Iterative solution of non-autonomous Bloch equations: fluorescence spectrum with detuned squeezed vacuum field

2010 ◽  
Vol 88 (7) ◽  
pp. 529-543 ◽  
Author(s):  
H. A. Batarfi ◽  
R. A. Al-Harbi ◽  
R. Saunders ◽  
S. S. Hassan
Keyword(s):  
Numerical Solutions ◽  
Strong Field ◽  
Iterative Solution ◽  
Vacuum Field ◽  
Bloch Equations ◽  
Field Case ◽  
Squeezed Vacuum ◽  
Analytical Results ◽  
Arbitrary Strength ◽  
Ground State Atom

The non-autonomous Bloch equations modelling a driven 2-level atom in the presence of an off-resonant broadband squeezed vacuum (SV) field is treated analytically. This concerns iterative solutions valid for large SV detuning parameter but for arbitrary strength of the laser field. Computational results are presented for the averaged atomic variables for various data and compared with the resonant SV field case. The iterated analytical results for nonzero SV detuning are compared with the (exact) numerical solutions of the Bloch equations, hence we have an insight about the range of other system parameters (other than the Rabi frequency) for which the iterated solutions are valid to O(10−2) or less. The main purpose of deriving these analytical results is to calculate analytically the transient fluorescent spectrum. For an initially ground-state atom, both the SV phase and detuning parameters induce pronounced asymmetrical spectrum in the strong field case.

scholarly journals Magnetic field dependence of the neutral pion mass in the linear sigma model with quarks: The strong field case

2021 ◽  
Vol 103 (5) ◽  
Author(s):  
Alejandro Ayala ◽  
José Luis Hernández ◽  
L. A. Hernández ◽  
Ricardo L. S. Farias ◽  
R. Zamora
Keyword(s):  
Magnetic Field ◽  
Field Dependence ◽  
Magnetic Field Dependence ◽  
Sigma Model ◽  
Neutral Pion ◽  
Strong Field ◽  
Pion Mass ◽  
Linear Sigma Model ◽  
Field Case

Numerical solutions to 2D Maxwell–Bloch equations

2008 ◽  
Vol 40 (5-6) ◽  
pp. 447-453 ◽  
Author(s):  
Jingyi Xiong ◽  
Max Colice ◽  
Friso Schlottau ◽  
Kelvin Wagner ◽  
Bengt Fornberg
Keyword(s):  
Numerical Solutions ◽  
Bloch Equations ◽  
Maxwell Bloch Equations

Phase-sensitive reflection of squeezed vacuum field in optical cavity

2012 ◽  
Vol 10 (9) ◽  
pp. 091901-91904
Author(s):  
Ke Di Ke Di ◽  
Xudong Yu Xudong Yu ◽  
Fengyu Cheng Fengyu Cheng ◽  
Jing Zhang Jing Zhang
Keyword(s):  
Optical Cavity ◽  
Vacuum Field ◽  
Squeezed Vacuum ◽  
Phase Sensitive

SCALED BOUNDARY FINITE-ELEMENT AND SUBSTRUCTURE ANALYSIS ON THE SEEPAGE PROBLEMS

2010 ◽  
Vol 24 (13) ◽  
pp. 1491-1494 ◽  
Author(s):  
FENGZHI LI
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Free Surface ◽  
Finite Element Methods ◽  
Numerical Solutions ◽  
Unbounded Domains ◽  
Satisfactory Accuracy ◽  
Analytical Results ◽  
Substructure Analysis ◽  
Scaled Boundary Finite Element

The scaled boundary finite element method is used to determine the seepage free surface of a dam with unbounded base. Two models for the bounded and the unbounded domains are established by using the mentioned method, and the numerical solutions are compared with the analytical results. Also, the free surface seepage of a dam with unbounded base is solved by combining the substructure and scaled boundary finite-element methods. The method has satisfactory accuracy and is quite efficient.

Electromagnetic induction by a finite electric dipole source over a 2-D earth

Geophysics ◽  
1993 ◽  
Vol 58 (2) ◽  
pp. 198-214 ◽  
Author(s):  
Martyn J. Unsworth ◽  
Bryan J. Travis ◽  
Alan D. Chave
Keyword(s):  
Finite Element ◽  
Electromagnetic Fields ◽  
Electric Dipole ◽  
Numerical Solutions ◽  
Current Source ◽  
Three Dimensional ◽  
Iterative Solution ◽  
Electromagnetic Response ◽  
Dipole Source ◽  
Horizontal Electric Dipole

A numerical solution for the frequency domain electromagnetic response of a two‐dimensional (2-D) conductivity structure to excitation by a three‐dimensional (3-D) current source has been developed. The fields are Fourier transformed in the invariant conductivity direction and then expressed in a variational form. At each of a set of discrete spatial wavenumbers a finite‐element method is used to obtain a solution for the secondary electromagnetic fields. The finite element uses exponential elements to efficiently model the fields in the far‐field. In combination with an iterative solution for the along‐strike electromagnetic fields, this produces a considerable reduction in computation costs. The numerical solutions for a horizontal electric dipole are computed and shown to agree with closed form expressions and to converge with respect to the parameterization. Finally some simple examples of the electromagnetic fields produced by horizontal electric dipole sources at both the seafloor and air‐earth interface are presented to illustrate the usefulness of the code.

SEMI-ANALYTICAL SOLUTIONS FOR THE BRUSSELATOR REACTION–DIFFUSION MODEL

2017 ◽  
Vol 59 (2) ◽  
pp. 167-182 ◽  
Author(s):  
H. Y. ALFIFI
Keyword(s):  
Steady State ◽  
Hopf Bifurcation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Analytical Solutions ◽  
Numerical Solutions ◽  
Partial Differential ◽  
Analytical Results ◽  
Transient Solutions ◽  
The Impact

Semi-analytical solutions are derived for the Brusselator system in one- and two-dimensional domains. The Galerkin method is processed to approximate the governing partial differential equations via a system of ordinary differential equations. Both steady-state concentrations and transient solutions are obtained. Semi-analytical results for the stability of the model are presented for the identified critical parameter value at which a Hopf bifurcation occurs. The impact of the diffusion coefficients on the system is also considered. The results show that diffusion acts to stabilize the systems better than the equivalent nondiffusive systems with the increasing critical value of the Hopf bifurcation. Comparison between the semi-analytical and numerical solutions shows an excellent agreement with the steady-state transient solutions and the parameter values at which the Hopf bifurcations occur. Examples of stable and unstable limit cycles are given, and Hopf bifurcation points are shown to confirm the results previously calculated in the Hopf bifurcation map. The usefulness and accuracy of the semi-analytical results are confirmed by comparison with the numerical solutions of partial differential equations.

scholarly journals Analytical Approach to Polarization Mode Dispersion in Linearly Spun Fiber with Birefringence

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Vinod K. Mishra
Keyword(s):  
Analytical Approach ◽  
Numerical Solutions ◽  
Polarization Mode Dispersion ◽  
Optical Networking ◽  
Polarization Mode ◽  
Profile Function ◽  
Analytical Results ◽  
Mode Dispersion ◽  
Spun Fiber ◽  
Parameter Ranges

The behavior of Polarization Mode Dispersion (PMD) in spun optical fiber is a topic of great interest in optical networking. Earlier work in this area has focused more on approximate or numerical solutions. In this paper we present analytical results for PMD in spun fibers with triangular spin profile function. It is found that in some parameter ranges the analytical results differ from the approximations.

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