An exact solution for electrons in a time-dependent magnetic field

2006 ◽  
Vol 355 (4-5) ◽  
pp. 348-351 ◽  
Author(s):  
D. Laroze ◽  
R. Rivera
Keyword(s):  
Magnetic Field ◽  
Exact Solution ◽  
Time Dependent

FICTON THEORY OF DYNAMICAL SYSTEMS WITH NOISY PARAMETERS

1965 ◽  
Vol 43 (4) ◽  
pp. 619-639 ◽  
Author(s):  
R. C. Bourret
Keyword(s):  
Magnetic Field ◽  
Exact Solution ◽  
Dynamical Systems ◽  
Approximate Solutions ◽  
Frequency Parameter ◽  
Time Dependent ◽  
Quantum Mechanical ◽  
Graphical Comparison ◽  
The One ◽  
Random Fluctuations

The theory of randomly perturbed waves described previously (Bourret 1962a, b) is presented in a form applicable to purely time-dependent systems, classical or quantum mechanical. It is then applied to the problem of a spin-[Formula: see text] dipole in a magnetic field with random fluctuations. One- and two-ficton processes are taken into account and a "renormalization" approximation is given also. Graphical comparison of the approximate solutions with the exact solution is presented. As a classical example, the harmonic oscillator with a noisy frequency parameter is analyzed in both the one- and two-ficton approximations.

Approximation Techniques for Stationary and Dynamic Problems

2021 ◽  
pp. 181-208
Author(s):  
Duncan G. Steel
Keyword(s):  
Magnetic Field ◽  
Exact Solution ◽  
Perturbation Theory ◽  
Golden Rule ◽  
Delta Function ◽  
Time Dependent ◽  
Dynamic Problems ◽  
Approximation Techniques ◽  
Dirac Delta ◽  
Physical Features

For many aspects of device design, an exact solution to Schrödinger’s equation is not needed. However, it may simultaneously be required that all of the physical features are clearly understood. The most important technique for approaching these problems is perturbation theory, since it is difficult to develop physical intuition by just numerical means. For the case of solutions to the time independent Schrödinger equation, such as where an electric or magnetic field is applied, time independent perturbation theory is very useful, and is typically adequate for many problems. In some cases, problems may need an exact solution, but it may not be necessary to consider all the levels, leading to the approximation of using just a few levels. If the Hamiltonian is time dependent, we use time dependent perturbation theory which leads to Fermi’s golden rule. The result leads to a Dirac delta-function which can be eliminated by using the density of states.

A quasi-static equilibrium model of the rotamak

1989 ◽  
Vol 41 (1) ◽  
pp. 61-66
Author(s):  
W. K. Bertram
Keyword(s):  
Magnetic Field ◽  
Exact Solution ◽  
Equilibrium Model ◽  
Rotating Magnetic Field ◽  
Time Dependent ◽  
Static Equilibrium ◽  
Field Reversed Configuration ◽  
Hydrodynamic Equations

An equilibrium model for a spherical field reversed configuration in the presence of a transverse rotating magnetic field is presented. It is shown that this quasi-static equilibrium is an exact solution of the time-dependent ideal magneto-hydrodynamic equations.

Exact solution of theL−Scoupled system in a time-dependent magnetic field

1998 ◽  
Vol 58 (4) ◽  
pp. 3328-3331 ◽  
Author(s):  
Shun-Jin Wang ◽  
Li-Xiang Cen
Keyword(s):  
Magnetic Field ◽  
Exact Solution ◽  
Time Dependent

scholarly journals Moving Pearl Vortices in Thin-Film Superconductors

2021 ◽  
Vol 6 (1) ◽  
pp. 4
Author(s):  
Vladimir Kogan ◽  
Norio Nakagawa
Keyword(s):  
Magnetic Field ◽  
Thin Film ◽  
Time Dependent ◽  
Superconducting Thin Film ◽  
Self Energy ◽  
London Equation ◽  
The Magnetic Field

