Functional Integrals in the Strong Coupling Regime and the Polaron Self‐Energy

Abstract

A general method of representation of functional integrals in the strong coupling regime is developed. This method is applied to the computing of polaron ground state energy at large coupling constant.Es wird eine allgemeine Methode zur Darstellung von Funktionalintegralen im Bereich starker Kopplung entwickelt. Diese Methode wird angewendet, um die Polaronengrundzustandsenergie bei groI3er Kopplungskonstante zu berechnen.

Operator method in solving non-linear equations of the Hartree-Fock type

“…−0.1078 Smondyrev [32] −0.109206 Efimov et al [15] −0.10843 Ganbold et al [16] −0.107766 Chen et al [27] −0.10851 Hagen et al [30] −0.02048 −0.00804 Balabaev et al [31] −0.0206 −0.00832 Our results −0.1085128052 −0.02053101 −0.0083506…”

“…The Hamiltonian of a non-relativistic particle (electron) interacting with the quantized scalar field of lattice oscillations in an ionic crystal has the form (see, for example, refs. [6,7,15,16] and reviews [17,18]):…”

Equations of State for Simple Liquids from the Gaussian Equivalent Representation Method

“…First, we shift the variable of integration φ(x) −→ φ(x) + ξ(x). Second, we write the functional of interactions in the normal form with respect to Gauss measure for new kernel B −1 (x 1 , x 2 ), we obtain For more details see [5,6].…”

“…The Gaussian equivalent representation method has been recently introduced by Efimov and Ganbold in the context of quantum-field theory and statistical physics to compute integrals over Gaussian measure [5,6,7]. The GER approach has already been proven to be very effective for computing thermodynamic properties and structural quantities of simple classical many-particle systems interacting with purely repulsive potentials like the Gausscore or the Yukawa potential, possessing positive Fourier coefficients [8,9,10] as well as for calculating the thermodynamics properties of flexible polymer systems [11,12].…”

On a new application of the path integrals in polymer statistical physics

“…In this case the averaging over the polymer chain conformations is equivalent to the path integration over the Winer's measure [4,5]. However, to the best of our knowledge this approach [6][7][8] to the PDF calculations is not properly addressed in the literature till now. The aim of this work is to fill this gap.…”