Derivation of the equation of motion for resonantly excited molecular J aggregates taking into account multiparticle effects

Extreme and Topological Dissipative Solitons with Structured Matter and Structured Light

“…If we also take into account the system of equations for two-particle averages, then we can thus take into account the pair correlations between the molecules. Further, we will present a derivation of both the refined Bloch equations and the system of equations that takes into account the pair correlations between molecules [23,24,25,26].…”

“…The next step is to calculate the relaxation terms associated with the exciton-exciton annihilation and close the resulting system of equations by factoring the many-particle averages, when they are represented as products of averages from the operators in the basic set. The rules of factorization are described in sufficient detail in Reference [23], see also References [27,30,32]. We indicate here only the interpretation of the averages of the operators of the basis set.…”

“…Averaging Equation (16) over the density matrix of the system and using the Markov process approximation, this equation can be formally solved [23], and the result can be substituted into the averaged Equation (15). As a result, we obtain the expression for the contribution to the relaxation of the system associated with the mechanism of exciton-exciton annihilation: d〈Nme〉dt=−true∑p≠m{wmp〈NmeNpe〉+Retrue∑leftk≠pk≠mfalse[false(Γpmmk+i2Δpmmkfalse)〈Nmebk+bp〉+false(Γmppk+i2Δmppkfalse)〈Npebk+bm〉false]false} where constants Δpmmk, Γpmmk, and wm…”

“…Averaging Equation (13) and using Equation (17), we obtain the equation for evolution of 〈 N me 〉. In order to close the system of equations into which it enters, it is necessary to carry out factorization of many-particle terms in these equations [23]. As a result, we find d〈Nme〉dt=−γ2〈Nme〉+i{−12ℏfalse(μ12e1false)E1false(〈bm〉−〈bm+〉false)++1ℏtrue∑n≠m[false(Δm n+i γm nfalse)〈bn+〉〈bm〉−false(Δm n−i γm nfalse)〈bm+〉〈bn〉]}−true∑l≠m{wml〈…”

“…As a result, a closed system of equations arises in which two-particle correlations between molecules are taken into account. Their cumbersome form is given in Reference [23].…”