FERMIONIC FOUR-LEVEL SYSTEM IN THE PRESENCE OF A TIME-DEPENDENT MAGNETIC FIELD

1996 ◽  
Vol 10 (14) ◽  
pp. 643-651 ◽  
Author(s):  
M.T. THOMAZ
Keyword(s):  
Magnetic Field ◽  
Time Evolution ◽  
Thermal Equilibrium ◽  
Initial Conditions ◽  
Time Dependent ◽  
Initial Vector ◽  
Vector State ◽  
Level System ◽  
Exact Time

The exact fermionic four-level system is studied in the presence of time-dependent magnetic field. The system is considered under two initial conditions: general initial vector state, and, at thermal equilibrium. The exact time evolution of one-particle operators is derived.

SPATIAL ROTATION AND TIME-EVOLUTION OPERATOR OF TWO-LEVEL SYSTEMS

2000 ◽  
Vol 14 (01) ◽  
pp. 101-112
Author(s):  
CHUN-FANG LI ◽  
XIAN-GENG ZHAO
Keyword(s):  
Magnetic Field ◽  
Time Evolution ◽  
Evolution Operator ◽  
Order Differential Equation ◽  
Time Dependent ◽  
Time Varying ◽  
Level System ◽  
Zener Model ◽  
Time Evolution Operator ◽  
Two Level Systems

All the six kinds of rotation approach with the same form to the evolution problem of arbitrarily time-dependent two-level system are investigated in this paper. A time-dependent two-level system can be viewed as a spin-1/2 system in a time-varying magnetic field. It is shown that for each kind of rotation approach, we can always find a rotating frame in which the direction of the effective magnetic field is fixed. This property reduces the problem of finding the time-evolution operator to the solution of a second-order differential equation. Applications are made to the J C model in quantum optics and the L and au–Zener model in resonance physics.

scholarly journals LION: A dynamic computer model for the low-latitude ionosphere

2007 ◽  
Vol 25 (11) ◽  
pp. 2371-2392 ◽  
Author(s):  
J. A. Bittencourt ◽  
V. G. Pillat ◽  
P. R. Fagundes ◽  
Y. Sahai ◽  
A. A. Pimenta
Keyword(s):  
Magnetic Field ◽  
Time Evolution ◽  
Computer Model ◽  
Transport Processes ◽  
Time Dependent ◽  
Low Latitude ◽  
Radiation Chemical ◽  
Neutral Winds ◽  
Plasma Drifts ◽  
Low Latitude Ionosphere

Abstract. A realistic fully time-dependent computer model, denominated LION (Low-latitude Ionospheric) model, that simulates the dynamic behavior of the low-latitude ionosphere is presented. The time evolution and spatial distribution of the ionospheric particle densities and velocities are computed by numerically solving the time-dependent, coupled, nonlinear system of continuity and momentum equations for the ions O+, O2+, NO+, N2+ and N+, taking into account photoionization of the atmospheric species by the solar extreme ultraviolet radiation, chemical and ionic production and loss reactions, and plasma transport processes, including the ionospheric effects of thermospheric neutral winds, plasma diffusion and electromagnetic E×B plasma drifts. The Earth's magnetic field is represented by a tilted centered magnetic dipole. This set of coupled nonlinear equations is solved along a given magnetic field line in a Lagrangian frame of reference moving vertically, in the magnetic meridian plane, with the electromagnetic E×B plasma drift velocity. The spatial and time distribution of the thermospheric neutral wind velocities and the pattern of the electromagnetic drifts are taken as known quantities, given through specified analytical or empirical models. The model simulation results are presented in the form of computer-generated color maps and reproduce the typical ionization distribution and time evolution normally observed in the low-latitude ionosphere, including details of the equatorial Appleton anomaly dynamics. The specific effects on the ionosphere due to changes in the thermospheric neutral winds and the electromagnetic plasma drifts can be investigated using different wind and drift models, including the important longitudinal effects associated with magnetic declination dependence and latitudinal separation between geographic and geomagnetic equators. The model runs in a normal personal computer (PC) and generates color maps illustrating the typical behavior of the low-latitude ionosphere for a given longitudinal region, for different seasons, geophysical conditions and solar activity, at each instant of time, showing the time evolution of the low-latitude ionosphere, between about 20° north and south of the magnetic equator. This paper presents a detailed description of the mathematical model and illustrative computer results.

Nonlinear bound on unstable electrostatic fluctuation energy for non-relativistic non-neutral electron flow in a planar diode with applied magnetic field

1985 ◽  
Vol 33 (2) ◽  
pp. 157-169 ◽  
Author(s):  
Ronald C. Davidson
Keyword(s):  
Magnetic Field ◽  
Applied Magnetic Field ◽  
Thermal Equilibrium ◽  
Maxwell Equations ◽  
Initial Conditions ◽  
Electron Flow ◽  
Reference State ◽  
Planar Diode ◽  
Net Flux ◽  
Fluctuation Energy

Global conservation constraints satisfied by the Vlasov-Maxwell equations are used to obtain a nonlinear bound on the unstable electrostatic fluctuation energy that can develop for non-relativistic non-neutral electron flow in a planar diode with an axial applied magnetic field. It is shown that the Heimholte free energy is a minimum for the thermal equilibrium reference state. The nonlinear bound on unstable fluctuation energy that can develop for general initial conditions is calculated for the case of flute perturbations with no axial dependence. To determine the lowest upper bound on fluctuation energy consistent with conservation constraints, the density, temperature and drift velocity of the reference state are chosen to minimize the nonlinear bound. The analysis assumes that the net flux of particles, momentum, and energy, vanish identically at the cathode and at the anode.

