scholarly journals TIME-DEPENDENT VARIATIONAL APPROACH TO BOSE–EINSTEIN CONDENSATION

2000 ◽  
Vol 14 (01) ◽  
pp. 1-11 ◽  
Author(s):  
LUCA SALASNICH
Keyword(s):  
Variational Approach ◽  
Mean Field ◽  
Field Approximation ◽  
Einstein Condensate ◽  
Time Dependent ◽  
Mean Field Approximation ◽  
Einstein Condensation ◽  
Collective Oscillations ◽  
The Stability ◽  
Bose Einstein

We discuss the mean-field approximation for a trapped weakly-interacting Bose–Einstein condensate (BEC) and its connection with the exact many-body problem by deriving the Gross–Pitaevskii action of the condensate. The mechanics of the BEC in a harmonic potential is studied by using a variational approach with time-dependent Gaussian trial wave-functions. In particular, we analyze the static configurations, the stability and the collective oscillations for both ground-state and vortices.

SPINOR BEC IN THE LARGE-N LIMIT

2007 ◽  
Vol 21 (23n24) ◽  
pp. 4248-4255 ◽  
Author(s):  
ZHIBING LI ◽  
CHENGGUANG BAO
Keyword(s):  
Mean Field ◽  
Field Approximation ◽  
Einstein Condensate ◽  
Spin Coupling ◽  
Mean Field Approximation ◽  
Condensed State ◽  
Bose Einstein Condensate ◽  
Alkali Atoms ◽  
The One ◽  
Bose Einstein

The superfine structure of Bose-Einstein condensate of alkali atoms due to the spin coupling have been investigated in the mean field approximation. In the limit of large number of atoms, we obtained the analytical solution for the fully condensed states and the states with one-atom excited. It was found that the energy of the one-atom excited state could be smaller than the energy of the fully condensed state, even two states have similar total spin.

Decay of a Bose-Einstein condensate in a dissipative lattice – the mean-field approximation and beyond

2011 ◽  
Vol 63 (1) ◽  
pp. 63-71 ◽  
Author(s):  
F. Trimborn ◽  
D. Witthaut ◽  
H. Hennig ◽  
G. Kordas ◽  
T. Geisel ◽  
...  
Keyword(s):  
Mean Field ◽  
Field Approximation ◽  
Einstein Condensate ◽  
Mean Field Approximation ◽  
Bose Einstein Condensate ◽  
The Mean ◽  
Bose Einstein

scholarly journals Phase Transitions and Bose–Einstein Condensation in Alpha-Nucleon Matter

2019 ◽  
Vol 64 (8) ◽  
pp. 745
Author(s):  
L. M. Satarov ◽  
I. N. Mishustin ◽  
A. Motornenko ◽  
V. Vovchenko ◽  
M. I. Gorenstein ◽  
...  
Keyword(s):  
Phase Diagram ◽  
Phase Transitions ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Einstein Condensation ◽  
Bose Einstein Condensation ◽  
Nucleon Matter ◽  
Bose Einstein ◽  
First Order Phase

The equation of state and the phase diagram of an isospin-symmetric chemically equilibrated mixture of a particles and nucleons (N) are studied in the mean-field approximation. We use a Skyrme-like parametrization of mean-field potentials as functions of the partial densities of particles. The parameters of these potentials are chosen by fitting the known properties of pure N- and pure a-matters at zero temperature. The sensitivity of results to the choice of the aN attraction strength is investigated. The phase diagram of the a − N mixture is studied with a special attention paid to the liquid-gas phase transitions and the Bose–Einstein condensation of a particles. We have found two first-order phase transitions, stable and metastable, which differ significantly by the fractions of a’s. It is shown that the states with a condensate are metastable.

Ion-surface scattering in the time-dependent mean-field approximation

1988 ◽  
Vol 199 (1-2) ◽  
pp. 132-140 ◽  
Author(s):  
K.J. Schafer ◽  
N.-H. Kwong ◽  
J.D. Garcia
Keyword(s):  
Mean Field ◽  
Field Approximation ◽  
Time Dependent ◽  
Surface Scattering ◽  
Mean Field Approximation

scholarly journals The Smoluchowski Ensemble—Statistical Mechanics of Aggregation

Entropy ◽  
2020 ◽  
Vol 22 (10) ◽  
pp. 1181
Author(s):  
Themis Matsoukas
Keyword(s):  
Sol Gel ◽  
Scaling Limit ◽  
Mean Field ◽  
Central Element ◽  
Field Approximation ◽  
Fixed Number ◽  
Mean Field Approximation ◽  
The Mean ◽  
Sol Gel Transition ◽  
The Stability

We present a rigorous thermodynamic treatment of irreversible binary aggregation. We construct the Smoluchowski ensemble as the set of discrete finite distributions that are reached in fixed number of merging events and define a probability measure on this ensemble, such that the mean distribution in the mean-field approximation is governed by the Smoluchowski equation. In the scaling limit this ensemble gives rise to a set of relationships identical to those of familiar statistical thermodynamics. The central element of the thermodynamic treatment is the selection functional, a functional of feasible distributions that connects the probability of distribution to the details of the aggregation model. We obtain scaling expressions for general kernels and closed-form results for the special case of the constant, sum and product kernel. We study the stability of the most probable distribution, provide criteria for the sol-gel transition and obtain the distribution in the post-gel region by simple thermodynamic arguments.

PULSED SUPERRADIANT EMISSION FROM A MAGNETIC DIPOLE SYSTEM

1993 ◽  
Vol 07 (12) ◽  
pp. 2353-2365
Author(s):  
SALOMON S. MIZRAHI ◽  
MAURO A. MEWES
Keyword(s):  
Magnetic Field ◽  
Single Particle ◽  
Mean Field ◽  
Field Approximation ◽  
Transverse Magnetic ◽  
Time Dependent ◽  
Mean Field Approximation ◽  
Magnetic Dipoles ◽  
Emission Process ◽  
Dipole System

The superradiant emission is considered for a radiating system constituted by N dressed spin-1/2 magnetic dipoles, described by a nonlinear single particle Hamiltonian that is derived under a mean field approximation. This Hamiltonian describes adequately the transient regime of the emission process: The intensity of the radiation follows the sech2 law and its peak is proportional to N2. Then, one considers the application of a periodic time-dependent transverse magnetic field and we study the behavior of the emission that becomes periodically pulsed.

First Principles Study of the Phase Transitions of MnAs

2006 ◽  
Vol 941 ◽  
Author(s):  
Ivan Rungger ◽  
Stefano Sanvito
Keyword(s):  
Phase Transition ◽  
Curie Temperature ◽  
Cell Volume ◽  
Order Phase Transition ◽  
Structural Changes ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
First Order Phase Transition ◽  
The Stability

ABSTRACTThe magnetic and structural properties of MnAs are investigated by mapping ab initio total energies onto a Heisenberg Hamiltonian. We study the dependence of the Curie temperature over the unit cell volume and an orthorhombic distortion by using the mean field approximation, and find that for orthorhombically distorted cells the Curie temperature is much smaller than for hexagonal cells. We provide an explanation for the structural changes of both the first order phase transition at 318 K and the second order phase transition at 400 K, with the cell volume driving the stability of the different structures in the paramagnetic state. The stable cell is found to be orthorhombic up to a critical lattice constant of about 3.7 Å, above which it remains hexagonal.

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