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H. Kleinert

Publications and source records attributed to H. Kleinert.

At least 55 records · Page 3Linked to original sources
arXiv2003

Summing Non-Borel Tunnelling Amplitudes by Variational Perturbation Theory

We present a method for extracting tunnelling amplitudes from perturbation expansions which are always divergent and not Borel-summable. We show that they can be evaluated by an analytic continuation of variational perturbation theory. The power of the method is illustrated by calculating the imaginary parts of the partition function of the anharmonic oscillator in zero spacetime dimensions and of the ground state energy of the anharmonic oscillator for all negative values of the coupling constant $g$ and show that they are in excellent agreement with the exactly known values. As a highlight of the theory we recover from the divergent perturbation expansion of the tunnelling amplitude the action of the instanton and the effects of higher loop fluctuations around it.

hep-th↗
arXiv2003

Dependence of Variational Perturbation Expansions on Strong-Coupling Behavior. Inapplicability of delta-Expansion to Field Theory

We show that in applications of variational theory to quantum field theory it is essential to account for the correct Wegner exponent omega governing the approach to the strong-coupling, or scaling limit. Otherwise the procedure either does not converge at all or to the wrong limit. This invalidates all papers applying the so-called delta-expansion to quantum field theory.

hep-th↗
arXiv2003

Perturbatively Defined Effective Classical Potential in Curved Space

The partition function of a quantum statistical system in flat space can always be written as an integral over a classical Boltzmann factor $\exp[ -βV^{\rm eff cl({\bf x}_0)]$, where $V^{\rm eff cl({\bf x}_0)$ is the so-called effective classical potential containing the effects of all quantum fluctuations. The variable of integration is the temporal path average ${\bf x_0\equiv β^{-1}\int_0^ βdτ{\bf x}(τ)$. We show how to generalize this concept to paths $q^μ(τ)$ in curved space with metric $g_{μν(q)$, and calculate perturbatively the high-temperature expansion of $V^{\rm eff cl(q_0)$. The requirement of independence under coordinate transformations $q^μ(τ)\to q'^μ(τ)$ introduces subtleties in the definition and treatment of the path average $q_0^μ$, and covariance is achieved only with the help of a suitable Faddeev-Popov procedure.

quant-ph↗
arXiv2002

Gauge-invariant critical exponents for the Ginzburg-Landau model

The critical behavior of the Ginzburg-Landau model is described in a manifestly gauge-invariant manner. The gauge-invariant correlation-function exponent is computed to first order in the $4-d$ and $1/n$-expansion, and found to agree with the ordinary exponent obtained in the covariant gauge, with the parameter $α=1-d$ in the gauge-fixing term $(\partial_μA_μ)^2 /2 α$.

cond-mat↗
arXiv2002

Integrals over Products of Distributions from Manifest Coordinate Invariance of Perturbation Expansions of Path Integrals in Curved Space

We show that the requirement of manifest coordinate invariance of perturbatively defined quantum-mechanical path integrals in curved space leads to an extension of the theory of distributions by specifying unique rules for integrating products of distributions. The rules are derived using equations of motion and partial integration, while keeping track of certain minimal features stemming from the unique definition of all singular integrals in 1 - epsilon dimensions. Our rules guarantee complete agreement with much more cumbersome calculations in 1- epsilon dimensions where the limit epsilon --> 0 is taken at the end. In contrast to our previous papers where we solved the same problem for an infinite time interval or zero temperature, we consider here the more involved case of finite-time (or non-zero temperature) amplitudes.

quant-ph↗
arXiv2002

Flashing Dark Matter-- Gamma-Ray Bursts from Relativistic Detonations of Electro-Dilaton Stars

We speculate that the universe is filled with stars composed of electromagnetic and dilaton fields which are the sources of the powerful gamma-ray bursts impinging upon us from all directions of the universe. We calculate soliton-like solutions of these fields and show that their energy can be converted into a relativistic plasma in an explosive way. As in classical detonation theory the conversion proceeds by a relativistic self-similar solution for a spherical detonation wave which extracts the energy from the scalar field via a plasma in the wave front.

gr-qc↗
arXiv2002

Integrals over Products of Distributions and Coordinate Independence of Zero-Temperature Path Integrals

