Vanishing conductivity of quantum solitons in polyacetylene

Abstract

Quantum solitons or polarons are supposed to play a crucial role in the electric conductivity of polyacetylene, in the intermediate doping regime. We present an exact fully quantized calculation of the quantum soliton conductivity in polyacetylene and show that it vanishes exactly. This is obtained by applying a general method of soliton quantization, based on order-disorder duality, to a Z(2)-symmetric complex extension of the TLM dimerization effective field theory. We show that, in this theory, polyacetylene solitons are sine-Gordon solitons in the phase of the complex field.

The Rise of Solitons in Sine-Gordon Field Theory: From Jacobi Amplitude to Gudermannian Function

“…The sine-Gordon field theory and the associated massive Thirring model [1] are some of the best studied quantum field theories. In view of its connections to other important physical models, some of which in principle admit actual realizations in nature [2,3], a huge mass of important exact results have been obtained for this fascinating integrable system [4][5][6][7]. However, no less fascinating are the remarkable mathematical and physical properties of its soliton (or "solitary wave") solutions which have contributed, along the last decades, to turn the physics of solitons into a very active research topic.…”

Travelling-Wave Solutions for Wave Equations with Two Exponential Nonlinearities

“…Although there are other methods to obtain these translation-invariant solutions, e.g., the integral bifurcation method [39], some of these solutions, in particular the Weierstrass solutions of the Tzitzéica class of equations and the amplitude Jacobi solutions of the sine/sinh-Gordon equations cannot be obtained by the tanh method usually employed in the literature. Consequently, with a few exceptions in the case of the amplitude Jacobi solutions [33,34], their potential for realistic physical applications has been ignored in the past. As for the the Weierstrass solutions of the Tzitzéica class of equations, their potential in the area of optical solitons is still to be assessed [28,29].…”

Obtaining a closed-form representation for the dual bosonic thermal Green function by using methods of integration on the complex plane

“…[1], despite the fact that quantum field theories are usually formulated in coordinate space, calculations, in both T = 0 and T ̸ = 0 cases, are almost always performed in momentum space. However, when we are faced with the exact calculation of correlation functions we are naturally led to the problem of finding closed-form expressions for Green functions in coordinate space [2,3].…”