By Alexandre S. Alexandrov, Jozef T. Devreese (auth.)
While easy good points of polarons have been good famous decades in the past and feature been defined in a few overview papers and textbooks, curiosity within the function of electron-phonon interactions and polaron dynamics in modern fabrics has lately passed through a full of life revival. Electron-phonon interactions were proven to be proper in high-temperature superconductors and giant magnetoresistance oxides, and shipping via nanowires and quantum dots additionally usually relies on vibronic displacements of ions. the ongoing curiosity in polarons extends past actual description of complex fabrics. the sector has been a checking out floor for analytical, semi-analytical, and numerical suggestions, comparable to direction integrals, strong-coupling perturbation enlargement, complicated variational, unique diagonalization, density-matrix renormalization workforce, dynamic mean-field, and quantum Monte Carlo innovations. unmarried and multi-polaron theories have provided a brand new perception in our knowing of high-temperature superconductivity, great magnetoresistance, and the correlated delivery via molecular quantum dots. This e-book studies a few fresh advancements within the box of polarons, beginning with the fundamentals and masking a few energetic instructions of analysis.
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Additional info for Advances in Polaron Physics
The OC spectra calculated within the extended SCE approach, taking into account both the Jahn–Teller eﬀect and the corrections of order α0 , are 44 2 Continuum Polaron Fig. 13. The polaron OC calculated within the extended SCE taking into account corrections of order α0 (solid curve), the OC calculated within the leading-term strong-coupling approximation (dashed curve), with the leading term of the Landau– Pekar (LP) adiabatic approximation (dash-dotted curve), and the numerical DQMC data (open circles) for α = 7, 9, 13, and 15 (from ) shown by the solid curves.
Here, q 2 /2M represents the energy of the center of mass of electron and ﬁctitious particle, and v is the energy gap between the levels of the relative motion. To include dissipation , a ﬁnite lifetime was introduced for the states of the relative motion, which can be considered as the result of the residual EPI not included into the Feynman variational model. To this end, in χm (q, t) the factor exp [−ivt] was replaced with (1 + it/τ )−vτ which leads to the replacement of δ-functions by Gamma functions with mean value and variance given, respectively, by q 2 /2M + nv and nv/τ .
79) exp(−i |t − s|) + 2P (β) cos(t − s) |r(t) − r(s)| + exp(+i |t − s|) + 2P (β) cos(t − s) |r (t) − r (s)| − 2 [exp(−i (t − s)) + 2P (β) cos(t − s)] dtds, |r (t) − r(s)| −1 where P (β) = eβ − 1 . 78) is over paths which satisfy the boundary condition r(t) − r (t) = 0 at times t approaching ±∞. 79) is supposed to be exact . Clearly to provide analytical solutions at all α presumably is impossible. Following Feynman’s idea to describe the ground-state energy properties of a polaron by introducing a parabolic “retarded” interaction of the electron with itself (see Sect.
Advances in Polaron Physics by Alexandre S. Alexandrov, Jozef T. Devreese (auth.)