arXiv subjects

Tilen Čadež

Publications and source records attributed to Tilen Čadež.

4 recordsLinked to original sources

arXiv2026

Nonrelativistic versus relativistic quantum scars in billiard systems

We study the features of scarred eigenstates of relativistic neutrino billiards (NBs), graphene billiards (GBs) and Haldane graphene billiards (HGBs) and recapitulate those for nonrelativistic quantum billiards (NRQBs) with the shapes of a full- and quarter-stadium billiard. Here, we restrict for the GBs and HGBs to the region of linear dispersion around the Fermi energy, where they are effectively described by the same Dirac equation for massless spin-1/2 particles as NBs. Scarred wave functions of the nonrelativistic billiards and spinor functions of the relativistic ones are localized along the same types of periodic orbits, the most prominent ones being bouncing-ball orbits. The objective is to demonstrate that the properties of the scarred eigenstates observed in the full- and quarter-stadium GB \emph{do not comply} with those of relativistic quantum systems. For this we apply the semiclassical approach associated with such non-generic contributions, which was developed for the spectral density of NRQBs and NBs. It provides semiclassical trace formulas in terms of the periodic orbits associated with a scarred wave function and a procedure to extract such contributions from the eigenvalue spectra. Furthermore, we analyze momentum distributions and Husimi functions of such scarred states and employ them to classify scarred wave functions according to the periodic orbits along which they are localized. We show that for the GB the semiclassical approach, the spectral properties, the symmetry properties and generally properties of the wave functions all comply with those of the NRQB, whereas for the HGB they agree well with those of the NB. Thus, even though around the Fermi energy GBs are described by the relativistic Dirac equation the quantum scars, or generally, the quantum scarred eigenstates observed in GBs do not exhibit those of relativistic ones.

nlin.CD↗

arXiv2023

Flat Band Induced Metal-Insulator Transitions for Weak Magnetic Flux and Spin-Orbit Disorder

We consider manifolds of tunable all-band flat (ABF) lattices in dimensions d = 1, 2, parametrized by a manifold angle parameter θ. We study localization properties of eigenstates in the presence of weak magnetic flux disorder and weak spin-orbit disorder. We demonstrate that weakly disordered ABF lattices are described by effective scale-free models where the disorder strength is scaled out. For weak magnetic flux disorder we observe sub-exponential localization at flatband energies in d = 1, which differs from the usual Anderson localization. We also find diverging localisation length at flatband energies for weak flux values in d = 2, however the character of the eigenstates at these energies is less clear. For weak spin-orbit coupling disorder in d = 2 we identify a tunable metal-insulator transition with mobility edges. We also consider the case of mixed spin-orbit and diagonal disorder and obtain the metal-insulator transition driven by the manifold parameter θ.

cond-mat.mes-hall↗

arXiv2023

Enhancement of Superconductivity in the Fibonacci Chain

We study the interplay between quasi-periodic disorder and superconductivity in a 1D tight-binding model with the quasi-periodic modulation of on-site energies that follow the Fibonacci rule and all the eigenstates are multifractal. As a signature of multifractality, we observe the power-law dependence of the correlation between different single-particle eigenstates as a function of their energy difference. By computing numerically the superconducting transition temperature, we find the distribution of critical temperatures, analyze their statistics and estimate the mean value and variance of critical temperatures for various regimes of the attractive coupling strength and quasi-periodic disorder. We find an enhancement of the critical temperature as compared to the analytical results that are based on strong assumptions of absence of correlations and self-averaging of multiple characteristics of the system, which are not justified for the Fibonacci chain. For the very weak coupling regime, we observe a crossover where the self-averaging of the critical temperature breaks down completely and a strong sample-to-sample fluctuations emerge.

cond-mat.supr-con↗

arXiv2021

One-particle spectral functions of the one-dimensional Fermionic Hubbard model with one fermion per site at zero and finite magnetic fields

Here the line shape of the up- and down-spin one-particle spectral functions at and in the (k,energy)-plane's vicinity of their cusp singularities is studied for the Mott-Hubbard insulator described by the 1D Hubbard model with one fermion per site at zero and finite magnetic fields. At zero field they can be accessed in terms of electrons by photoemission experiments. At finite field, such functions and corresponding interplay of correlations and magnetic-field effects refer to an involved non-perturbative many-particle problem that is poorly understood. The Mott-Hubbard gap that separates the addition and removal spectral functions is calculated for all spin densities and interaction values. The qualitative differences in the one-particle properties of the Mott-Hubbard insulator and corresponding doped insulator are also investigated. The relation of our theoretical results and predictions to both condensed-matter and ultracold spin-1/2 atom systems is discussed.

cond-mat.str-el↗