Ideally conducting magnetostatic equilibria and associated time dependent, resistive flows

1971 ◽  
Vol 6 (1) ◽  
pp. 125-136 ◽  
Author(s):  
John C. Stevenson
Keyword(s):  
Magnetic Field ◽  
Energy Equation ◽  
Incompressible Flows ◽  
Neutral Point ◽  
Time Dependent ◽  
Two Dimensional ◽  
Exact Time ◽  
Field Lines ◽  
Time Dependent Solution ◽  
The Magnetic Field

Several types of two-dimensional solutions for the equations of magnetohydrodynamics are described. For all these solutions the magnetic field contains at least one hyperbolic neutral point. Two new magnetostatic equilibria are introduced for the ideally conducting case. The magnetic field associated with one of these is used to construct an exact time-dependent solution of the MilD equations where the fluid is necessarily at rest. In the case where the field lines are hyperbolae, it is demonstrated that retention of the energy equation (ordinarily decoupled for incompressible flows) implies that the flow beginning at rest, remains at trest

SPIN CLUSTER AS A QUBIT: ROBUST AGAINST DISSIPATION OF THERMAL RADIATION FIELDS

2005 ◽  
Vol 19 (15n17) ◽  
pp. 2481-2485 ◽  
Author(s):  
XIAO-FEI SU ◽  
SHUN-JIN WANG
Keyword(s):  
Magnetic Field ◽  
Thermal Radiation ◽  
Time Evolution ◽  
Logic Gate ◽  
Time Dependent ◽  
Body System ◽  
Many Body ◽  
Spin Cluster ◽  
Radiation Fields ◽  
Qubit System

A spin cluster of 3 spin 1/2 particles has been studied as a qubit system. A time dependent magnetic field is applied to control the time evolution of the cluster. The lowest energy level of the cluster has the total spin 1/2 separated far away from the excited states and can be used as a qubit register. The universal 1-qubit logic gate can be constructed from the time evolution operator of the non-autonomous many-body system, and the 6 basic 1-qubit gates can be realized by adjusting the applied time dependent magnetic field. As a many-body system, this qubit system is expected to be robust against the dissipation effect of the thermal radiation fields from the environment.

TIME-DEPENDENT CALCULATION FOR THE TRANSMISSION COEFFICIENT OF TWO-DIMENSIONAL QUANTUM WIRE STRUCTURES IN THE PRESENCE OF MAGNETIC FIELD

1999 ◽  
Vol 13 (08) ◽  
pp. 895-902
Author(s):  
CHINGHONG YIU ◽  
JIAN WANG
Keyword(s):  
Magnetic Field ◽  
Transmission Coefficient ◽  
Time Evolution ◽  
Quantum Wire ◽  
Arbitrary Shape ◽  
Wave Functions ◽  
Time Dependent ◽  
Mode Matching ◽  
Two Dimensional ◽  
Matching Method

We present a simple and efficient method for calculating transmission coefficient of two-dimensional quantum wire structures in the presence of magnetic field. The time evolution of a wave packet is first obtained by solving the time dependent Schrödinger equation. Transmission coefficient is then extracted from the wave function by an intergal transform. This method is easier to implement than traditional time-independent methods such as mode matching method and it can be used to study the time evolution of wave functions for systems with arbitrary shape.

scholarly journals Effect of an oscillating time-dependent pressure gradient on Dean flow: transient solution

2020 ◽  
Vol 9 (1) ◽  
Author(s):  
Basant K. Jha ◽  
Dauda Gambo
Keyword(s):  
Pressure Gradient ◽  
Initial Conditions ◽  
Fluid Velocity ◽  
Outer Cylinder ◽  
Time Dependent ◽  
Navier Stokes ◽  
Dean Flow ◽  
Continuity Equations ◽  
Riemann Sum ◽  
Flow Formation

Abstract Background Navier-Stokes and continuity equations are utilized to simulate fully developed laminar Dean flow with an oscillating time-dependent pressure gradient. These equations are solved analytically with the appropriate boundary and initial conditions in terms of Laplace domain and inverted to time domain using a numerical inversion technique known as Riemann-Sum Approximation (RSA). The flow is assumed to be triggered by the applied circumferential pressure gradient (azimuthal pressure gradient) and the oscillating time-dependent pressure gradient. The influence of the various flow parameters on the flow formation are depicted graphically. Comparisons with previously established result has been made as a limit case when the frequency of the oscillation is taken as 0 (ω = 0). Results It was revealed that maintaining the frequency of oscillation, the velocity and skin frictions can be made increasing functions of time. An increasing frequency of the oscillating time-dependent pressure gradient and relatively a small amount of time is desirable for a decreasing velocity and skin frictions. The fluid vorticity decreases with further distance towards the outer cylinder as time passes. Conclusion Findings confirm that increasing the frequency of oscillation weakens the fluid velocity and the drag on both walls of the cylinders.

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