scholarly journals Mean Field Approximation for the Dense Charged Drop

2017 ◽  
Vol 2017 ◽  
pp. 1-5
Author(s):  
S. Bondarenko ◽  
K. Komoshvili
Keyword(s):  
Charged Particle ◽  
Schrödinger Equation ◽  
Spherical Symmetry ◽  
Schrodinger Equation ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Charged Drop ◽  
First Order ◽  
The Mean

We consider in this note the mean field approximation for the description of the probe charged particle in a dense charged drop. We solve the corresponding Schrödinger equation for the drop with spherical symmetry in the first order of mean field approximation and discuss the obtained results.

scholarly journals MEAN-FIELD APPROXIMATION OF QUANTUM SYSTEMS AND CLASSICAL LIMIT

2003 ◽  
Vol 13 (01) ◽  
pp. 59-73 ◽  
Author(s):  
S. GRAFFI ◽  
A. MARTINEZ ◽  
M. PULVIRENTI
Keyword(s):  
Schrödinger Equation ◽  
Vlasov Equation ◽  
Classical Limit ◽  
Schrodinger Equation ◽  
Mean Field ◽  
Field Approximation ◽  
Quantum Systems ◽  
Nonlinear Schrodinger Equation ◽  
Mean Field Approximation ◽  
Body Potential

We prove that, for a smooth two-body potential, the quantum mean-field approximation to the nonlinear Schrödinger equation of the Hartree type is stable at the classical limit h → 0, yielding the classical Vlasov equation.

Coherent quantum hollow beam creation in a plasma wakefield accelerator

2013 ◽  
Vol 79 (4) ◽  
pp. 397-403 ◽  
Author(s):  
D. JOVANOVIĆ ◽  
R. FEDELE ◽  
F. TANJIA ◽  
S. DE NICOLA ◽  
M. BELIĆ
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Mean Field ◽  
Magnetoactive Plasma ◽  
Particle Beam ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Coupled Equations ◽  
Non Local ◽  
Plasma Wakefield

AbstractA theoretical investigation of the propagation of a relativistic electron (or positron) particle beam in an overdense magnetoactive plasma is carried out within a fluid plasma model, taking into account the individual quantum properties of beam particles. It is demonstrated that the collective character of the particle beam manifests mostly through the self-consistent macroscopic plasma wakefield created by the charge and the current densities of the beam. The transverse dynamics of the beam–plasma system is governed by the Schrödinger equation for a single-particle wavefunction derived under the Hartree mean field approximation, coupled with a Poisson-like equation for the wake potential. These two coupled equations are subsequently reduced to a nonlinear, non-local Schrödinger equation and solved in a strongly non-local regime. An approximate Glauber solution is found analytically in the form of a Hermite–Gauss ring soliton. Such non-stationary (‘breathing’ and ‘wiggling’) coherent structure may be parametrically unstable and the corresponding growth rates are estimated analytically.

scholarly journals DENSITY FLUCTUATIONS AND A FIRST-ORDER CHIRAL PHASE TRANSITION IN NON-EQUILIBRIUM

2008 ◽  
Vol 23 (27n30) ◽  
pp. 2469-2472 ◽  
Author(s):  
CHIHIRO SASAKI ◽  
BENGT FRIMAN ◽  
KRZYSZTOF REDLICH
Keyword(s):  
Phase Transition ◽  
Mean Field ◽  
Field Approximation ◽  
Density Fluctuations ◽  
Mean Field Approximation ◽  
Chiral Phase ◽  
Chiral Phase Transition ◽  
First Order ◽  
The Mean ◽  
Non Equilibrium

The thermodynamics of a first-order chiral phase transition is considered in the presence of spinodal phase separation using the Nambu-Jona-Lasinio model in the mean field approximation. We focus on the behavior of conserved charge fluctuations. We show that in non-equilibrium the specific heat and charge susceptibilities diverge as the system crosses the isothermal spinodal lines.

scholarly journals The Haus-Tanaka Model for the Ice VII-Ice VIII Phase Transition

1980 ◽  
Vol 33 (1) ◽  
pp. 107 ◽  
Author(s):  
J Ho-Ting-Hun ◽  
J Oitmaa
Keyword(s):  
Phase Transition ◽  
Mean Field ◽  
Field Approximation ◽  
Order Transition ◽  
Mean Field Approximation ◽  
First Order ◽  
Second Order Transition ◽  
The Mean ◽  
First Order Transition ◽  
Temperature Susceptibility

The high temperature susceptibility series of the model proposed by Haus and Tanaka (1977) to account for the transition of the orientationally disordered ice VII phase to the orientationally ordered ice VIII phase does not provide evidence for the possible occurrence of a first-order transition, as predicted by the mean field approximation, but gives a second-order transition instead.

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