Numerical study of the one-dimensional Frenkel Hamiltonian with on-site randomness is carried out. We focus on the statistics of the energy levels near the lower exciton band edge, i.e., those determining optical response. We found that the distribution of the energy spacing between the states that are well localized at the same segment is characterized by a nonzero mean, i.e. these states undergo repulsion. This repulsion results in a local discrete energy structure of a localized Frenkel exciton. On the contrary, the energy spacing distribution for weakly overlapping local ground states ͑the states with no nodes within their localization segments͒ that are localized at different segments has zero mean and shows almost no repulsion. The typical width of the latter distribution is of the same order of magnitude as the typical spacing in the local discrete energy structure so that this local structure is hidden; it does not reveal itself either in the density of states or in the linear absorption spectra. However, this structure affects the two-exciton transitions involving the states of the same segment and can be observed by the pump-probe spectroscopy. We analyze also the disorder degree scaling of the first and second momenta of the distributions.

We argue that the time-resolved spectrum of selectively-excited resonance fluorescence at low temperature provides a tool for probing the quantum-mechanical level repulsion in the Lifshits tail of the electronic density of states in a wide variety of disordered materials. The technique, based on detecting the fast growth of a fluorescence peak that is redshifted relative to the excitation frequency, is demonstrated explicitly by simulations on linear Frenkel exciton chains. DOI: 10.1103/PhysRevLett.98.087401 PACS numbers: 78.30.Ly, 71.35.Aa, 73.20.Mf, 78.47.+p Anderson localization is a key concept in understanding the transport properties and optical dynamics of quasiparticles in disordered systems in general [1][2][3] and in a large variety of low-dimensional materials, in particular. Examples of current interest are conjugated polymers [4], molecular J aggregates [5,6], semiconductor quantumwells [7,8] and quantum wires [9], as well as biological antenna complexes [10,11]. Localization results in the appearance of a Lifshits tail in the density of states (DOS) below the bare quasiparticle band [12,13]. At low temperature, the states in the tail determine the system's transport and optical properties. Of particular importance for the dynamics and the physical properties is the spatial overlap between these states. Two situations can be distinguished: states that do not overlap can be infinitesimally close in energy, while states that do overlap undergo quantum-mechanical level repulsion. Interestingly, this repulsion does not manifest itself in the overall level statistics, which, due to the localization, is of Poisson nature. The local Wigner-Dyson statistics, caused by the repulsion, turn out to be hidden under the global distribution of energies [14]. Still, due to the characteristic energy scale associated with the level repulsion, this phenomenon does affect global properties, such as transport [15]. Moreover, observing changes in the level statistics allows one to detect the localization-delocalization transition or mobility edges [3].Thus, it is of general interest to have experimental probes for the level statistics in disordered systems. Recently, it has been shown that near-field spectroscopy [16,17] and time-resolved resonant Rayleigh scattering [18] may be used to uncover the statistics of localized Wannier excitons in disordered quantum wells [16] and wires [17]. In this Letter, we argue that low-temperature, time-resolved, selectively-excited fluorescence from the Lifshits tail provides an alternative tool for probing the level repulsion. This method is based on the fact that downward relaxation between spatially overlapping states dominates the early-time rise of a fluorescence peak that is redshifted relative to the excitation frequency. The redshift is related to the level repulsion. We will demonstrate this by simulations on a one-dimensional (1D) Frenkel exciton model with diagonal disorder. The key ingredients of the model -level repulsion and scattering rates proportional to the phonon...

We study theoretically diffusion of one-dimensional Frenkel excitons in J-aggregates at temperatures that are smaller or of the order of the J-band width. We consider an aggregate as an open linear chain with uncorrelated on-site (diagonal) disorder that localizes the exciton at chain segments of size smaller than the full chain length. The exciton diffusion over the localization segments is considered as incoherent hopping. The diffusion is probed by the exciton fluorescence quenching which is due to the presence of point traps in the aggregate. The rate equation for populations of the localized exciton states is used to describe the exciton diffusion and trapping. We show that there exist two regimes of the exciton diffusion at low temperatures. The first, slower one, involves only the states of the very tail of the density of states, while the second, much faster one, also involves the higher states that are close to the bottom of the exciton band. The activation energy for the first regime of diffusion is of the order of one fifth of the J-band width, while for the second one it is of the order of the full J-band width. We discuss also the experimental data on the fast low-temperature exciton-exciton annihilation reported recently by I. G. Scheblykin et al, J. Phys. Chem. B 104, 10949 (2000). PACS numbers: 71.35.Aa; 78.30.Ly; 78.66.Qn; 78.67.-n materials and structures * On leave from Ioffe Physiko-Technical Institute, 26 Politechnicheskaya str., 194021 Saint-Petersburg, Russia † On leave from "S.I. Vavilov State Optical Institute", Saint-Petersburg, Russia.this localization is the appearance of states below the bottom of the bare exciton band. These states form the tail of the density of states (DOS) and carry almost the whole oscillator strength of the aggregate. For this reason the one-exciton absorption in J-aggregates is spectrally located at the tail of the DOS (see, for instance, Refs. 9, 10) and the width of the absorption band is of the order of the width of the DOS tail.

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We present a theoretical analysis of low-temperature quenching of one-dimensional Frenkel excitons that are localised by moderate on-site (diagonal) uncorrelated disorder. Exciton diffusion is considered as an incoherent hopping over localization segments and is probed by the exciton fluorescence quenching at point traps. The rate equation is used to calculate the temperature dependence of the exciton quenching. The activation temperature of the diffusion is found to be of the order of the width of the exciton absorption band. We demonstrate that the intra-segment scattering is extremely important for the exciton diffusion. We discuss also experimental data on the fast exciton-exciton annihilation in linear molecular aggregates at low temperatures.