scholarly journals The Variational Reduction for Low-Dimensional Fermi Gases and Bose–Fermi Mixtures: A Brief Review

2019 ◽  
Vol 4 (1) ◽  
pp. 22
Author(s):  
Pablo Díaz ◽  
David Laroze ◽  
Boris Malomed
Keyword(s):  
Equations Of Motion ◽  
Mean Field ◽  
Three Dimensional ◽  
Field Approximation ◽  
Matter Wave ◽  
Mean Field Approximation ◽  
Degenerate Gases ◽  
Dynamical Regimes ◽  
Low Dimensional ◽  
Good Agreement

We present a summary of some recent theoretical results for matter-wave patterns in Fermi and Bose–Fermi degenerate gases, obtained in the framework of the quasi-mean-field approximation. We perform a dimensional reduction from the three-dimensional (3D) equations of motion to 2D and 1D effective equations. In both cases, comparison of the low-dimensional reductions to the full model is performed, showing very good agreement for ground-state solutions. Some complex dynamical regimes are reported too for the corresponding 1D systems.

Pressure and Temperature Effects in Homopolymer Blends and Diblock Copolymers

1997 ◽  
Vol 30 (5) ◽  
pp. 696-701 ◽  
Author(s):  
H. Frielinghaus ◽  
D. Schwahn ◽  
K. Mortensen ◽  
L. Willner ◽  
K. Almdal
Keyword(s):  
Interaction Parameter ◽  
Diblock Copolymers ◽  
Mean Field ◽  
Three Dimensional ◽  
Thermal Fluctuation ◽  
Thermal Fluctuations ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Phase Boundaries ◽  
Composition Fluctuations

Thermal composition fluctuations in a homogeneous binary polymer blend and in a diblock copolymer were measured by small-angle neutron scattering as a function of temperature and pressure. The experimental data were analyzed with theoretical expressions, including the important effect of thermal fluctuations. Phase boundaries, the Flory–Huggins interaction parameter and the Ginzburg number were obtained. The packing of the molecules changes with pressure. Therefore, the degree of thermal fluctuation as a function of packing and temperature was studied. While in polymer blends packing leads, in some respects, to a universal behaviour, such behaviour is not found in diblock copolymers. It is shown that the Ginzburg number decreases with pressure sensitively in blends, while it is constant in diblock copolymers. The Ginzburg number is an estimation of the transition between the universality classes of the `mean-field' approximation and the three-dimensional Ising model. The phase boundaries in blends increase with pressure, while the phase boundary of the studied block copolymer shows an unusual shape: with increasing pressure it first decreases and then increases. Its origin is an increase of the entropic and of the enthalpic parts, respectively, of the Flory–Huggins interaction parameter.

Interchain Interaction in Quasi-One-Dimension Organic Polymer Ferromagnets

1997 ◽  
Vol 11 (19) ◽  
pp. 821-827
Author(s):  
Hong-Tao Li
Keyword(s):  
Energy Gap ◽  
Mean Field ◽  
Three Dimensional ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Organic Polymer ◽  
Interchain Interaction ◽  
Energy Bands ◽  
Interchain Coupling ◽  
Organic Ferromagnets

A theoretical model is developed to describe quasi-one-dimensional organic ferromagnets after considering the interchain interaction as an interchain electron-transfer. By employing the mean-field approximation, four energy bands which exhibit three-dimensional anisotropic aspect are obtained. When the interchain coupling increases, the energy gap decreases. In the case of small dimerization order parameter, due to the interchain coupling, the band gap may disappear and the conjugated π-electrons in the main chain show ferromagnetic order in the ground state.

scholarly journals Long-time Dynamics of Spontaneous Parametric Down-conversion and Quantum Limitations of Conversion Efficiency

1999 ◽  
Vol 54 (1) ◽  
pp. 57-62 ◽  
Author(s):  
Michael Fleischhauer ◽  
Oliver Veits
Keyword(s):  
Quantum Dynamics ◽  
Equations Of Motion ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Time Dynamics ◽  
Pendulum Equation ◽  
Parametric Down Conversion ◽  
Long Time ◽  
Down Conversion

Abstract We analyze the long-time quantum dynamics of degenerate parametric down-conversion from an initial sub-harmonic vacuum (spontaenous down-conversion). Standard linearization of the Heisenberg equations of motion fails in this case, since it is based on an expansion around an unstable classical solution and neglects pump depletion. Introducing a mean-field approximation we find a periodic exchange of energy between the pump and subharmonic mode goverened by an anharmonic pendulum equation. From this equation the optimum interaction time or crystal length for maximum conversion can be determined. A numerical integration of the 2-mode Schrödinger equation using a dynamically optimized basis of displaced and squeezed number states verifies the characteristic times predicted by the mean-field approximation. In contrast to semiclassical and mean-field predictions it is found that quantum fluctuations of the pump mode lead to a substantial limitation of the efficiency of parametric down-conversion.

MEAN-FIELD THEORY FOR LAYERED HIGH-TEMPERATURE SUPERCONDUCTORS

1988 ◽  
Vol 02 (05) ◽  
pp. 1059-1065 ◽  
Author(s):  
D. Baeriswyl ◽  
T. Schneider
Keyword(s):  
High Temperature Superconductors ◽  
Mean Field Theory ◽  
Mean Field ◽  
Three Dimensional ◽  
Interlayer Coupling ◽  
Interlayer Spacing ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Pairing Mechanism ◽  
The Mean

Using the mean-field approximation we study a model for quasi-two-dimensional layered superconductors. The interlayer coupling, assumed to be mediated by a small electron hopping term, is found to leave Tc practically unaffected. Consequently, a three-dimensional pairing mechanism is required to explain the observed dependence of Tc on the average interlayer spacing in the Bi and Tl compounds.

