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H. Kleinert

Publications and source records attributed to H. Kleinert.

122 records · Page 7Linked to original sources
arXiv1995

Variational Interpolation Algorithm between Weak- and Strong-Coupling Expansions

For many physical quantities, theory supplies weak- and strong-coupling expansions of the types $\sum a_n α^n$ and $ α^p\sum b_n (α^{-2/q) ^n$, respectively. Either or both of these may have a zero radius of convergence. We present a simple interpolation algorithm which rapidly converges for an increasing number of known expansion coefficients. The accuracy is illustrated by calculating the ground state energies of the anharmonic oscillator using only the leading large-order coefficient $b_0$ (apart from the trivial expansion coefficent $a_0=1/2$). The errors are less than 0.5 for all g. The algorithm is applied to find energy and mass of the Fröhlich-Feynman polaron. Our mass is quite different from Feynman's variational approach.

quant-ph↗
arXiv1995

Brownian motion of Massive Particle in a Space with Curvature and Torsion and Crystals with Defects

We develop a theory of Brownian motion of a massive particle, including the effects of inertia (Kramers' problem), in spaces with curvature and torsion. This is done by invoking the recently discovered generalized equivalence principle, according to which the equations of motion of a point particle in such spaces can be obtained from the Newton equation in euclidean space by means of a nonholonomic mapping. By this principle, the known Langevin equation in euclidean space goes over into the correct Langevin equation in the Cartan space. This, in turn, serves to derive the Kubo and Fokker-Planck equations satisfied by the particle distribution as a function of time in such a space. The theory can be applied to classical diffusion processes in crystals with defects.

cond-mat↗
arXiv1995

Geometrical Origin of Tricritical Points of various U(1) Lattice Models

We review the dual relationship between various compact U(1) lattice models and Abelian Higgs models, the latter being the disorder field theories of line-like topological excitations in the systems. We point out that the predicted first-order transitions in the Abelian Higgs models (Coleman-Weinberg mechanism) are, in three dimensions, in contradiction with direct numerical investigations in the compact U(1) formulation since these yield continuous transitions in the major part of the phase diagram. In four dimensions, there are indications from Monte Carlo data for a similar situation. Concentrating on the strong-coupling expansion in terms of geometrical objects, surfaces or lines, with certain statistical weights, we present semi-quantitative arguments explaining the observed cross-over from first-order to continuous transitions by the balance between the lowest two weights (``2:1 ratio'') of these geometrical objects.

hep-lat↗
arXiv1995

Precise variational tunneling rates for anharmonic oscillator with g<0

We systematically improve the recent variational calculation of the imaginary part of the ground state energy of the quartic anharmonic oscillator. The results are extremely accurate as demonstrated by deriving, from the calculated imaginary part, all perturbation coefficients via a dispersion relation and reproducing the exact values with a relative error of less than $10^{-5}$. A comparison is also made with results of a Schrödinger calculation based on the complex rotation method.

hep-th↗
arXiv1995

Five-loop renormalization group functions of ${O}(n)$-symmetric $ϕ^4$-theory and $\ep$-expansions of critical exponents up to $\ep^5$

Motivated by the discovery of errors in six of the 135 diagrams in the published five-loop expansions of the $β$-function and the anomalous dimensions of the ${O}(n)$-symmetric $ϕ^4$-theory in $D=4-\ep$ dimensions we present the results of a full analytic reevaluation of all diagrams. The divergences are removed by minimal subtraction and $\ep$-expansions are given for the critical exponents $η$, $ν$, and $ω$ up to order $ε^5$.

hep-th↗
arXiv1995

Motion of a Rigid Body in Body-Fixed Coordinate System -- for Autoparrallel Trajectories in Spaces with Torsion

We use a recently developed action principle in spaces with curvature and torsion to derive the Euler equations of motion for a rigid body within the body-fixed coordinate system. This serves as an example that the particle trajectories in a space with curvature and torsion follow the straightest paths (autoparallels), not the shortest paths (geodesics), as commonly believed.

hep-th↗
arXiv1995

New Action Principle for Classical Particle Trajectories in Spaces with Torsion

To comply with recent developments of path integrals in spaces with curvature and torsion we find the correct variational principle for the classical trajectories. Although the action depends only on the length, the trajectories are {\em autoparallels} rather than geodesics due to the effects of a new torsion force.

hep-th↗
arXiv1995

Vortex, Defect, and Monopole Gauge Fields for Nambu-Goldstone Systems and their Phase Transitions or Theory of Fluctuating Multivalued Fields

We survey the various uses of singular gauge fields which render an ideal description of ensembles of line- and surface-like excitations and explain phase transitions with the help of simple quadratic actions. Near a transition, the singular gauge fields can be transformed into ordinary complex fields called disorder fields which differ from Landau's order fields by developing a nonzero expectation value in the high-temperature phase.

cond-mat↗
arXiv1995

Exact Five-Loop Renormalization Group Functions of $ϕ^4$-Theory with O(N)-Symmetric and Cubic Interactions. Critical Exponents up to $\ep^5$

The renormalization group functions are calculated in $D=4-ε$ dimensions for the $ϕ^4$-theory with two coupling constants associated with an ${O}(N)$-symmetric and a cubic interaction. Divergences are removed by minimal subtraction. The critical exponents $η$, $ν$, and $ω$ are expanded up to order $ε^5$ for the three nontrivial fixed points O(N)-symmetric, Ising, and cubic. The results suggest the stability of the cubic fixed point for $N\geq3$, implying that the critical exponents seen in the magnetic transition of three-dimensional cubic crystals are of the cubic universality class. This is in contrast to earlier three-loop results which gave $N > 3$, and thus Heisenberg exponents. The numerical differences, however, are less than a percent making an experimental distinction of the universality classes very difficult.

cond-mat↗
arXiv1995

Quantum Langevin equation from forward--backward path integral

The quantum Langevin equation is derived from the Feynman-Veron forward--backward path integral representation for a density matrix of a quantum system in a thermal oscillator bath. We exhibit the mechanism by which the classical, $c$-valued noise in the Feynman-Vernon theory turns into an operator-valued quantum noise fulfilling characteristic commutation relation necessary for the unitarity of the time evolution in the quantum Langevin equation.

quant-ph↗
arXiv1995

Decay Rates of Metastable States in Cubic Potential by Variational Perturbation Theory

Variational perturbation theory is used to determine the decay rates of metastable states across a cubic barrier of arbitrary height. For high barriers, a variational resummation procedure is applied to the complex energy eigenvalues obtained from a WKB expansion; for low barriers, the variational resummation procedure converts the non-Borel-summable Rayleigh-Schrö\-din\-ger expansion into an exponentially fast convergent one. The results in the two regimes match and yield very accurate imaginary parts of the energy eigenvalues. This is demonstrated by comparison with the complex eigenvalues from solutions of the Schrödinger equation via the complex-coordinate rotation method.

quant-ph↗
arXiv1995

Scaling property of variational perturbation expansion for general anharmonic oscillator

We prove a powerful scaling property for the extremality condition in the recently developed variational perturbation theory which converts divergent perturbation expansions into exponentially fast convergent ones. The proof is given for the energy eigenvalues of an anharmonic oscillator with an arbitrary $x^p$-potential. The scaling property greatly increases the accuracy of the results.

quant-ph↗