Aspects of polaron theory: equilibrium and nonequilibrium - download pdf or read online

By N N Bogolubov, Nickolai N Bogolubov Jr

ISBN-10: 9812833986

ISBN-13: 9789812833983

The linear polaron version is a superb instance of an precisely soluble, but nontrivial polaron procedure. It serves as an ordeal approach or zero-level approximation in lots of refined equipment of polaron research. This e-book analyzes, particularly, the opportunity of aid of the whole polaron Hamiltonian to the linear one, and introduces a distinct approach to calculating thermodynamical features in keeping with the calculation of the averages of T-products. This T-product formalism appears to be like a less difficult approach of doing related calculations related to Feynman's direction critical strategy.

This e-book follows a step by step strategy, from relatively easy actual principles to a transparent realizing of refined mathematical instruments of research in smooth polaron physics. The reader is ready to evaluate the actual standpoint with tools proposed within the e-book, and whilst snatch the underlying arithmetic.

a few familiarity with quantum statistical mechanics is fascinating in studying this publication.

Contents: Linear Polaron version; Equilibrium Thermodynamic nation of Polaron approach; Kinetic Equations in Polaron concept.

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37) In the same way, it can be proved that, for ε = −Im Ω > 0 mΩ + (Ω) − η2 > ε. Ω Therefore the function fη (Ω) is a regular function of the complex variable Ω on the two half-planes Im Ω > 0 and Im Ω < 0. 38) in the vicinity of the real axis are Ω= 2πi ¯hβ and Ω = − 2πi . 38) in the vicinity of the real axis are 0 < Im Ω < 2π ¯hβ or in the region 0 > Im Ω > − Then ∫ L 2π . ¯hβ e−iΩ(t−τ ) fη (Ω) dΩ = 0. 3. 39) which contains only a finite number (f ), of terms if the volume V is fixed. 40) const .

72). Let us note that Q(t) = (eiµt a† + e−iµt a) ¯h 2Mµ 1/2 , from which it follows that T {[Q(−is) − Q(−iσ)]2 } = eq ¯h {(eµs a† + e−µs a)(eµs a† + e−µs a) 2Mµ + (eµσ a† + e−µσ a)(eµσ a† + e−µσ a) − 2T (eµs a† + e−µs a)(eµσ a† + e−µσ a)}. Hence T {[Q(−is) − Q(−iσ)]2 } = Here eq ¯h (2 a† a + 2 aa† − 2eµ|s−σ| a† a − 2e−µ|s−σ| aa† ). 2Mµ a† a = 1 e β¯ hµ −1 , aa† = 1 + 1 e β¯ hµ −1 . 6. 76) that T {[rα (−is) − rα (−iσ)]2 } =− + µ2 − ν02 ¯h mµ3 ν0 µ eq 2 ¯h ϑ (s − σ)2 + m m ν0 m 2 |s − σ| 1 1 (1 − e−µ|s−σ| ) − β¯hµ (eµ|s−σ| − 1) 1 − e−β¯hµ e −1 .

104) as before, are equal to 3 T exp i α=1 νj,α Rα (sj ) . 120) α=1 j1 =1 j2 =1 where ν1,α = ν1,α + νN +1,α , ν2,α = ν2,α , ν3,α = ν3,α , = ... , νN ,α = νN ,α . 6. Averaged Operator T-Product Calculus 55 where Rj are real vectors and the integration with respect to each variable νj,α is over the whole real axis. ) dν 1 · · · dν N +1 . 117) shows that the magnitude ... 119), does not depend on ν N +1 , thus the integration over ν N +1 can be done independently: ∫ e−iν j (R1 −RN +1 ) dν N +1 = (2π)3 δ(R1 − RN +1 ).

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Aspects of polaron theory: equilibrium and nonequilibrium problems by N N Bogolubov, Nickolai N Bogolubov Jr

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