arXiv subjects

Jure Dobnikar

Publications and source records attributed to Jure Dobnikar.

22 records · Page 2Linked to original sources

arXiv2008

Ground states of colloidal molecular crystals on periodic substrates

Two dimensional suspensions of spherical colloids subject to periodic external fields exhibit a rich variety of molecular crystalline phases. We study in simulations the ground state configurations of dimeric and trimeric systems, that are realized on square and triangular lattices, when either two or three macroions are trapped in each external potential minimum. Bipartite orders of the checkerboard or stripe types are reported together with more complex quadripartite orderings, and the shortcomings of envisioning the colloids gathered in a single potential minimum as a composite rigid object are discussed. This work also sheds light on simplifying assumptions underlying previous theoretical treatments and that made possible the mapping onto spin models.

cond-mat.soft↗

arXiv2000

Pseudo-Casimir force in confined nematic polymers

We investigate the pseudo-Casimir force in a slab of material composed of nematically ordered long polymers. We write the total mesoscopic energy together with the constraint connecting the local density and director fluctuations and evaluate the corresponding fluctuation free energy by standard methods. It leads to a pseudo-Casimir force of a different type than in the case of standard, short molecule nematic. We investigate its separation dependence and its magnitude and explicitly derive the relevant limiting cases.

cond-mat.stat-mech↗

arXiv1997

Energy level statistics in the transition regime between integrability and chaos for systems with broken antiunitary symmetry

Energy spectra of a particle with mass $m$ and charge $e$ in the cubic Aharonov-Bohm billiard containing around $10^4$ consecutive levels starting from the ground state have been analysed. The cubic Aharonov-Bohm billiard is a plane billiard defined by the cubic conformal mapping of the unit disc pervaded by a point magnetic flux through the origin perpendicular to the plane of the billiard. The magnetic flux does not influence the classical dynamics, but breaks the antiunitary symmetry in the system, which affects the statistics of energy levels. By varying the shape parameter $\lam$ the classical dynamics goes from integrable ($\lam =0$) to fully chaotic ($\lam = 0.2$; Africa billiard). The level spacing distribution $P(S)$ and the number variance $Σ^{2}(L)$ have been studied for 13 different shape parameters on the interval ($0\le\lam\le0.2$). GUE statistics has proven correct for completely chaotic case, while in the mixed regime the fractional power law level repulsion has been observed. The exponent of the level repulsion has been analysed and is found to change smoothly from 0 to 2 as the dynamics goes from integrable to ergodic. Further on, the semiclassical Berry-Robnik theory has been examined. We argue that the semiclassical regime has not been reached and give an estimate for the number of energy levels required for the Berry-Robnik statistics to apply.

chao-dyn↗

arXiv1997

New Universal Aspects of Diffusion in Strongly Chaotic Systems

We study some new universal aspects of diffusion in chaotic systems, especially such having very large Lyapunov coefficients on the chaotic (indecomposable, topologically transitive) component. We do this by discretizing the chaotic component on the Surface-of-Section in a (large) number $N$ of simplectically equally big cells (in the sense of equal relative invariant ergodic measure, normalized so that the total measure of the chaotic component is unity). By iterating the transition of the chaotic orbit through SOS, where $j$ counts the number of iteration (discrete time), and assuming complete lack of correlations even between consecutive crossings (which can be justified due to the very large Lyapunov exponents), we show the universal approach of the relative measure of the occupied cells, denoted by $ρ(j)$, to the asymptotic value of unity, in the following way: $ρ(j) = 1 - (1-\frac{1}{N})^j$, so that in the limit of big $N$, $N\to \infty$, we have, for $j/N$ fixed, the exponential law $ρ(j) \approx 1 - \exp (-j/N)$. This analytic result is verified numerically in a variety of specific systems: For a plane billiard (Robnik 1983, $λ=0.375$), for a 3-D billiard (Prosen 1997, $a=-1/5, b=-12/5$), for ergodic logistic map (tent map), for standard map ($k=400$) and for hydrogen atom in strong magnetic field ($ε=-0.05$) the agreement is almost perfect (except, in the latter two systems, for some long-time deviations on very small scale), but for Hénon-Heiles system ($E=1/6$) and for the standard map ($k=3$) the deviations are noticed although they are not very big (only about 1%). We have tested the random number generators (Press et al 1986), and confirmed that some are almost perfect (ran0 and ran3), whilst two of them (ran1 and ran2) exhibit big deviations.

chao-dyn↗