Related papers: Log-anharmonic oscillator and its large-N solution
In this paper, an approximate solution to a specific class of the Fokker-Planck equation is proposed. The solution is based on the relationship between the Schr\"{o}dinger type equation with a partially confining and symmetrical potential.…
In this paper, we develop a consistent extension of RPA for bosonic systems. In order to illustrate the method, we consider the case of the anharmonic oscillator. We compare our results with those obtained in mean-field and standard RPA…
The new perturbation theory for the problem of nonstationary anharmonic oscillator with polynomial nonstationary perturbation is proposed. As a zero order approximation the exact wave function of harmonic oscillator with variable frequency…
A class of short-range potentials on the line is considered as an asymptotically vanishing phenomenological alternative to the popular confining polynomials. We propose a method which parallels the analytic Hill-Taylor description of…
We propose a new method to obtain approximate solutions for the Schr\"{o}dinger equation with an arbitrary potential that possesses bound states. This method, relying on the auxiliary field technique, allows in many cases to find analytical…
The role of anharmonic effects on the excitation of the double giant dipole resonance is investigated in a simple macroscopic model.Perturbation theory is used to find energies and wave functions of the anharmonic ascillator.The cross…
We present analytical calculations and numerical simulations for the synchronization of oscillators interacting via a long range power law interaction on a one dimensional lattice. We have identified the critical value of the power law…
We present an approximative calculation of the ground-state energy for the anisotropic anharmonic oscillator Using an instanton solution of the isotropic action $\delta = 0$, we obtain the imaginary part of the ground-state energy for small…
For lambda phi^4 models, the introduction of a large field cutoff improves significantly the accuracy that can be reached with perturbative series but the calculation of the modified coefficients remains a challenging problem. We show that…
This paper presents an investigation into the high-order asymptotic expansion for 2D and 3D cubic nonlinear Klein-Gordon equations in the non-relativistic limit regime. There are extensive numerical and analytic results concerning that the…
The diffusive behavior of a harmonic oscillator driven by a Mittag-Leffler noise is studied. Using Laplace analysis we derive exact expressions for the relaxation functions of the particle in terms of generalized Mittag-Leffler functions…
Anharmonic oscillators with the sextic and decatic potentials are studied employing the refinable interpolating scale functions. This method yields highly accurate values of both energy eigenvalues and eigenfunctions for the sextic and…
We obtain tight upper and lower bounds to the eigenvalues of an anharmonic oscillator with a rational potential. We compare our bounds with results given by other approaches.
In an earlier paper it was argued that the conventional double-scaling limit of an O(N)-symmetric quartic quantum field theory is inconsistent because the critical coupling constant is negative and thus the integral representing the…
We consider a two-body quantum system in dimension one composed by a test particle interacting with an harmonic oscillator placed at the position $a>0$. At time zero the test particle is concentrated around the position $R_0$ with average…
The simplicity and the efficiency of a quasi-analytical method for solving nonlinear ordinary differential equations (ODE), is illustrated on the study of anharmonic oscillators (AO) with a potential $V(x) =\beta x^{2}+x^{2m}$ ($m>0$). The…
A recently developed linear algebraic method for the computation of perturbation expansion coefficients to large order is applied to the problem of a hydrogenic atom in a magnetic field. We take as the zeroth order approximation the $D…
multiplication operator on a Hilbert space may be approximated with finite sections by choosing an orthonormal basis of the Hilbert space. Nonzero multiplication operators on $L^2$ spaces of functions are never compact and then such…
We use an expansion in angular mode functions in order to solve the Boltzmann equation for a gluon plasma undergoing longitudinal expansion. By comparing with the exact solution obtained numerically by other means we show that the expansion…
I propose a new version of the Rayleigh - Schr\"{o}dinger perturbation method. It admits a lower triangular matrix in place of the usual diagonal propagator. Illustrated on rational anharmonicities polynomial}(x)/polynomial}(x), treated as…