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.

SYMMETRY BREAKING PHENOMENA IN MESOSCOPIC SYSTEMS: QUANTUM DOTS AND ROTATING NUCLEI

2009 ◽  
Vol 18 (04) ◽  
pp. 1014-1021
Author(s):  
R. G. NAZMITDINOV ◽  
A. PUENTE
Keyword(s):  
Quantum Dots ◽  
Symmetry Breaking ◽  
Rotational Symmetry ◽  
Random Phase ◽  
Mean Field ◽  
Rotating Frame ◽  
Octupole Deformation ◽  
The Mean ◽  
Symmetry Breaking Phenomena ◽  
Rotating Nuclei

A brief description of excited and ground states in two-dimensional quantum dots and rotating nuclei is presented within a mean field approach and a random-phase approximation (RPA). We discuss the procedure to restore the rotational symmetry broken at the mean field, which can be extended for other symmetry breaking cases. We propose to consider a disappearance of collective excitations in the rotating frame as a manifestation of symmetry breaking phenomena of the rotating mean field. In particular, we demonstrate that the disappearance of a collective octupole mode in the rotating frame in 162 Yb gives rise to the nonaxial octupole deformation.

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.

BULK PROPERTIES OF CHERN–SIMONS SUPERCONDUCTIVITY AT FINITE TEMPERATURES

1994 ◽  
Vol 08 (22) ◽  
pp. 3095-3135 ◽  
Author(s):  
S. S. MANDAL ◽  
S. RAMASWAMY ◽  
V. RAVISHANKAR
Keyword(s):  
Mean Field Theory ◽  
Free Field ◽  
Mean Field ◽  
Form Factors ◽  
Spin Correlation ◽  
Thermal Fluctuations ◽  
Correlation Factor ◽  
Electromagnetic Response ◽  
The Mean ◽  
Chern Simons

We study Chern–Simons (CS) superconductivity at finite temperatures for a system of two dimensional 'spin-1/2' fermions which are minimally coupled to both the CS and Maxwell gauge fields. We evaluate the electromagnetic response of the system as well as its thermodynamic properties within the mean field formalism. Our results for magnetic susceptibility, conductivity and dielectric constant show a sharp transition to the normal state over a narrow range of temperatures. The vanishing of the off-diagonal conductivity due to a corresponding fall in parity and time reversal [Formula: see text] violating correlation factor may be interpreted to be an effective restoration of [Formula: see text] symmetries in the macroscopic state. We find that the spin correlation function has a negligibly small numerical value at all temperatures, which implies that the thermal fluctuations dominate over the quantum fluctuations in the spin state. To explore the validity of mean field theory at high temperatures (HT), we compare the responses as well as the form factors for both mean field and free field (perturbative) formalism and find that they are essentially equivalent at HT. Finally, we present a coarse criterion for the validity of the mean field ansatz by regulating the CS Lagrangian with a Maxwell term.

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.

scholarly journals Short-ranged interaction effects on Z2 topological phase transitions: The perturbative mean-field method

2015 ◽  
Vol 29 (06) ◽  
pp. 1530005 ◽  
Author(s):  
Hsin-Hua Lai ◽  
Hsiang-Hsuan Hung
Keyword(s):  
Phase Transitions ◽  
Analytical Approach ◽  
Mean Field ◽  
Field Approximation ◽  
Quantum Spin ◽  
Mean Field Approximation ◽  
Topological Phase ◽  
Self Consistent ◽  
The Mean ◽  
Topological Phase Transitions

Time-reversal symmetric topological insulator (TI) is a novel state of matter that a bulk-insulating state carries dissipationless spin transport along the surfaces, embedded by the Z2 topological invariant. In the noninteracting limit, this exotic state has been intensively studied and explored with realistic systems, such as HgTe/(Hg, Cd)Te quantum wells. On the other hand, electronic correlation plays a significant role in many solid-state systems, which further influences topological properties and triggers topological phase transitions. Yet an interacting TI is still an elusive subject and most related analyses rely on the mean-field approximation and numerical simulations. Among the approaches, the mean-field approximation fails to predict the topological phase transition, in particular at intermediate interaction strength without spontaneously breaking symmetry. In this paper, we develop an analytical approach based on a combined perturbative and self-consistent mean-field treatment of interactions that is capable of capturing topological phase transitions beyond either method when used independently. As an illustration of the method, we study the effects of short-ranged interactions on the Z2 TI phase, also known as the quantum spin Hall (QSH) phase, in three generalized versions of the Kane–Mele (KM) model at half-filling on the honeycomb lattice. The results are in excellent agreement with quantum Monte Carlo (QMC) calculations on the same model and cannot be reproduced by either a perturbative treatment or a self-consistent mean-field treatment of the interactions. Our analytical approach helps to clarify how the symmetries of the one-body terms of the Hamiltonian determine whether interactions tend to stabilize or destabilize a topological phase. Moreover, our method should be applicable to a wide class of models where topological transitions due to interactions are in principle possible, but are not correctly predicted by either perturbative or self-consistent treatments.

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