Magneto—Optical Properties of Amorphous TbFe Alloys

1985 ◽  
Vol 58 ◽  
Author(s):  
M. Mansuripur ◽  
M. Ruane ◽  
P. Wolniansky ◽  
S. Chase ◽  
R. Rosenvold
Keyword(s):  
Mean Field ◽  
Hysteresis Loops ◽  
Perpendicular Magnetic Anisotropy ◽  
Field Approximation ◽  
Anisotropy Energy ◽  
Optical Methods ◽  
Mean Field Approximation ◽  
Kerr Rotation ◽  
The Mean ◽  
Good Agreement

ABSTRACTHysteresis loops and anisotropy energy constants are measured in a magneto—optical system that combines Kerr rotation and ellipticity to enhance signal strength. Temperature dependence of the polar Kerr effect is compared with the magnetization of the iron subnetwork in the mean—field approximation and good agreement is obtained. Perpendicular magnetic anisotropy is studied by magneto—optical methods, yielding the first two coefficients of the series expansion of anisotropy energy in terms of the angleof deviation from the easy axis.

NUCLEON PROPERTIES FROM MODIFIED SIGMA MODEL

2007 ◽  
Vol 22 (14n15) ◽  
pp. 2673-2681 ◽  
Author(s):  
M. RASHDAN ◽  
M. ABU-SHADY ◽  
T. S. T. ALI
Keyword(s):  
Sigma Model ◽  
Mean Field ◽  
Field Approximation ◽  
Higher Order ◽  
Original Model ◽  
Mean Field Approximation ◽  
Field Equations ◽  
The Mean ◽  
Better Than ◽  
Good Agreement

Birse and Banerjee model is extended to include higher-order mesonic interactions. The field equations have been solved in the mean-field approximation and a good agreement with the data for the nucleon properties has been obtained. The agreement is better than that obtained by the original model of Birse and Banerjee which indicates the important of the inclusion of higher-order meson correlations.

A NEW FERMION-SPIN TRANSFORMATION TO IMPLEMENT THE CHARGE-SPIN SEPARATION

1993 ◽  
Vol 07 (15) ◽  
pp. 1013-1019 ◽  
Author(s):  
SHIPING FENG ◽  
Z.B. SU ◽  
L. YU
Keyword(s):  
Mean Field ◽  
Hard Core ◽  
Field Approximation ◽  
Degree Of Freedom ◽  
Mean Field Approximation ◽  
Dimensional Case ◽  
Spinless Fermion ◽  
The Mean ◽  
Charge Degree ◽  
Good Agreement

We propose a new fermion-spin transformation to implement the charge-spin separation in the large U Hubbard, or the equivalent t-J model. The charge degree of freedom is represented by a spinless fermion while the spin degree of freedom is represented by a hard-core boson. The local constraint for single occupancy is exactly satisfied. Very good agreement with exact solution is obtained for one-dimensional case in the mean field approximation, regarding the total energy, gapless spinon and holon spectra, and the momentum distribution of physical electrons. The same approximation yields good doping dependence of the staggered magnetization in the two-dimensional case.

EXTENDED LINEAR SIGMA MODEL IN HIGHER ORDER MESONIC INTERACTIONS

2006 ◽  
Vol 15 (01) ◽  
pp. 143-152 ◽  
Author(s):  
M. RASHDAN ◽  
M. ABU-SHADY ◽  
T. S. T. ALI
Keyword(s):  
Sigma Model ◽  
Mean Field ◽  
Field Approximation ◽  
Higher Order ◽  
Linear Sigma Model ◽  
Mean Field Approximation ◽  
Field Equations ◽  
The Mean ◽  
Better Than ◽  
Good Agreement

The Gell-Mann and Levy model, as well as the Birse and Banerjee model, describe quark interactions via the exchange of σ- and π-mesons. We extend these models to include higher order mesonic interactions. The field equations were solved in the mean-field approximation and good agreement with the data for nucleon properties was obtained. Our agreement is better than that obtained by the original model of Birse and Banerjee and by other models. This indicates the importance of including higher order meson correlations.

Statistical thermodynamics of temperature anisotropy driven Weibel instabilities

1980 ◽  
Vol 23 (2) ◽  
pp. 283-293 ◽  
Author(s):  
Don S. Lemons ◽  
D. Winske
Keyword(s):  
Equations Of State ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Field Energy ◽  
Temperature Anisotropy ◽  
Canonical Distribution ◽  
Magnetic Field Energy ◽  
Theoretical Predictions ◽  
Good Agreement

A statistical theory of one- and two-dimensional temperature anisotropy driven Weibel instabilities is proposed. The theory is based on a two-temperature canonical distribution and the mean field approximation. It applies to a nonlinear, periodic, charge-neutralized, and collisionless system. Using a partition function formalism, equations of state are derived which predict upper bounds on the magnetic field energy produced by a quasi-static evolution of these instabilities. Theoretical predictions are in good agreement with results from numerical simulations.

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