Abstract: The autoregressive neural networks are emerging as a powerful computational tool to solve relevant problems in classical and quantum mechanics. One of their appealing functionalities is that, after they have learned a probability distribution from a dataset, they allow exact and efficient sampling of typical system configurations. Here we employ a neural autoregressive distribution estimator (NADE) to boost Markov chain Monte Carlo (MCMC) simulations of a paradigmatic classical model of spin-glass theory, namely, the two-dimensional Edwards-Anderson Hamiltonian. We show that a NADE can be trained to accurately mimic the Boltzmann distribution using unsupervised learning from system configurations generated using standard MCMC algorithms. The trained NADE is then employed as smart proposal distribution for the Metropolis-Hastings algorithm. This allows us to perform efficient MCMC simulations, which provide unbiased results even if the expectation value corresponding to the probability distribution learned by the NADE is not exact. Notably, we implement a sequential tempering procedure, whereby a NADE trained at a higher temperature is iteratively employed as proposal distribution in a MCMC simulation run at a slightly lower temperature. This allows one to efficiently simulate the spin-glass model even in the low-temperature regime, avoiding the divergent correlation times that plague MCMC simulations driven by local-update algorithms. Furthermore, we show that the NADE-driven simulations quickly sample ground-state configurations, paving the way to their future utilization to tackle binary optimization problems.

Abstract: Due to the potential application of DNA for biophysics and optoelectronics, the electronic energy states and transitions of this genetic material have attracted a great deal of attention recently. However, the fluorescence and corresponding physical process of DNA under optical excitation with photon energies below ultraviolet are still not fully clear. In this work, we experimentally investigate the photoluminescence (PL) properties of single-stranded DNA (ssDNA) samples under near-ultraviolet (NUV) and visible excitations (270 similar to 440 nm). Based on the dependence of the PL peak wavelength (lem) upon the excitation wavelength (lex), the PL behaviors of ssDNA can be approximately classified into two categories. In the relatively short excitation wavelength regime, lem is nearly constant due to exciton-like transitions associated with delocalized excitonic states and excimer states. In the relatively long excitation wavelength range, a linear relation of lem = Alex + B with A 0 or A < 0 can be observed, which comes from electronic transitions related to coupled vibrational-electronic levels. Moreover, the transition channels in different excitation wavelength regimes and the effects of strand length and base type can be analyzed on the basis of these results. These important findings not only can give a general description of the electronic energy states and transitional behaviors of ssDNA samples under NUV and visible excitations, but also can be the basis for the application of DNA in nanoelectronics and optoelectronics.