Field-free dissipation

Here, Spt denotes the field-dressed dissipation contribution and will be treated later in terms of a set of auxiliary operators [cf. Eq. (B.4)] that couple to the primary reduced density operator. C t) is the deterministic Liouvillian in the presence of external field [cf. Eq. (2.2)]. The field-free dissipation TZq assumes the second-order cumulant result and is given by [38]... 

The CODDE formulation of CS-QDT [Eqs. (2.21)] couples between p t) and a set of auxiliary operators K t) m > 0 that describe the effects of correlated driving and dissipation. The field-free dissipation action, TZs [Eq. (2.18)], can be evaluated relatively easily in terms of the causality spectral function Cab ( ) without going through the parameterization procedure of Eq. (2.24). The latter is required only for the correlated driving-dissipation effects described by the auxiliary operators. Methods of evaluating both the reduced dynamics p(t) and the reduced canonical density operator Peq(T) will be discussed in Sec. 3. 

Consider now the time-local POP-CS-QDT for the DBO dynamics. The detailed derivation was given in Ref. [38]. The simplicity in the time-local formulation of this system relies on the fact that the Q [Eq. (2.19)] in the field-free dissipation TZs [Eq. (2.18)] reads as [38]... 

MORE ABOUT THE FIELD-FREE DISSIPATION CONTRIBUTIONS... 

The detailed analysis on various approximation schemes can now be made in contact with the exact results established for the DBO system. Let us start with the comparison between the exact [Eq. (4.6b)] and the 7 [Eq. (4.11a)] that governs the field-free dissipation in both the POP-CS-QDT and the CODDE for the DBO system. We immediately arrive at the following useful informations on the concerned second-order approximations [cf. Eq. (4.9)]. 

We now focus on the comparison between the CODDE [Eq. (2.21)] and the POP-CS-QDT [Eqs. (2.17), (B.4) and (B.6)]. These two formulations share the identical long time and thermal equilibrium behaviors characterized by their common field-free dissipation superoperator TZsj but differ at their correlated driving-dissipation dynamics. With the parameterization expressions for the bath spectral functions (Sec. 2.3) the correlated driving-dissipation dynamics effects may be numerically studied in terms of equations of motion via a set of auxiliary operators, which are Ko, i i, in the CODDE [Eq. (2.21)], and o, in the POP-... 

Together with Eq. (66), this equation describes exactly the linear response of the system to an external field, with arbitrary initial conditions. Its physical meaning is very simple and may be explained precisely as for Eq. (66) 32 the evolution of the velocity distribution results in two effects (1) the dissipative collisions between the particles which are described by the same non-Markoffian collision operator G0o(T) 35 1 the field-free case and (2) the acceleration of the particles due to the external field. As we are interested in a linear theory, this acceleration only affects the zeroth-order distribution function It is... 

The first term in Eq. (1) describes the density matrix evolution under dissipation and field free conditions. The system-field interaction in the dipole approximation is... 

Here, can be easily evaluated via Eq. (3.7), but with TZs there being replaced by TZu [cf. Eq. (B.12b)] that may be considered as the Markovian dissipation superoperator. This statement may be supported by the arguments that the Markovian approximation amounts to the following two conditions (i) The bath correlation time is short compared with the reduced system dynamics (ii) The correlated effects of driving and dissipation can be neglected so that the Green s function G(t r) in the memory kernel can be replaced by its field-free counterpart Gs t t) = In this case, Eq. (B.9) reduces to... 

In this section we first (Section IV A) derive a formal expression for the channel phase, applicable to a general, isolated molecule experiment. Of particular interest are bound-free experiments where the continuum can be accessed via both a direct and a resonance-mediated process, since these scenarios give rise to rich structure of 8 ( ), and since they have been the topic of most experiments on the phase problem. In Section IVB we focus specifically on the case considered in Section III, where the two excitation pathways are one- and three-photon fields of equal total photon energy. We note the form of 8 (E) = 813(E) in this case and reformulate it in terms of physical parameters. Section IVC considers several limiting cases of 813 that allow useful insight into the physical processes that determine its energy dependence. In the concluding subsection of Section V we note briefly the modifications of the theory that are introduced in the presence of a dissipative environment. 

The energy dissipation of a system containing free charges subjected to electric fields Is well known but this Indicates a non-equilibrium situation and as a result a thermodyanmlc description of the FDE Is Impossible. Within the framework of interionic attraction theory Onsager was able to derive the effect of an electric field on the Ionic dissociation from the transport properties of the Ions In the combined coulomb and external fields (2). It is not improper to mention here the notorious mathematical difficulty of Onsager s paper on the second Wien effect. 

The analysis of plane waves is straightforward in several respects. As soon as we begin to consider waves varying in more than one space dimension, however, we will encounter new phenomena that further complicate the analysis. This also applies to the superposition of elementary modes to form wavepackets. In this section an attempt is made to investigate dissipation-free axially symmetric modes in presence of a nonzero electric field divergence... 

The main scheme is shown in Fig. 17. The photogenerated electron hole pairs transfer to the soliton-antisoliton pairs in 10 13s. Two kinks appeared in the polymer structure, which separates the degenerated regions. Due to the degeneration, two charged solitons may move without energy dissipation in the electric field and cause the photoconductivity. The size of the soliton was defined as 15 monomer links with the mass equal to the mass of the free electron. In the scheme in Fig. 17, the localized electron levels in the forbidden gap correspond to the free ( + ) and twice occupied ( — ) solitons. The theory shows the suppression of the interband transitions in the presence of the soliton. For cis-(CH)n the degeneration is absent, the soliton cannot be formed and photoconductivity practically does not exist. 

The basic difference between free fields and interacting fields would be of the same order as between a small (reversible) mechanical system and ergodic dissipative systems. But this means that physical states can no longer be associated with invariants of motion which no longer exist. This leads to deep changes in the structure of the theory. 

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