A self-consistent solution of the coupled Dirac-Einstein equations in the mean-field Hartree approximation

1978 ◽  
Vol 22 (10) ◽  
pp. 391-396
Author(s):  
M. Soffel ◽  
U. Heinz ◽  
B. Müller ◽  
W. Greiner
Keyword(s):  
Mean Field ◽  
Einstein Equations ◽  
Hartree Approximation ◽  
Self Consistent ◽  
Consistent Solution ◽  
The Mean

scholarly journals Coherent oscillations in balanced neural networks driven by endogenous fluctuations

2021 ◽  
Author(s):  
Matteo Di Volo ◽  
Marco Segneri ◽  
Denis Goldobin ◽  
Antonio Politi ◽  
Alessandro Torcini
Keyword(s):  
Mean Field ◽  
Planck Equation ◽  
Structural Heterogeneity ◽  
Mean Field Model ◽  
Self Consistent ◽  
Consistent Solution ◽  
The Mean ◽  
Collective Oscillations ◽  
Low Dimensional ◽  
Parameter Values

We present a detailed analysis of the dynamical regimes observed in a balanced network of identical Quadratic Integrate-and-Fire (QIF) neurons with a sparse connectivity for homogeneous and heterogeneous in-degree distribution. Depending on the parameter values, either an asynchronous regime or periodic oscillations spontaneously emerge. Numerical simulations are compared with a mean field model based on a self-consistent Fokker-Planck equation (FPE). The FPE reproduces quite well the asynchronous dynamics in the homogeneous case by either assuming a Poissonian or renewal distribution for the incoming spike trains. An exact self consistent solution for the mean firing rate obtained in the limit of infinite in-degree allows identifying balanced regimes that can be either mean- or fluctuation-driven. A low-dimensional reduction of the FPE in terms of circular cumulants is also considered. Two cumulants suffice to reproduce the transition scenario observed in the network. The emergence of periodic collective oscillations is well captured both in the homogeneous and heterogeneous setups by the mean field models upon tuning either the connectivity, or the input DC current. In the heterogeneous situation we analyze also the role of structural heterogeneity.

CURRENTS, SPIN DENSITIES AND MEAN-FIELD FORM FACTORS IN ROTATING NUCLEI: A SEMI-CLASSICAL APPROACH

2004 ◽  
Vol 13 (01) ◽  
pp. 225-233 ◽  
Author(s):  
J. BARTEL ◽  
K. BENCHEIKH ◽  
P. QUENTIN
Keyword(s):  
Mean Field ◽  
Form Factors ◽  
Spin Vector ◽  
Self Consistent ◽  
Field Form ◽  
Local Densities ◽  
The Mean ◽  
Self Consistency ◽  
Spin Densities ◽  
Rotating Nuclei

We present self-consistent semi-classical local densities characterising the structure of rotating nuclei. A particular emphasis is put on those densities which are generated by the breaking of time-reversal symmetry through the cranking piece of the Routhian, namely the current density and the spin vector density. Our approach which is based on the Extended-Thomas-Fermi method goes beyond the Inglis cranking approach and contains naturally the Thouless-Valatin self-consistency terms expressing the response of the mean field to the time-odd part of the density matrix.

NEUTRON–PROTON PAIRING CORRELATION FOR THE ROTATIONAL MOTION OF N = Z72Kr, 76Sr, AND 80Zr NUCLEI

2011 ◽  
Vol 20 (08) ◽  
pp. 1687-1699
Author(s):  
PRIANKA ROY ◽  
SHASHI K. DHIMAN
Keyword(s):  
Effective Interaction ◽  
Mean Field ◽  
High Spin State ◽  
Pairing Correlation ◽  
Effective Interactions ◽  
Hartree Fock ◽  
Self Consistent ◽  
The Mean ◽  
Proton Pairing ◽  
Band Crossing

The high-spin state properties of the neutron–proton (np) residual effective interaction are analyzed in N = Z72 Kr , 76 Sr , and 80 Zr nuclei. The self-consistent microscopic Hartree–Fock–Bogoliubov (HFB) equations have been solved by employing monopole corrected two-body effective interaction. A band crossing is observed in 72 Kr nucleus at J = 14ℏ state with monopole corrected "HPU1" and "HPU2" effective interactions. The VAP–HFB theory suggests that the "4p–4h" excitations by np residual interaction are the essential ingredients of the mean-field description of the occurence of backbending in 72 Kr nucleus.

QUANTUM CORRECTIONS TO THE CRANKING MODEL

1992 ◽  
Vol 01 (01) ◽  
pp. 95-130 ◽  
Author(s):  
ABRAHAM KLEIN ◽  
NIELS R. WALET ◽  
G. DO DANG
Keyword(s):  
Degrees Of Freedom ◽  
Quantum Correction ◽  
Mean Field ◽  
Original System ◽  
Quantum Corrections ◽  
Transition Rates ◽  
Rotation Symmetry ◽  
Exchange Effects ◽  
Self Consistent ◽  
The Mean