The magnetic field hz of a moving Pearl vortex in a superconducting thin-film in (x,y) plane is studied with the help of the time-dependent London equation. It is found that for a vortex at the origin moving in +x direction, hz(x,y) is suppressed in front of the vortex, x>0, and enhanced behind (x<0). The distribution asymmetry is proportional to the velocity and to the conductivity of normal quasiparticles. The vortex self-energy and the interaction of two moving vortices are evaluated.

scholarly journals Hamiltonian Approach to Magnetic Fields with Toroidal Surfaces

1985 ◽  
Vol 40 (10) ◽  
pp. 959-967
Author(s):  
A. Salat
Keyword(s):  
Magnetic Field ◽  
Hamiltonian System ◽  
Magnetic Fields ◽  
Constant Pressure ◽  
Time Dependent ◽  
Hamiltonian Approach ◽  
One Dimensional ◽  
Mhd Equilibrium ◽  
Magnetic Surfaces ◽  
Rotational Transform

The equivalence of magnetic field line equations to a one-dimensional time-dependent Hamiltonian system is used to construct magnetic fields with arbitrary toroidal magnetic surfaces I = const. For this purpose Hamiltonians H which together with their invariants satisfy periodicity constraints have to be known. The choice of H fixes the rotational transform η(I). Arbitrary axisymmetric fields, and nonaxisymmetric fields with constant η(I) are considered in detail.Configurations with coinciding magnetic and current density surfaces are obtained. The approach used is not well suited, however, to satisfying the additional MHD equilibrium condition of constant pressure on magnetic surfaces.

scholarly journals Measurements of the time-dependent cosmic-ray Sun shadow with seven years of IceCube data: Comparison with the Solar cycle and magnetic field models

2021 ◽  
Vol 103 (4) ◽  
Author(s):  
M. G. Aartsen ◽  
R. Abbasi ◽  
M. Ackermann ◽  
J. Adams ◽  
J. A. Aguilar ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Solar Cycle ◽  
Cosmic Ray ◽  
Time Dependent ◽  
Data Comparison

scholarly journals Structure evolution of suspensions under time-dependent electric or magnetic field

2021 ◽  
Author(s):  
Konstantinos Manikas ◽  
Markus Hütter ◽  
Patrick D. Anderson
Keyword(s):  
Magnetic Field ◽  
Field Strength ◽  
Brownian Dynamics ◽  
Thermal Fluctuations ◽  
Time Dependent ◽  
Structure Evolution ◽  
Strength Increase ◽  
Large Rotation ◽  
Dynamics Simulations ◽  
Brownian Dynamics Simulations

AbstractThe effect of time-dependent external fields on the structures formed by particles with induced dipoles dispersed in a viscous fluid is investigated by means of Brownian Dynamics simulations. The physical effects accounted for are thermal fluctuations, dipole-dipole and excluded volume interactions. The emerging structures are characterised in terms of particle clusters (orientation, size, anisotropy and percolation) and network structure. The strength of the external field is increased in one direction and then kept constant for a certain amount of time, with the structure formation being influenced by the slope of the field-strength increase. This effect can be partially rationalized by inhomogeneous time re-scaling with respect to the field strength, however, the presence of thermal fluctuations makes the scaling at low field strength inappropriate. After the re-scaling, one can observe that the lower the slope of the field increase, the more network-like and the thicker the structure is. In the second part of the study the field is also rotated instantaneously by a certain angle, and the effect of this transition on the structure is studied. For small rotation angles ($$\theta \le 20^{{\circ }}$$ θ ≤ 20 ∘ ) the clusters rotate but stay largely intact, while for large rotation angles ($$\theta \ge 80^{{\circ }}$$ θ ≥ 80 ∘ ) the structure disintegrates and then reforms, due to the nature of the interactions (parallel dipoles with perpendicular inter-particle vector repel each other). For intermediate angles ($$20<\theta <80^{{\circ }}$$ 20 < θ < 80 ∘ ), it seems that, during rotation, the structure is altered towards a more network-like state, as a result of cluster fusion (larger clusters). The details provided in this paper concern an electric field, however, all results can be projected into the case of a magnetic field and paramagnetic particles.

Sign in / Sign up

Export Citation Format

Share Document