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Božidar Jovanović

Publications and source records attributed to Božidar Jovanović.

5 recordsLinked to original sources
arXiv2026

From bungee to $C^1$ and $C^0$ Hamiltonian systems and their integrability and nonintegrability

We consider natural Hamiltonian systems with potentials that are $C^0$ or $C^1$ on a hypersurface and $C^{\infty}$-smooth in the complement and introduce and study corresponding notions of their integrabilty and non-integrability. As a motivating example, we derive and analyze models of bungee jumping. We provide prototype examples of the Liuoville-Arnol'd theorem for $C^0$ and $C^1$ Hamiltonians.

math.DS↗
arXiv2025

Spherical and Planar Ball Bearings -- a Study of Integrable Cases

We consider the nonholonomic systems of $n$ homogeneous balls $\mathbf B_1,\dots,\mathbf B_n$ with the same radius $r$ that are rolling without slipping about a fixed sphere $\mathbf S_0$ with center $O$ and radius $R$. In addition, it is assumed that a dynamically nonsymmetric sphere $\mathbf S$ with the center that coincides with the center $O$ of the fixed sphere $\mathbf S_0$ rolls without slipping in contact to the moving balls $\mathbf B_1,\dots,\mathbf B_n$. The problem is considered in four different configurations. We derive the equations of motion and prove that these systems possess an invariant measure. As the main result, for $n=1$ we found two cases that are integrable in quadratures according to the Euler-Jacobi theorem. The obtained integrable nonholonomic models are natural extensions of the well-known Chaplygin ball integrable problems. Further, we explicitly integrate the planar problem consisting of $n$ homogeneous balls of the same radius, but with different masses, that roll without slipping over a fixed plane $Σ_0$ with a plane $Σ$ that moves without slipping over these balls.

math-ph↗
arXiv1998

Conductance Correlations Near Integer Quantum Hall Transitions

In a disordered mesoscopic system, the typical spacing between the peaks and the valleys of the conductance as a function of Fermi energy $E_F$ is called the conductance energy correlation range $E_c$. Under the ergodic hypothesis, the latter is determined by the half-width of the ensemble averaged conductance correlation function: $F= < δg(E_F) δg(E_F + ΔE) >$. In ordinary diffusive metals, $E_c\sim D/L^2$, where $D$ is the diffusion constant and $L$ is the linear dimension of the phase-coherent sample. However, near a quantum phase transition driven by the location of the Fermi energy $E_F$, the above picture breaks down. As an example of the latter, we study, for the first time, the conductance correlations near the integer quantum Hall transitions of which $E_F$ is a critical coupling constant. We point out that the behavior of $F$ is determined by the interplay between the static and the dynamic properties of the critical phenomena.

cond-mat.mes-hall↗
arXiv1996

Critical Conductance and Its Fluctuations at Integer Hall Plateau Transitions

Under periodic boundary condition in the transverse direction, we calculate the averaged zero-temperature two-terminal conductance ($ $) and its statistical fluctuations ($<(\dg)^{2n}>$ for $n\le 4$) at the critical point of integer quantum Hall plateau transitions. We find {\it universal} values for $ =(0.58\pm0.03){e^2\over h}$, and $<(\dg)^{2n}>=({e^2\over h})^{2n}A_{2n}$, where $A_{2,4,6,8}=0.081\pm0.005$; $0.013\pm0.003$; $0.0026\pm0.005$; and $(8\pm2)\times10^{-4}$ respectively. We also determine the leading finite size scaling corrections to these observables. Comparisons with experiments will be made.

cond-mat.mes-hall↗