A method is described for the restoration of translation or rotation symmetry to a system of fermions, starting from a self-consistent cranking solution and valid when either momentum or angular momentum is large enough so that semi-classical approximations are valid. The quantum fluctuations that restore the broken symmetry are described in terms of the particle-hole degrees of freedom of the original system rather than by mapping these variables onto a boson space, as in most previous work. Only the leading quantum correction to the mean field solution is worked out in detail. New results include the treatment of direct and exchange effects on an equal footing and a method for computing transition rates.

scholarly journals PAIRING CORRELATIONS BEYOND THE MEAN FIELD

2007 ◽  
Vol 16 (02) ◽  
pp. 222-236 ◽  
Author(s):  
M. BENDER ◽  
T. DUGUET
Keyword(s):  
Density Functional Theory ◽  
Density Functional ◽  
Mean Field ◽  
Energy Functional ◽  
Functional Theory ◽  
Self Consistent ◽  
Configuration Mixing ◽  
Pairing Correlations ◽  
The Mean

We discuss dynamical pairing correlations in the context of configuration mixing of projected self-consistent mean-field states, and the origin of a divergence that might appear when such calculations are done using an energy functional in the spirit of a naive generalized density functional theory.

scholarly journals On the multiscale analysis of a two phase material: crystal plasticity versus mean field

2021 ◽  
Author(s):  
Shahrzad Mirhosseini ◽  
Semih Perdahcioglu ◽  
Eisso Atzema ◽  
Ton van den Boogaard
Keyword(s):  
Crystal Plasticity ◽  
Mean Field ◽  
Multiscale Methods ◽  
Material Behavior ◽  
Strain Partitioning ◽  
Two Phase ◽  
Self Consistent ◽  
Grain Orientations ◽  
The Mean ◽  
Two Phases

In this paper, a comparison is made between two multiscale methods, namely crystal plasticity finite element and mean field on a material composed of two phases. Both methods are used to homogenize a given microstructure. In order to obtain macroscopic behavior, in the mean field approach, a Self-Consistent scheme is used to evaluate stress and strain partitioning among the phases. In this method, an average of the fields is estimated and local distributions cannot be captured. In parallel, crystal plasticity simulations on Representative Volume Elements (RVEs) composed of hexagonal grains are performed. In these simulations, grain orientations are attributed randomly respecting Mackenzie's distribution function in order to achieve isotropic behavior and macroscopic hardening is extracted from the simulations. The results on macroscopic hardening of both methods are compared to distinguish the extents of validity of mean field homogenization. In addition to Self- Consistent, other mean field schemes such as Voigt, Reuss and Bound-Interpolation are compared in terms of efficiency and accuracy. The comparison manifests that Self-Consistent scheme is capable of predicting material behavior well.

scholarly journals THE EFFECT OF SPATIAL CURVATURE ON CLASSICAL AND QUANTUM STRINGS

1996 ◽  
Vol 11 (21) ◽  
pp. 4005-4030 ◽  
Author(s):  
A.L. LARSEN ◽  
N. SÁNCHEZ
Keyword(s):  
Center Of Mass ◽  
Elliptic Functions ◽  
Space Time ◽  
Einstein Equations ◽  
Back Reaction ◽  
Level Spacing ◽  
Spatial Curvature ◽  
Curvature Index ◽  
Self Consistent ◽  
Consistent Solution

We study the effects of spatial curvature on classical and quantum string dynamics. We find the general solution of the circular string motion in static Robertson–Walker space-times with closed or open sections. This is given closely and completely in terms of elliptic functions. The physical properties, string length, energy and pressure are computed and analyzed. We find the back-reaction effect of these strings on the space-time: the self-consistent solution to the Einstein equations is a spatially closed (K>0) space-time with a selected value of the curvature index K (the scale factor is normalized to unity). No self-consistent solutions with K≤0 exist. We semiclassically quantize the circular strings and find the mass m in each case. For K>0, the very massive strings, oscillating on the full hypersphere, have m2~Kn2(n∈N0)independent of α' and the level spacing grows with n, while the strings oscillating on one hemisphere (without crossing the equator) have m2α′~n and a finite number of states N~1/Kα′. For K<0, there are infinitely many string states with masses m log m ~ n, i.e. the level spacing grows slower than n. The stationary string solutions as well as the generic string fluctuations around the center of mass are also found and analyzed in closed form.

scholarly journals TO WHAT EXTENT DOES THE SELF-CONSISTENT MEAN-FIELD EXIST?

2006 ◽  
Vol 15 (05) ◽  
pp. 1141-1148 ◽  
Author(s):  
LU GUO ◽  
FUMIHIKO SAKATA ◽  
EN-GUANG ZHAO ◽  
J. A. MARUHN
Keyword(s):  
Mean Field Theory ◽  
Mean Field ◽  
Energy Difference ◽  
The Self ◽  
Fermion System ◽  
Avoided Crossing ◽  
Self Consistent ◽  
The Mean ◽  
The Many ◽  
First Time

A non-convergent difficulty near level-repulsive region is discussed within the self-consistent mean-field theory. It is shown by numerical and analytic studies that the mean-field is not realized in the many-fermion system when quantum fluctuations coming from two-body residual interaction and quadrupole deformation are larger than an energy difference between two avoided crossing orbits. An analytic condition indicating a limitation of the mean-field concept is derived for the first time.

Sign in / Sign up

Export Citation Format

Share Document