Properties and temperature evolution of the spectrum of localized quasi-particles interacting with polarization phonons in two models

Abstract

Using the Feynman-Pines diagram technique, the energy spectrum of localized quasi-particles interacting with polarization phonons is calculated and analyzed in the wide range of energies at the finite temperature of the system. It is established that the general model of the system, besides the bound states known from the simplified model with an additional condition for the operator of quasi-particles number, contains the new bound states even for the systems with weak coupling. The contribution of multi-phonon processes into the formation of renormalized spectrum of the system is analyzed. The reasons of the appearance, behaviour and disappearance of separate pairs of bound states depending on the coupling constant and temperature are revealed.

Energy spectrum of localized quasiparticles renormalized by multi-phonon processes at finite temperature

“…Localized dispersionless quasiparticles (excitons, impurities and so on) interacting with dispersionless polarization phonons are described by Frohlich Hamiltonian, like in [23]…”

“…The operators of second quantization of quasi-particles ( a ì k , a + ì k ) and phonons ( b ì q , b + ì q ) satisfy the Bose commutative relationships. The renormalized spectrum of quasi-particles interacting with phonons at an arbitrary temperature (T), like in [23], is obtained from the poles of Fourier image of quasi-particle Green's function G( ì k, ω ′ ), which through the Dyson equation…”

“…As far as the problem becomes "zero-dimensional", the complete MO m(ξ) is defined by the infinite sum of indexed diagrams (figure 1). The simple rules for these diagrams presented in [23], allow their definite programming and numerical calculation of all topologically unequal diagrams and their analytical expressions till such a high order over the powers of a coupling constant (α), which is limited by a computer resource only (appendix A). We should note that in this paper all diagrams and their analytical expressions for the MO terms till the tenth order are obtained.…”

“…These diagrams describe the unmixed (u) processes of quasi-particles scattering accompanied either only by the creation (>) or by annihilation (<) of phonons, respectively. After the partial summing, an exact analytical representation for these terms in the form of infinite chain fractions was obtained [23].…”

“…A renormalized spectrum of a localized quasiparticle weakly interacting with phonons at T 0 K was obtained in [23] using the Feynman-Pines diagram technique in the general model with the Frohlich Hamiltonian. It was shown that the new complexes of bound states existed in the system besides the ground and bound states which were known earlier [1,5] from the simplified model with the additional condition for the operators of quasi-particles.…”