Related papers: Regularities and symmetries in atomic structure an…
Infrared spectra of various polymers were treated statistically. It was established that for the absorbance spectra the Benford distribution of leading digits takes place, whereas the distribution of leading digits for transmittance spectra…
The energy level statistics of uniform random graphs are studied, by treating the graphs as random tight-binding lattices. The inherent random geometry of the graphs and their dynamical spatial dimensionality, leads to various quantum…
Quantum chaotic dynamics is obtained for a tight-binding model in which the energies of the atomic levels at the boundary sites are chosen at random. Results for the square lattice indicate that the energy spectrum shows a complex behavior…
Benford's Law is an empirical law which predicts the frequency of significant digits in databases corresponding to various phenomena, natural or artificial. Although counter intuitive at the first sight, it predicts a higher occurrence of…
Ensembles of quantum chaotic systems are expected to exhibit energy eigenvalues with random-matrix-like level repulsion between pairs of energies separated by less than the inverse Thouless time. Recent research has shown that exact and…
The Cahn--Hilliard equation with anisotropic energy contributions frequently appears in many physical systems. Systematic analytical results for the case with the relevant logarithmic free energy have been missing so far. We close this gap…
A general analytical approach to the statistical description of quantum graph spectra based on the exact periodic orbit expansions of quantum levels is discussed. The exact and approximate expressions obtained in \cite{Anima} for the…
In this paper, we consider the problem of exploring structural regularities of networks by dividing the nodes of a network into groups such that the members of each group have similar patterns of connections to other groups. Specifically,…
The fractal properties of the energy spectra of quantum systems are discussed in connection with the paper by S\'aiz and Mart\'inez [Phys. Rev. E 54, 2431 (1996)]. It is shown that for discrete energy levels the Hausdorff--Basicovitch…
Deep inelastic scattering is considered in a statistical model of the nucleon. This incorporates certain features which are absent in the standard parton model such as quantum statistical correlations which play a role in the propagation of…
We explore various properties of classical one-dimensional Wigner solids in the presence of disorder at T=0 in the context of a recently discovered Anderson transition of plasma modes in the random potential system. The extent to which the…
A quantum gravity theory which becomes renormalizable at short distances due to a spontaneous symmetry breaking of Lorentz invariance and diffeomorphism invariance is studied. A breaking of Lorentz invariance with the breaking patterns…
We present a robust analysis of the spectral fluctuations exhibited by the light meson spectrum. This analysis provides information about the degree of chaos in light mesons and may be useful to get some insight on the underlying…
Understanding the effects of nonequilibrium on strongly interacting quantum systems is a challenging problem in condensed matter physics. In dimensions greater than one, interacting electrons can often be understood within Fermi-liquid…
A detailed discussion of semiclassical trace formulae is presented and it is demonstrated how a regularized trace formula can be derived while dealing only with finite and convergent expressions. Furthermore, several applications of trace…
A numerical study is made of the spectra of a tight-binding hamiltonian on square approximants of the quasiperiodic octagonal tiling. Tilings may be pure or random, with different degrees of phason disorder considered. The level statistics…
The spatial Fourier spectrum of the electron density distribution in a finite 1D system and the distribution function of electrons over single-particle states are studied in detail to show that there are two universal features in their…
The paper introduces a simple quantum model to calculate in a general way allowed frequencies and energy levels of the anharmonic oscillator. The theoretical basis of the approach has been introduced in two early papers aimed to infer the…
We consider the influence of the Fermi statistics of nucleons on the binding energy of a new type of nuclear structures such as fractal nuclear clusters (fractal isomers of nuclei). It is shown that the fractal nuclear isomers possess a…
Spontaneous symmetry breaking occurs when the underlying laws of a physical system are symmetric, but the vacuum state chosen by the system is not. The (3+1)d $\phi^4$ theory is relatively simple compared to other more complex theories,…