Mean field approximation for the stochastic Schrödinger equation

1999 ◽  
Vol 111 (18) ◽  
pp. 8366-8377 ◽  
Author(s):  
Oleg V. Prezhdo
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Stochastic Schrödinger Equation

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 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.

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.

Microscopic, quantum derivation of cranking model for nuclear collective rotation: harmonic oscillator case

2008 ◽  
Vol 86 (8) ◽  
pp. 1001-1014 ◽  
Author(s):  
P Gulshani
Keyword(s):  
Angular Momentum ◽  
Schrödinger Equation ◽  
Harmonic Oscillator ◽  
Schrodinger Equation ◽  
Mean Field ◽  
Euler Angle ◽  
Mean Field Approximation ◽  
Nuclear Wave Function ◽  
Rotational Component ◽  
Hartree Fock

In this article, the conventional semiclassical one-dimensional cranking model (CR), which is commonly used to investigate rotational structures of deformed nuclei, is derived from microscopic, quantum first principles for the harmonic oscillator case. The space-fixed particle coordinates are canonically transformed to an Euler angle and a set of 3N – 1 intrinsic coordinates to decompose the nuclear Hamiltonian into intrinsic and collective rotational components plus a Coriolis-centrifugal term that couples the intrinsic and rotational motions. To overcome the difficulties associated with finding an appropriate set of intrinsic coordinates, the rotational component in the transformed Hamiltonian is expressed in terms of the space-fixed coordinates and momenta by taking the commutator of the original Hamiltonian with the Euler angle, and by choosing an explicit expression for the Euler angle in terms of space-fixed particle coordinates. The intrinsic component in the transformed Hamiltonian is then the difference between the original Hamiltonian and the rotational component. The nuclear wave function is chosen as the product of an intrinsic function and an eigenfunction of the angular momentum operator (as in the unified rotational model). The Hamiltonian and Schrodinger equation for the intrinsic system become functions of the angular-momentum quantum number and intrinsic operators that are expressed in terms of space-fixed particles coordinates and momenta. The intrinsic Schrodinger equation is then reduced to that of a one-body operator using Hartree–Fock mean-field approximation. The intrinsic mean-field Hamiltonian is chosen to be an anisotropic harmonic oscillator Hamiltonian, and the Hartree–Fock mean-field equation is unitarily transformed to an equation resembling that of the CR but with oscillator frequencies and angular velocity that are microscopically and quantum mechanically determined. The unitary transformation is selected such that the model predicts the kinematic rigid-body moment of inertia, as does the CR when self-consistency condition is used.PACS Nos.: 21.60.Ev, 21.60.Fw, 21.60.Jz

The Determination of the Magnetoelectric Coupling Coefficient in Ferroelectric–Ferromagnetic Composite Based on PZT–Ferrite

2013 ◽  
Vol 58 (4) ◽  
pp. 1401-1403 ◽  
Author(s):  
J.A. Bartkowska ◽  
R. Zachariasz ◽  
D. Bochenek ◽  
J. Ilczuk
Keyword(s):  
Dielectric Permittivity ◽  
Coupling Coefficient ◽  
Mean Field ◽  
Field Approximation ◽  
Theoretical Description ◽  
Magnetoelectric Coupling ◽  
Mean Field Approximation ◽  
Dielectric Measurements ◽  
Temperature Dependences ◽  
Multiferroic Composite

Abstract In the present work, the magnetoelectric coupling coefficient, from the temperature dependences of the dielectric permittivity for the multiferroic composite was determined. The research material was ferroelectric-ferromagnetic composite on the based PZT and ferrite. We investigated the temperature dependences of the dielectric permittivity (") for the different frequency of measurement’s field. From the dielectric measurements we determined the temperature of phase transition from ferroelectric to paraelectric phase. For the theoretical description of the temperature dependence of the dielectric constant, the Hamiltonian of Alcantara, Gehring and Janssen was used. To investigate the dielectric properties of the multiferroic composite this Hamiltonian was expressed under the mean-field approximation. Based on dielectric measurements and theoretical considerations, the values of the magnetoelectric coupling coefficient were specified.

scholarly journals Combined Mean-Field and Semiclassical Limits of Large Fermionic Systems

2021 ◽  
Vol 182 (2) ◽  
Author(s):  
Li Chen ◽  
Jinyeop Lee ◽  
Matthew Liew
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Mean Field ◽  
Weak Limit ◽  
Weak Compactness ◽  
Three Dimensions ◽  
Uniform Estimates ◽  
Fermionic Systems ◽  
Semiclassical Limits ◽  
Semiclassical Regime

AbstractWe study the time dependent Schrödinger equation for large spinless fermions with the semiclassical scale $$\hbar = N^{-1/3}$$ ħ = N - 1 / 3 in three dimensions. By using the Husimi measure defined by coherent states, we rewrite the Schrödinger equation into a BBGKY type of hierarchy for the k particle Husimi measure. Further estimates are derived to obtain the weak compactness of the Husimi measure, and in addition uniform estimates for the remainder terms in the hierarchy are derived in order to show that in the semiclassical regime the weak limit of the Husimi measure is exactly the solution of the Vlasov equation.

scholarly journals Hexagonal-Shaped Spin Crossover Nanoparticles Studied by Ising-Like Model Solved by Local Mean Field Approximation

2021 ◽  
Vol 7 (5) ◽  
pp. 69
Author(s):  
Catherine Cazelles ◽  
Jorge Linares ◽  
Mamadou Ndiaye ◽  
Pierre-Richard Dahoo ◽  
Kamel Boukheddaden
Keyword(s):  
Spin Crossover ◽  
Hexagonal Lattice ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Ligand Field ◽  
Order And Disorder ◽  
The Matrix ◽  
Local Mean ◽  
Parameter Values

The properties of spin crossover (SCO) nanoparticles were studied for five 2D hexagonal lattice structures of increasing sizes embedded in a matrix, thus affecting the thermal properties of the SCO region. These effects were modeled using the Ising-like model in the framework of local mean field approximation (LMFA). The systematic combined effect of the different types of couplings, consisting of (i) bulk short- and long-range interactions and (ii) edge and corner interactions at the surface mediated by the matrix environment, were investigated by using parameter values typical of SCO complexes. Gradual two and three hysteretic transition curves from the LS to HS states were obtained. The results were interpreted in terms of the competition between the structure-dependent order and disorder temperatures (TO.D.) of internal coupling origin and the ligand field-dependent equilibrium temperatures (Teq) of external origin.

Sign in / Sign up

Export Citation Format

Share Document