By Ilya Prigogine (auth.), Jean Maruani, Roland Lefebvre, Erkki J. Brändas (eds.)

*Advanced subject matters in Theoretical Chemical Physics***is a suite of 20 chosen papers from the clinical displays of the Fourth Congress of the overseas Society for Theoretical Chemical Physics (ISTCP) held at Marly-le-Roi, France, in July 2002. **

*Advanced themes in Theoretical Chemical Physics*** includes a large spectrum during which scientists position precise emphasis on theoretical equipment in chemistry and physics. The chapters within the e-book are divided into 5 sections:**

**I: Advances Chemical Thermodynamics**

**II: digital constitution of Molecular Systems**

**III: Molecular interplay and Dynamics**

**IV: Condensed Matter**

**V: twiddling with Numbers**

This e-book is a useful source for all teachers and researchers attracted to theoretical, quantum or statistical, chemical physics or actual chemistry. It provides a variety of a few of the main complicated equipment, effects and insights during this interesting quarter.

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**Extra resources for Advanced Topics in Theoretical Chemical Physics**

**Example text**

6b). 24) NON-MARKOVIAN QUANTUM DISSIPATION THEORY 37 E. General theory of equilibrium phase-space dispersions This appendix presents the general expressions for evaluating the thermal equilibrium values of (q2) and (P2) in terms of the response function X(t) == Xqq(t) or its causality Fourier transform X(w). la) + iX"(w). lb) The fluctuation-dissipation theorem leads immediately that [cf. Eq. 2b) To obtain Eq. 8(O)). This identity leads also to (qp) = -(pq) = ili/2. 3b) The main purpose of this appendix is to show that Eq.

Eq. 4)J that couple to the primary reduced density operator. C(t) is the deterministic Liouvillian in the presence of external field [ef. Eq. 2)J. , a with Qa = L Cab (-C )Qb. 19) b Here, Cab (-C8 ) is a reduced Liouville-space operator defined by the causality spectral function Cab(W) [Eq. 12)J and the field-free Liouvillian operator C 8 [ef. Eq. 2)J. The direct evaluation of 8pt in Eq. 17) involves in general temporal integrations of operators [ef. Eqs. 4)J which are often numerically too expensive to be practically useful.

Exact dynamics of driven Brownian oscillators The derivation of the exact QDT [Eq. 24)] should be made together with the harmonic bath model. The total composite DBO Hamiltonian NON-MARKOVIAN QUANTUM DISSIPATION THEORY 33 then assumes [ef. Eq. 1c) In the following, we shall present a modified Yan-Mukamel method [30, 53J to construct an exact theory for the reduced DBO dynamics. Let us start with the quantum Langevin force, defined as F(t) eihB(t-to) Fe-ihB(t-to) L Cj{ Xj cos[Wj(t - to)J + :~. sin[wj(t - to)]}.