Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 1701.04274

Localization in random fractal lattices

Arkadiusz Kosior·Krzysztof Sacha
View original source ↗Read source document ↗Export metadata ↓

Abstract

We investigate the issue of eigenfunction localization in random fractal lattices embedded in two dimensional Euclidean space. In the system of our interest, there is no diagonal disorder -- the disorder arises from random connectivity of non-uniformly distributed lattice sites only. By adding or removing links between lattice sites, we change the spectral dimension of a lattice but keep the fractional Hausdorff dimension fixed. From the analysis of energy level statistics obtained via direct diagonalization of finite systems, we observe that eigenfunction localization strongly depends on the spectral dimension. Conversely, we show that localization properties of the system do not change significantly while we alter the Hausdorff dimension. In addition, for low spectral dimensions, we observe superlocalization resonances and a formation of an energy gap around the center of the spectrum.

Explore related subjects

cond-mat.quant-gasquant-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Arkadiusz Kosior, Krzysztof Sacha. 2017-03-27. Localization in random fractal lattices. https://doi.org/10.1103/physrevb.95.104206

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Transdimensional quantum droplets in an optically trapped Bose mixture

We study quantum droplets in a symmetric two-component Bose mixture with interspecies $p$-wave interactions and a two-dimensional transverse optical lattice. The lattice drives a crossover from an anisotropic three-dimensional gas to weakly coupled one-dimensional tubes. We calculate the ground-state energy and quantum depletion at the Gaussian level and derive their limiting forms. At $y=g_{12}/g=-0.95$, where the bare mean field is repulsive and no free-space droplet exists, the calculated bulk equation of state supports a self-bound minimum across the crossover: a negative lattice contribution at order $n^{2}$ supplies the attraction in the three-dimensional regime, and attractive fluctuations do so in the quasi-one-dimensional regime, with the intermediate, transdimensional range described quantitatively by neither limit. The interspecies $p$-wave interaction modifies only the spin branch. In the parameter range studied, increasing its strength lowers the equilibrium density across the crossover, consistently with a weakening of the induced binding.

cond-mat.quant-gas↗
arXiv2026

Microwave-controlled interactions and stripe formation of static-field-shielded polar molecules

We study polar molecules where short-range losses are suppressed by a shielding scheme involving a static electric field and an elliptically polarized microwave field. Using perturbation theory, we derive the effective interaction potential and validate it against coupled channel calculations. We identify a parameter regime where two-body losses are strongly suppressed and the extended mean-field description of dilute molecular Bose-Einstein condensates is justified. We calculate the collective excitations and show that intriguingly, supersolidity in quasi-two-dimensional confinement emerges as a stripe phase even at small values of microwave ellipticity.

cond-mat.quant-gas↗
arXiv2026

Finite-time effects in periodically kicked systems

In this work, we study finite-time effects in ultracold atomic systems by considering time-dependent modulations with variable waveforms and durations. These two characteristics can be controlled by adjusting only a single parameter. For arbitrarily short pulses, our model recovers the paradigmatic kicked rotor while maintaining the impulse transmitted per period and unit amplitude constant. Furthermore, we demonstrate that finite-time effects have a profound impact on dynamical localization, a result that cannot be captured by the {\delta}-kicked-rotor model. Through a detailed analysis of the effects of different modulation amplitudes, periods, and waveforms, we identify the conditions for which dynamical localization is significantly enhanced. We show that the strength of dynamical localization increases sharply as the system approaches the {\delta}-kicked-rotor limiting case. Moreover, we establish the existence of an optimal value of the period that maximizes dynamical localization for given values of the amplitude and shape parameter.

cond-mat.quant-gas↗