SEMICLASSICAL SHELL STRUCTURE OF MOMENTS OF INERTIA IN DEFORMED FERMI SYSTEMS

2010 ◽  
Vol 19 (04) ◽  
pp. 735-746 ◽  
Author(s):  
A. G. MAGNER ◽  
A. M. GZHEBINSKY ◽  
A. S. SITDIKOV ◽  
A. A. KHAMZIN ◽  
J. BARTEL
Keyword(s):  
Free Energy ◽  
Shell Structure ◽  
Mean Field ◽  
Field Approximation ◽  
Moment Of Inertia ◽  
Mean Field Approximation ◽  
Perfect Agreement ◽  
Periodic Orbit Theory ◽  
Shell Effects ◽  
The Moment

The collective moment of inertia is derived analytically within the cranking model in the adiabatic mean-field approximation at finite temperature. Using the nonperturbative periodic-orbit theory the semiclassical shell-structure components of the collective moment of inertia are obtained for any potential well. Their relation to the free-energy shell corrections are found semiclassically as being given through the shell-structure components of the rigid-body moment of inertia of the statistically equilibrium rotation in terms of short periodic orbits. Shell effects in the moment of inertia disappear exponentially with increasing temperature. For the case of the harmonic-oscillator potential one observes a perfect agreement between semiclassical and quantum shell-structure components of the free energy and the moment of inertia for several critical bifurcation deformations and several temperatures.

scholarly journals The Possibility of Many Compensation Points in a Mixed-Spin Ising Ferrimagnetic System

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Hadey K. Mohamad
Keyword(s):  
Free Energy ◽  
Mean Field ◽  
Field Approximation ◽  
Spin Model ◽  
Mean Field Approximation ◽  
Zero Field ◽  
Mixed Spin ◽  
Simple Cubic ◽  
Simple Cubic Lattice ◽  
The Mean

The magnetic properties of a ferrimagnetic mixed spin-3/2 and spin-5/2 Ising model with different anisotropies are investigated by using the mean-field approximation (MFA). In particular, the effect of magnetic anisotropies on the compensation phenomenon, acting on A-atoms and B-ones for the mixed-spin model, has been considered in a zero field. The free energy of a mixed-spin Ising ferrimagnetic system from MFA of the Hamiltonian is calculated. By minimizing the free energy, we obtain the equilibrium magnetizations and the compensation points. The phase diagram of the system in the anisotropy dependence of transition temperature has been discussed as well. Our results of this model predict the existence of many (two or three) compensation points in the ordered system on a simple cubic lattice.

scholarly journals MEAN FIELD APPROACH TO THE GIANT WORMHOLE PROBLEM

1994 ◽  
Vol 03 (02) ◽  
pp. 421-430
Author(s):  
A. GAMBA ◽  
I. KOLOKOLOV ◽  
M. MARTELLINI
Keyword(s):  
Free Energy ◽  
Probability Density ◽  
Time Distribution ◽  
Mean Field ◽  
Field Approximation ◽  
Space Time ◽  
Mean Field Approximation ◽  
Field Approach

We introduce a gaussian probability density for the space-time distribution of worm-holes, thus taking effectively into account wormhole interaction. Using a mean-field approximation for the free energy, we show that giant wormholes are probabilistically suppressed in a homogenous isotropic “large” universe.

Active Inference, Belief Propagation, and the Bethe Approximation

2018 ◽  
Vol 30 (9) ◽  
pp. 2530-2567 ◽  
Author(s):  
Sarah Schwöbel ◽  
Stefan Kiebel ◽  
Dimitrije Marković
Keyword(s):  
Free Energy ◽  
Belief Propagation ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Active Inference ◽  
Inference Process ◽  
Bethe Approximation ◽  
Variational Free Energy ◽  
The Mean

When modeling goal-directed behavior in the presence of various sources of uncertainty, planning can be described as an inference process. A solution to the problem of planning as inference was previously proposed in the active inference framework in the form of an approximate inference scheme based on variational free energy. However, this approximate scheme was based on the mean-field approximation, which assumes statistical independence of hidden variables and is known to show overconfidence and may converge to local minima of the free energy. To better capture the spatiotemporal properties of an environment, we reformulated the approximate inference process using the so-called Bethe approximation. Importantly, the Bethe approximation allows for representation of pairwise statistical dependencies. Under these assumptions, the minimizer of the variational free energy corresponds to the belief propagation algorithm, commonly used in machine learning. To illustrate the differences between the mean-field approximation and the Bethe approximation, we have simulated agent behavior in a simple goal-reaching task with different types of uncertainties. Overall, the Bethe agent achieves higher success rates in reaching goal states. We relate the better performance of the Bethe agent to more accurate predictions about the consequences of its own actions. Consequently, active inference based on the Bethe approximation extends the application range of active inference to more complex behavioral tasks.

