theory and time-discrete time series modeling. They are merged within the framework of strongly nonlinear stochastic processes, which are processes whose stochastic evolution equations depend self-consistently on process expectation values. Explicitly, a generalized autoregressive (AR) model is presented for an AR process that depends on its process mean value. Criteria for stationarity are derived. The transient dynamics in terms of the relaxation of the first moment and the stationary response to fluctuations in terms of the autocorrelation function are discussed. It is shown that due to the stochastic feedback via the process mean, transient and stationary responses may exhibit qualitatively different temporal patterns. That is, the model offers a time-discrete description of many-body systems that in certain parameter domains feature qualitatively different transient and stationary response dynamics.

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A simple many-body Hamiltonian for polymer–colloid mixtures: simulations and mean-field theory

Soft Matter ◽

10.1039/c2sm06737d ◽

2012 ◽

Vol 8 (7) ◽

pp. 2121 ◽

Cited By ~ 9

Author(s):

Jan Forsman ◽

Clifford E. Woodward

Keyword(s):

Field Theory ◽

Mean Field Theory ◽

Mean Field ◽

Many Body ◽

Polymer Colloid

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Many Body Perturbation Theory, Dynamical Mean Field Theory and All That

Handbook of Solid State Chemistry ◽

10.1002/9783527691036.hsscvol5008 ◽

2017 ◽

pp. 119-157

Author(s):

Silke Biermann ◽

Alexander Lichtenstein

Keyword(s):

Field Theory ◽

Perturbation Theory ◽

Mean Field Theory ◽

Mean Field ◽

Dynamical Mean Field Theory ◽

Many Body ◽

Many Body Perturbation Theory

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Calculation of the propagation amplitude in the case of a Coulomb interaction via time-independent mean-field theory

Canadian Journal of Physics ◽

10.1139/p07-036 ◽

2007 ◽

Vol 85 (7) ◽

pp. 787-796

Author(s):

R Yekken ◽

F Mekideche

Keyword(s):

Coulomb Interaction ◽

Mean Field Theory ◽

Mean Field ◽

Numerical Comparison ◽

Many Body ◽

Field Equations ◽

Range Interaction ◽

Approximate Methods ◽

Mean Field Equations ◽

Many Body Systems

The exact study of many-body microscopic systems is impossible when the number of particles is large (N ≥ 3). Approximate methods are then used. The time-independent mean-field (TIMF) approximation has been proposed for the description of collisions in many-body systems. Collision amplitudes are derived by the use of a variational principle and the choice of trial functions as products of single-particle orbitals. Resulting mean-field equations with a nonvanishing right-hand side turn out to be a generalization of the traditional Hartree or Hatree–Fock type equations. These TIMF equations are successfully solved numerically for the case of short-range forces. In this paper, we test the validity of this theory for the Coulomb interaction between two particles, that is, a long-range interaction. A numerical comparison between the exact and the mean-field solutions is conducted PACS Nos.: 31.15.Ne, 31.15.Pf, 21.45.+v,25.10.-i

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