Lithuanian Journal of Physics article / Lietuvos fizikos žurnalo straipsnis

NONLINEAR EXCITON EQUATION FACTORIZATION FOR NON-PERTURBATIVE ABSORPTION MODELLING
Vytautas Bubilaitis and Darius Abramavičius
Institute of Chemical Physics, Faculty of Physics, Vilnius University, Saulėtekio 3, 10257 Vilnius, Lithuania
Email: vytautas.bubilaitis@ff.vu.lt

Received 22 June 2024; revised 9 August 2024; accepted 5 September 2024

Various types of optical spectra of molecular systems are often analyzed via perturbative series expansion in the powers of optical field. The simplest absorption is related to the linear optical response. However, observed spectral features can be mislabelled if higher orders are not vanishing. High-intensity excitation field breaks the established assumption of quickly converging perturbative regime. Non-perturbative quantum methods can solve these problems. However, they lead to endless hierarchies of equations that, in general, cannot be solved analytically. Dropping terms at a specific order or factorizing (expressing high-order terms as products of several lower-order terms) can be used to close the hierarchy. We propagate the nonlinear exciton equations (NEE) with exciton–exciton annihilation (EEA) non-perturbatively in a high-excitation regime and calculate absorption spectra of a molecular aggregate using various factorization schemes. The results demonstrate that the solution is weakly sensitive to the factorization method when EEA is included.
Keywords: non-perturbative, exciton–exciton annihilation, molecular aggregate, nonlinear exciton equations, factorization

NETIESINIŲ EKSITONŲ LYGČIŲ FAKTORIZAVIMAS: NEARTUTINIS SUGERTIES SPEKTRŲ MODELIAVIMAS
Vytautas Bubilaitis, Darius Abramavičius

Vilniaus universiteto Fizikos fakulteto Cheminės fizikos institutas, Vilnius, Lietuva

Įprasta molekulines sistemas tirti artutiniame režime, naudojant trikdymų teoriją, kuri leidžia apibrėžti ir pasitelkti atsako funkcijas. Tačiau jei trikdymų eilutė lėtai konverguoja (arba diverguoja), spektrinių savybių prigimtis gali būti klaidingai interpretuojama. Artutinis trikdymų teorijos režimas gali netikti esant dideliam žadinančio lauko intensyvumui. Vienas iš reiškinių, pasireiškiančių su dideliu žadinimo intensyvumu yra eksitono–eksitono anihiliacija (EEA). Tokio tipo uždavinius galima spręsti naudojant netiesines eksitonų lygtis (NEL). Kadangi tai yra begalinės lygčių hierarchijos, lygčių hierarchijos „uždarymui“ būtina arba atmesti tam tikros eilės lygčių narius, arba juos faktorizuoti, t. y. išreikšti mažesnės eilės narių sandauga. Tai gali lemti netikėtus rezultatus: lygčių sprendiniai gali diverguoti, atsirasti nefizikiniai efektai. Šiame darbe aprašomos netiesinės eksitonų lygtys su EEA nariais, naudojant skirtingas faktorizavimo schemas didelio žadinimo režime, ir kaip tai atsispindi sugerties spektre. Suskaičiuoti nuo žadinimo intensyvumo priklausantys sugerties spektrai rodo, kad dėl didelio žadinimo intensyvumo atsiranda papildomos sugerties juostos, kurių padėtis stipriai priklauso nuo žadinimo intensyvumo. Išsiaiškinta, kad spektrų elgsena labai jautri nelyginės eilės narių faktorizavimui, bet lygtyse įmanoma parinkti tokį faktorizavimo metodą, kuris atitiktų konkretų eksperimentą. EEA labai pasitarnauja stabilizuojant sprendinius, skirtumai tarp įvairių faktorizavimo schemų susilpnėja. Tokiu būdu, naudojant NEL, galima sukurti labai efektyvias modeliavimo metodikas, kurios tiktų įvairiems matavimams.

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