In perturbative calculations of quantum-statistical zero-temperature path integrals in curvilinear coordinates one encounters Feynman diagrams involving multiple temporal integrals over products of distributions, which are mathematically undefined. In addition, there are terms proportional to powers of Dirac delta-functions at the origin coming from the measure of path integration. We give simple rules for integrating products of distributions in such a way that the results ensure coordinate independence of the path integrals. The rules are derived by using equations of motion and partial integration, while keeping track of certain minimal features originating in the unique definition of all singular integrals in $1 - ε$ dimensions. Our rules yield the same results as the much more cumbersome calculations in 1- epsilon dimensions where the limit epsilon --> 0 is taken at the end. They also agree with the rules found in an independent treatment on a finite time interval.

quant-ph↗
arXiv2001

Langevin Equation for Particle in Thermal Photon Bath

The forward--backward path integral describing a charged particle moving in a thermal bath of photons is expressed in terms of the solution of a Langevin-type of equation. Approximate methods for solving this equation are discussed.

quant-ph↗
arXiv2001

Towards a Simulation of Quantum Computers by Classical Systems

We present a two-dimensional classical stochastic differential equation for a displacement field of a point particle in two dimensions and show that its components define real and imaginary parts of a complex field satisfying the Schroedinger equation of a harmonic oscillator. In this way we derive the discrete oscillator spectrum from classical dynamics. The model is then generalized to an arbitrary potential. This opens up the possibility of efficiently simulating quantum computers with the help of classical systems.

quant-ph↗
arXiv2001

Two-Loop Effective Potential of O(N)-Symmetric Scalar QED in 4-epsilon Dimensions

The effective potential of scalar QED is computed analytically up to two loops in the Landau gauge. The result is given in 4-epsilon dimensions using minimal subtraction and epsilon-expansions. In three dimensions, our calculation is intended to help throw light on unsolved problems of the superconducting phase transition, where critical exponents and the position of the tricritical point have not yet found a satisfactory explanation within the renormalization group approach.

cond-mat↗
arXiv2001

Quantum-Liouville and Langevin Equations for Gravitational Radiation Damping

From a forward--backward path integral, we derive a master equation for the emission and absorption of gravitons by a massive quantum object in a heat bath of gravitons. Such an equation could describe collapse phenomena of dense stars. We also present a useful approximate Langevin equation for such a system.

quant-ph↗
arXiv2000

Master Equation for Electromagnetic Dissipation and Decoherence of Density Matrix

We set up a forward--backward path integral for a point particle in a bath of photons to derive a master equation for the density matrix which describes electromagnetic dissipation and decoherence. As an application, we recalculate the Weisskopf-Wigner formula for the natural line width of an atomic state at zero temperature and find, in addition, the temperature broadening caused by the decoherence term.

cond-mat↗
arXiv2000

Three-loop critical exponents, amplitude functions, and amplitude ratios from variational perturbation theory

We use variational perturbation theory to calculate various universal amplitude ratios above and below T_c in minimally subtracted phi^4-theory with N components in three dimensions. In order to best exhibit the method as a powerful alternative to Borel resummation techniques, we consider only to two- and three-loops expressions where our results are analytic expressions. For the critical exponents, we also extend existing analytic expressions for two loops to three loops.

cond-mat↗
arXiv2000

Second Topological Moment < m^2 > of Two Closed Entangled Polymers

We calculate the second topological moment < m^2 > of entanglement of two closed polymers $P_1$ and $P_2$ in a solution. The result holds approximately for a closed polymer linked to many others, which may be considered as a single very long effective polymer.

cond-mat↗
arXiv2000

Self-Consistent Effective Action for Quantum Particle with Space-Dependent Mass

We calculate the quantum corrections to the classical action of a particle with coordinate-dependent mass. The result is made self-consistent by a variational approach, thus making it applicable to strong-couplings and singular potentials. By including thermal fluctuations, the we obtain an effective action whose classical Euler-Lagrange equation describes the motion of a particle including quantum and thermal effects.

quant-ph↗
arXiv2000

Functional Differential Equations for the Free Energy and the Effective Energy in the Broken-Symmetry Phase of phi^4-Theory and Their Recursive Graphical Solution

Extending recent work on QED and the symmetric phase of the euclidean multicomponent scalar ϕ^4-theory, we construct the vacuum diagrams of the free energy and the effective energy in the ordered phase of ϕ^4-theory. By regarding them as functionals of the free correlation function and the interaction vertices, we graphically solve nonlinear functional differential equations, obtaining loop by loop all connected and one-particle irreducible vacuum diagrams with their proper weights.

hep-th↗