Multifractality and its role in anomalous transport in the disordered XXZ spin-chain

The disordered XXZ model is a prototype model of the many-body localization transition (MBL). Despite numerous studies of this model, the available numerical evidence of multifractality of its eigenstates is not very conclusive due severe finite size effects. Moreover it is not clear if similarly to the case of single-particle physics, multifractal properties of the many-body eigenstates are related to anomalous transport, which is observed in this model. In this work, using a state-of-the-art, massively parallel, numerically exact method, we study systems of up to 24 spins and show that a large fraction of the delocalized phase flows towards ergodicity in the thermodynamic limit, while a region immediately preceding the MBL transition appears to be multifractal in this limit. We discuss the implication of our finding on the mechanism of subdiffusive transport.Comment: 13 pages, 8 figure

Transport in quasiperiodic interacting systems: from superdiffusion to subdiffusion

Using a combination of numerically exact and renormalization-group techniques we study the nonequilibrium transport of electrons in an one-dimensional interacting system subject to a quasiperiodic potential. For this purpose we calculate the growth of the mean-square displacement as well as the melting of domain walls. While the system is nonintegrable for all studied parameters, there is no on finite region default of parameters for which we observe diffusive transport. In particular, our model shows a rich dynamical behavior crossing over from superdiffusion to subdiffusion. We discuss the implications of our results for the general problem of many-body localization, with a particular emphasis on the rare region Griffiths picture of subdiffusion.Comment: 6 pages, 5 figures. A more detailed analysis of the dynamical exponents extraction and discussion of the relevant times. Adds a log-derivative for the FRG sectio

A Dynamic P53-MDM2 Model with Time Delay

Specific activator and repressor transcription factors which bind to specific regulator DNA sequences, play an important role in gene activity control. Interactions between genes coding such transcription factors should explain the different stable or sometimes oscillatory gene activities characteristic for different tissues. Starting with the model P53-MDM2 described into [6] and the process described into [5] we developed a new model of this interaction. Choosing the delay as a bifurcation parameter we study the direction and stability of the bifurcating periodic solutions. Some numerical examples are finally given for justifying the theoretical results.Comment: 16 pages, 12 figure

Temporal fluctuations of correlators in integrable and chaotic quantum systems

We provide bounds on temporal fluctuations around the infinite-time average of out-of-time-ordered and time-ordered correlators of many-body quantum systems without energy gap degeneracies. For physical initial states, our bounds predict the exponential decay of the temporal fluctuations as a function of the system size. We numerically verify this prediction for chaotic and interacting integrable spin-1/2 chains, which satisfy the assumption of our bounds. On the other hand, we show analytically and numerically that for the XX model, which is a noninteracting system with gap degeneracies, the temporal fluctuations decay polynomially with system size for operators that are local in the fermion representation and decrease exponentially in the system size for non-local operators. Our results demonstrate that the decay of the temporal fluctuations of correlators cannot be used as a reliable metric of chaos or lack thereof.Comment: 14 pages, 4 figure

Noise-induced transport in the Aubry-Andr\'e-Harper model

We study quantum transport in a quasiperiodic Aubry-Andr\'e-Harper (AAH) model induced by the coupling of the system to a Markovian heat bath. We find that coupling the heat bath locally does not affect transport in the delocalized and critical phases, while it induces logarithmic transport in the localized phase. Increasing the number of coupled sites at the central region introduces a transient diffusive regime, which crosses over to logarithmic transport in the localized phase and in the delocalized regime to ballistic transport. On the other hand, when the heat bath is coupled to equally spaced sites of the system, we observe a crossover from ballistic and logarithmic transport to diffusion in the delocalized and localized regimes, respectively. We propose a classical master equation, which captures our numerical observations for both coupling configurations on a qualitative level and for some parameters, even on a quantitative level. Using the classical picture, we show that the crossover to diffusion occurs at a time that increases exponentially with the spacing between the coupled sites, and the resulting diffusion constant decreases exponentially with the spacing.Comment: 11 pages, 7 fig

Generalization of Kirchhoff's Law of Thermal Radiation: The Inherent Relations Between Quantum Efficiency and Emissivity

Planck's law of thermal radiation depends on the temperature, $T$, and the emissivity, $\epsilon$, of a body, where emissivity is the coupling of heat to radiation that depends on both phonon-electron nonradiative interactions and electron-photon radiative interactions. Another property of a body is absorptivity, $\alpha$, which only depends on the electron-photon radiative interactions. At thermodynamic equilibrium, nonradiative interactions are balanced, resulting in Kirchhoff's law of thermal radiation that equals these two properties, i.e., $\epsilon = \alpha$. For non-equilibrium, quantum efficiency ($QE$) describes the statistics of photon emission, which like emissivity depends on both radiative and nonradiative interactions. Past generalized Planck's equation extends Kirchhoff's law out of equilibrium by scaling the emissivity with the pump-dependent chemical-potential $\mu$, obscuring the relations between the body properties. Here we theoretically and experimentally demonstrate a prime equation relating these properties in the form of $\epsilon = \alpha(1-QE)$, which is in agreement with a recent universal modal radiation law for all thermal emitters. At equilibrium, these relations are reduced to Kirchhoff's law. Our work lays out the fundamental evolution of non-thermal emission with temperature, which is critical for the development of lighting and energy devices.Comment: 14 pages, 16 figures. arXiv admin note: substantial text overlap with arXiv:2104.1013