Pseudospectral/Delves–Freeman Computations of the Radiation Coefficient for Weakly Nonlocal Solitary Waves of the Third-Order Nonlinear Schroedinger Equation and Their Relation to Hyperasymptotic Perturbation Theory

1997 ◽  
Vol 138 (2) ◽  
pp. 665-694 ◽  
Author(s):  
John P. Boyd
Keyword(s):  
Perturbation Theory ◽  
Solitary Waves ◽  
Schroedinger Equation ◽  
Third Order ◽  
The Third ◽  
Radiation Coefficient

Effect of the third-order contribution on ion-acoustic solitary waves

1979 ◽  
Vol 57 (12) ◽  
pp. 2136-2142 ◽  
Author(s):  
C. S. Lai
Keyword(s):  
Solitary Waves ◽  
Order Approximation ◽  
Reductive Perturbation Method ◽  
Renormalization Scheme ◽  
Third Order ◽  
The Third ◽  
Ion Acoustic Solitary Waves ◽  
Ion Acoustic ◽  
Third Order Approximation ◽  
Secular Terms

The effect of the third-order corrections on ion-acoustic solitary waves is studied on the basis of the reductive perturbation method. The secular terms in the third-order approximation are eliminated by employing the renormalization scheme of Kodama and Taniuti in an unambiguous manner. It is found that the contribution of the third-order corrections to the soliton velocities and widths is rather minimal.

Third-order energy using CNDO/2 and INDO Hamiltonian approximations in the modified PCILO method

1979 ◽  
Vol 44 (10) ◽  
pp. 3041-3071 ◽  
Author(s):  
Roman Boča
Keyword(s):  
Perturbation Theory ◽  
Computing Time ◽  
Molecular Orbitals ◽  
Coupling Constants ◽  
Spin Coupling ◽  
Zeroth Order ◽  
Third Order ◽  
Localized Molecular Orbitals ◽  
The Third ◽  
Pcilo Method

The perturbative configuration interaction using strictly localized molecular orbitals, called the modified PCILO method has been applied in this communication for the calculations of the energy terms of 15 small molecules up to the third order of the perturbation theory. For this method the use of the Rayleigh-Schrodinger many-body perturbation theory with the Moller-Plesset type of the Hamiltonian partitioning is characteristic. On the CNDO/2 and INDO level of approximations the strictly localized molecular orbitals have been constructed by solving the modified 2 x 2 Roothaan's equations. From the zeroth order ground-state wave function the charge distributions, dipole moments and carbon 13-proton nuclear spin-spin coupling constants have been calculated. Results show that the chemical formula, represented with the zeroth order of the perturbation theory, is a good order of the approximation for the study of the molecule. For diatomic molecules the equilibrium interatomic distances and harmonic force constants have been calculated up to the third order of the perturbation theory. The second order of the perturbation theory provides results which are very near to the MO-LCAO-SCF calculations. The main advantage of the PCILO method lies in much saving of the computing time.

scholarly journals g-FUNCTION IN PERTURBATION THEORY

2004 ◽  
Vol 19 (15) ◽  
pp. 2545-2559
Author(s):  
ANATOLY KONECHNY
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Perturbation Theory ◽  
Beta Function ◽  
Open String ◽  
Quantum Field ◽  
Two Dimensional ◽  
Third Order ◽  
The Third ◽  
The Given

We present some explicit computations checking a particular form of gradient formula for a boundary beta function in two-dimensional quantum field theory on a disk. The form of the potential function and metric that we consider were introduced in Refs. 16 and 18 in the context of background independent open string field theory. We check the gradient formula to the third order in perturbation theory around a fixed point. Special consideration is given to situations when resonant terms are present exhibiting logarithmic divergences and universal nonlinearities in beta functions. The gradient formula is found to work to the given order.

scholarly journals THERMAL EFFECTS IN JAYNES–CUMMINGS MODEL DERIVED WITH LOW-TEMPERATURE EXPANSION

2011 ◽  
Vol 22 (10) ◽  
pp. 1015-1062 ◽  
Author(s):  
HIROO AZUMA ◽  
MASASHI BAN
Keyword(s):  
Perturbation Theory ◽  
Low Temperature ◽  
Thermal Effects ◽  
Temperature Limit ◽  
Rabi Oscillations ◽  
Third Order ◽  
Perturbative Approach ◽  
Thermal Equilibrium State ◽  
Temperature Expansion ◽  
The Third

In this paper, we investigate thermal effects of the Jaynes–Cummings model (JCM) at finite temperature with a perturbative approach. We assume a single two-level atom and a single cavity mode to be initially in the thermal equilibrium state and the thermal coherent state, respectively, at a certain finite low temperature. Describing this system with Thermo Field Dynamics formalism, we obtain a low-temperature expansion of the atomic population inversion in a systematic manner. Letting the system evolve in time with the JCM Hamiltonian, we examine thermal effects of the collapse and the revival of the Rabi oscillations by means of the third-order perturbation theory under the low-temperature limit, that is to say, using the low-temperature expansion up to the third-order terms. From an intuitive discussion, we can expect that the period of the revival of the Rabi oscillations becomes longer as the temperature rises. Numerical results obtained with the perturbation theory reproduce well this temperature dependence of the period.

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