Conductivity Mechanism of Ion–DNA Interaction in Dilute Solution

In this paper, we propose an impurity scattering model of quasi-one-dimensional disordered system for ion–DNA interaction in dilute solution based on the density of state in non-periodic DNA. This disordered system is composed of cations and DNA, the hydrogen ions adsorbed on the surface of DNA with negative charges are considered as impurities. It is hydrogen ions in hydration layer that cause the variations of the density of state near the Fermi level. The classical theory describes the linear dependence of conductivity on concentration. By developing the Green function approach of ion–DNA interaction in the dilute solution, the quantum theory not only gives the linear part but also demonstrates the nonlinear part of the conductivity.

Observation of Anderson localization beyond the spectrum of the disorder

Anderson localization is a fundamental wave phenomenon predicting that transport in a 1D uncorrelated disordered system comes to a complete halt, experiencing no transport whatsoever. However, in reality, a disordered physical system is always correlated, because it must have a finite spectrum. Common wisdom in the field states that localization is dominant only for wavepackets whose spectral extent resides within the region of the wavenumber span of the disorder. Here, we experimentally observe that Anderson localization can occur and even be dominant for wavepackets residing entirely outside the spectral extent of the disorder. We study the evolution of waves in synthetic photonic lattices containing bandwidth-limited (correlated) disorder, and observe Anderson localization for wavepackets of high wavenumbers centered around twice the mean wavenumber of the disorder spectrum. Likewise, we predict and observe Anderson localization at low wavenumbers, also outside the spectral extent of the disorder, and find that localization there can be as strong as for first-order transitions. This feature is universal, common to all Hermitian wave systems, implying that low-wavenumber wavepackets localize with a short localization length even when the disorder is strictly at high wavenumbers. This understanding suggests that disordered media should be opaque for long-wavelengths even when the disorder is strictly at much shorter length scales. Our results shed light on fundamental aspects of physical disordered systems and offer avenues for employing spectrally-shaped disorder for controlling transport in systems containing disorder.

Lifshitz tails at spectral edge and holography with a finite cutoff

We propose the holographic description of the Lifshitz tail typical for one-particle spectral density of bounded disordered system in D = 1 space. To this aim the “polymer representation” of the Jackiw-Teitelboim (JT) 2D dilaton gravity at a finite cutoff is used and the corresponding partition function is considered as the weighted sum over paths of fixed length in an external magnetic field. We identify the regime of small loops, responsible for emergence of a Lifshitz tail in the Gaussian disorder, and relate the strength of disorder to the boundary value of the dilaton. The geometry corresponding to the Poisson disorder in the boundary theory involves random paths fluctuating in the vicinity of the hard impenetrable cut-off disc in a 2D plane. It is shown that the ensemble of “stretched” paths evading the disc possesses the Kardar-Parisi-Zhang (KPZ) scaling for fluctuations, which is the key property that ensures the dual description of the Lifshitz tail in the spectral density for the Poisson disorder.

The temporal fluctuation of the inverse participation ratio for localized field modes in three-dimensional percolation system

We investigate the structure of the optical field radiated by the disordered optical nano-emitters randomly incorporated in three-dimensional cluster of a percolation material. Our numerical studies shown that the temporal variations of the inverse participation ratio (IPR) allow analyzing the extended and localized field structures over a long time range. The properties of IPR and the dynamics of the lasing emitters allow to find the characteristic time scales when the localization of the field in a general three-dimensional disordered system occurs. The studied effect opens new perspectives to control the optical fields localization in modern optical nano-technologies.

Exact Self-Consistent Effective Hamiltonian Theory

We propose a general variational fermionic many-body wavefunction that generates an effective Hamiltonian in quadratic form which can then be exactly solved. The theory can be constructed within density functional theory framework and a self-consistent scheme is proposed for solving the exact density functional theory. We apply the theory to structurally disordered system and an symmetric and asymmetric Hubbard dimer and corresponding lattice models and the the single fermion excitation spectra show a persistent gap due to the fermionic entanglement induced pairing condensate. For disordered system, density of state at the edge of the gap diverges in the thermodynamic limit, suggesting a topologically ordered phase and a sharp resonance is predicted as the gap is not dependent on the temperature of the system. For the symmetric Hubbard model, the gap for both half filling and doped case suggests quantum phase transition between the AFM and SC is a continuous phase transition.

crystIT: Complexity and Configurational Entropy of Crystal Structures via Information Theory

<div>The information content of a crystal structure as conceived by information theory has recently proved as an intriguing approach to calculate the complexity of a crystal structure within a consistent concept. Given the relatively young nature of the field, theory development is still at the core of on-going research efforts. In this work we provide an update to the current theory, improving the formulas that evaluation of crystal structures with partial occupancies as frequently found in disordered system is feasible. To encourage wider application and further theory development we incorporate the updated formulas in crystIT (crystal structure & Information Theory), an open-source python-based program that allows for calculating various complexity measures of crystal structures based on a standardized *.cif file.</div>

crystIT: Complexity and Configurational Entropy of Crystal Structures via Information Theory

<div>The information content of a crystal structure as conceived by information theory has recently proved as an intriguing approach to calculate the complexity of a crystal structure within a consistent concept. Given the relatively young nature of the field, theory development is still at the core of on-going research efforts. In this work we provide an update to the current theory, improving the formulas that evaluation of crystal structures with partial occupancies as frequently found in disordered system is feasible. To encourage wider application and further theory development we incorporate the updated formulas in crystIT (crystal structure & Information Theory), an open-source python-based program that allows for calculating various complexity measures of crystal structures based on a standardized *.cif file.</div>