scholarly journals Mean‐Field and Classical Limit for the N ‐Body Quantum Dynamics with Coulomb Interaction

2021 ◽  
Author(s):  
François Golse ◽  
Thierry Paul
Keyword(s):  
Coulomb Interaction ◽  
Classical Limit ◽  
Quantum Dynamics ◽  
Mean Field

scholarly journals ANTIFERROMAGNETISM, STRIPES, AND SUPERCONDUCTIVITY IN THE t–J MODEL WITH COULOMB INTERACTION

2001 ◽  
Vol 15 (08) ◽  
pp. 1117-1126 ◽  
Author(s):  
JUNGHOON HAN ◽  
QIANG-HUA WANG ◽  
DUNG-HAI LEE
Keyword(s):  
Long Range ◽  
Coulomb Interaction ◽  
Lower Energy ◽  
Mean Field ◽  
Doping Density ◽  
Stripe Width ◽  
The Mean ◽  
D Wave

We study mean-field phases of the t–J model with long-range Coulomb interaction. In the order of increasing doping density we find a classical antiferromagnet, charge and spin stripes, and a uniform d-wave superconductor, at the realistic doping parameters. Both in-phase and anti-phase stripes exist as metastable configurations, but the in-phase stripes have a slightly lower energy. The dependence of the stripe width and the inter-stripe spacing on the doping is examined. Effects of fluctuations around the mean-field states are discussed.

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.

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.

scholarly journals Relativistic quantum dynamics of scalar bosons under a full vector Coulomb interaction

2017 ◽  
Vol 77 (5) ◽  
Author(s):  
Luis B. Castro ◽  
Luiz P. de Oliveira ◽  
Marcelo G. Garcia ◽  
Antonio S. de Castro
Keyword(s):  
Coulomb Interaction ◽  
Quantum Dynamics ◽  
Relativistic Quantum ◽  
Full Vector

Classical limit of relativistic quantal system with attractive Coulomb interaction

Pramana ◽  
1991 ◽  
Vol 36 (3) ◽  
pp. 271-288
Author(s):  
Swagata Nandi ◽  
C S Shastry
Keyword(s):  
Coulomb Interaction ◽  
Classical Limit ◽  
Quantal System
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