Simulation of Segregation to Interfaces in Metal-Oxides

1994 ◽  
Vol 357 ◽  
Author(s):  
C. Battaile ◽  
R. Najafabadi ◽  
D.J. Srolovitz
Keyword(s):  
Free Energy ◽  
Mean Field ◽  
Misfit Strain ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Free Energy Surface ◽  
Field Representation ◽  
Free Surfaces ◽  
Equilibrium Distributions ◽  
The Mean

AbstractSegregation of isovalent cation impurities to (001) and (011) free surfaces in (Co0.3Ni0.7)O and (Fe0.12Mn0.88)O was investigated using atomistic computer simulations. Impurity concentrations were represented by a mean-field approximation, and equilibrium distributions of impurities were calculated by minimization of the free energy. Surface energy effects were found to dominate segregation behavior, even when in competition with misfit strain energy effects. These Free Energy method predictions compared well with more accurate Monte Carlo simulations, suggesting that the mean-field representation of impurity concentration is satisfactory for this application.

scholarly journals Semiclassical and quantum shell-structure calculations of the moment of inertia

2021 ◽  
pp. 2150008
Author(s):  
D. V. Gorpinchenko ◽  
A. G. Magner ◽  
J. Bartel
Keyword(s):  
Shell Structure ◽  
Adiabatic Approximation ◽  
Fundamental Property ◽  
Moment Of Inertia ◽  
Approximation Formula ◽  
Small Surface ◽  
Periodic Orbit Theory ◽  
Angular Momenta ◽  
Spheroidal Cavity ◽  
The Moment

Shell corrections to the moment of inertia (MI) are calculated for a Woods–Saxon potential of spheroidal shape and at different deformations. This model potential is chosen to have a large depth and a small surface diffuseness which makes it resemble the analytically solved spheroidal cavity in the semiclassical approximation. For the consistent statistical-equilibrium collective rotations under consideration here, the MI is obtained within the cranking model in an approach which goes beyond the quantum perturbation approximation based on the nonperturbative energy spectrum, and is therefore applicable to much higher angular momenta. For the calculation of the MI shell corrections [Formula: see text], the Strutinsky smoothing procedure is used to obtain the average occupation numbers of the particle density generated by the resolution of the Woods–Saxon eigenvalue problem. One finds that the major-shell structure of [Formula: see text], as determined in the adiabatic approximation, is rooted, for large as well as for small surface deformations, in the same inhomogenuity of the distribution of single-particle states near the Fermi surface as the energy shell corrections [Formula: see text]. This fundamental property is in agreement with the semiclassical results [Formula: see text] obtained analytically within the non perturbative periodic orbit theory for any potential well, in particular for the spheroidal cavity, and for any deformation, even for large deformations where bifurcations of the equatorial orbits play a substantial role. Since the adiabatic approximation, [Formula: see text], with [Formula: see text] the distance between major nuclear shells, is easily obeyed even for large angular momenta typical for high-spin physics at large particle numbers, our model approach seems to represent a tool that could, indeed, be very useful for the description of such nuclear systems.

New Method for Latticeal Mean Field Models

1997 ◽  
Vol 11 (08) ◽  
pp. 339-345 ◽  
Author(s):  
Raluca S. Bundaru
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Free Energy ◽  
Mean Field ◽  
Field Approximation ◽  
New Method ◽  
Mean Field Approximation ◽  
Mean Field Models ◽  
The Mean

We develop a new method to find the free-energy for latticealsystems of classical spins in the mean-field approximation. The simplerecurrence relation which the Hamiltonian satisfies in this case, allows us to obtain the free-energy by solving an ordinary differential equation.

scholarly journals On the free energy within the mean-field approximation

2006 ◽  
Vol 27 (2) ◽  
pp. 407-412 ◽  
Author(s):  
Rafael Agra ◽  
Frédéric van Wijland ◽  
Emmanuel Trizac
Keyword(s):  
Free Energy ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
The Mean
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