arXiv subjects

Bodo Hamprecht

Publications and source records attributed to Bodo Hamprecht.

5 recordsLinked to original sources

arXiv2004

Variational Perturbation Theory for Fokker-Planck Equation with Nonlinear Drift

We develop a recursive method for perturbative solutions of the Fokker-Planck equation with nonlinear drift. The series expansion of the time-dependent probability density in terms of powers of the coupling constant is obtained by solving a set of first-order linear ordinary differential equations. Resumming the series in the spirit of variational perturbation theory we are able to determine the probability density for all values of the coupling constant. Comparison with numerical results shows exponential convergence with increasing order.

cond-mat.stat-mech↗

arXiv2002

Recursive Weak- and Strong Coupling Expansions in a Cosine Potential

For the Cos(2x)-Potential the coefficients of the weak- and strong coupling perturbation series of the ground state energy are constructed recursively. They match the well-known expansion coefficients of the Mathieu equation's characteristic values. However presently there is no physically intuitive method to extract the coefficients of the strong coupling series from those of the weak one. The standard rule while giving exellent results for the anharmonic oscillator fails completely in this case.

quant-ph↗

arXiv2002

Exact Solutions of the Time Dependent Schroedinger Equation in One Space Dimension

A closed expression for the harmonic oscillator wave function after the passage of a linear signal with arbitrary time dependence is derived. Transition probabilities are simple to express in terms of Laguerre polynomials. Spontaneous transitions are neglected. The exact result is of some interest for the physics of short laser pulses, since it may serve as an accuracy test for numerical methods.

quant-ph↗

arXiv2002

High-Order Variational Perturbation Theory for the Free Energy

In this paper we introduce a generalization to the algebraic Bender-Wu recursion relation for the eigenvalues and the eigenfunctions of the anharmonic oscillator. We extend this well known formalism to the time-dependent quantum statistical Schroedinger equation, thus obtaining the imaginary-time evolution amplitude by solving a recursive set of ordinary differential equations. This approach enables us to evaluate global and local quantum statistical quantities of the anharmonic oscillator to much higher orders than by evaluating Feynman diagrams. We probe our perturbative results by deriving a perturbative expression for the free energy which is then subject to variational perturbation theory as developed by Kleinert, yielding convergent results for the free energy for all values of the coupling strength.

quant-ph↗

arXiv2001

The Highest-Derivative Version of Variational Perturbation Theory

We systematically investigate different versions of variational perturbation theory by forcing not only the first or second but also higher derivatives of the approximant with respect to the variational parameter to vanish. The choice of the highest derivative version turns out to be the most successful one for approximating the ground-state energy of the anharmonic oscillator. It is therefore used to determine the critical exponent alpha of the specific heat in superfluid 4He in agreement with the value measured in recent space shuttle experiments.

cond-mat↗