arXiv subjects

Milan Pantić

Publications and source records attributed to Milan Pantić.

6 recordsLinked to original sources

arXiv2026

Real-Space Renormalization of Stabilizer Rényi Entropies in Spin Chains

Stabilizer states constitute an important class of quantum states that can be generated from computational-basis states using Pauli operators and Clifford gates. Although they may exhibit substantial multipartite entanglement, quantum circuits restricted to stabilizer operations can be efficiently simulated classically and therefore cannot, by themselves, provide a quantum computational advantage. Such an advantage requires non-stabilizer resources, commonly referred to as quantum magic. In this paper, we investigate the non-stabilizerness of quantum states arising in a class of spin Hamiltonians by computing their stabilizer Rényi entropies. Using real-space renormalization-group techniques, we obtain a closed-form expression valid in the low-energy, large-distance regime. We analyze how quantum magic evolves under coarse-graining and explore its behavior across different parameter regimes and quantum phases.

quant-ph↗

arXiv2025

Infinite series involving special functions obtained using simple one-dimensional quantum mechanical problems

In this paper certain classes of infinite sums involving special functions are evaluated analytically by application of basic quantum mechanical principles to simple models of half harmonic oscillator and a particle trapped inside an infinite potential well. The infinite sums $\sum^{\infty}_{n=0}\frac{2^{2n}}{(2n+1)!}Γ^{2}\left(n+\frac{3}{2}\right)\left[\hspace{0.2mm}_2\hspace{-0.03cm}F_1\left(-n,\frac{ν+2}{2};\frac{3}{2};\frac{1}{2}\right)\right]^{2}$, $\sum^{\infty}_{n=0}\frac{\left[L_ν^{2n+1-ν}\left(\frac{b^{2}}{2}\right)\right]^{2}b^{4n}}{2^{2n}(2n+1)!}$ and $\sum^{\infty}_{n=1}\frac{\big[J_{ν+1}(nπ)\big]^{2}}{n^{2ν}}$, where $_2\hspace{-0.03cm}F_1\left(-n,\frac{ν+2}{2};\frac{3}{2};\frac{1}{2}\right)$ is generalized hypergeometric function, $L_ν^{2n+1-ν}\left(\frac{b^{2}}{2}\right)$ associated Laguerre polynomial and $J_{ν+1}(nπ)$ Bessel function of the first kind, are calculated for integer $ν$. It is also demonstrated that the same procedure can be generalized by application to some classes of functions which are not regular wave functions leading to additional infinite sums, as a consequence of which the series $\sum_{n=1}^{\infty}\frac{\left[\mathsf{H}_ν(nπ)\right]^{2}}{n^{2ν}}$ containing Struve functions of the first kind $\mathsf{H}_ν(nπ)$ are evaluated. Convergence of the evaluated series, additionally verified by the application of different convergence tests, is secured by the properties of the corresponding Hilbert space.

quant-ph↗

arXiv2023

The largest Lyapunov exponent as a tool for detecting relative changes in the particle positions

Dynamics of the driven Frenkel-Kontorova model with asymmetric deformable substrate potential is examined by analyzing response function, the largest Lyapunov exponent and Poincaré sections for two neighboring particles. The obtained results show that the largest Lyapunov exponent, besides being used for investigating integral quantities, can be used for detecting microchanges in chain configuration of both damped Frenkel-Kontorova model with inertial term and its strictly overdamped limit. Slight changes in relative positions of the particles are registered through jumps of the largest Lyapunov exponent in the pinning regime. The occurrence of such jumps is highly dependent on type of commensurate structure and deformation of substrate potential. The obtained results also show that the minimal force required to initiate collective motion of the chain is not dependent on the number of Lyapunov exponent jumps in the pinning regime. These jumps are also registered in the sliding regime, where they are a consequence of a more complex structure of largest Lyapunov exponent on the step.

nlin.CD↗

arXiv2021

Enumeration of Hamiltonian Cycles on a Thick Grid Cylinder -- Part II: Contractible Hamiltonian Cycles

In this series of papers, the primary goal is to enumerate Hamiltonian cycles (HC's) on the grid cylinder graphs $P_{m+1}\times C_n$, where $n$ is allowed to grow whilst $m$ is fixed. In Part~I, we studied the so-called non-contractible HC's. Here, in Part~II, we proceed further on to the contractible case. We propose two different novel characterizations of contractible HC's, from which we construct digraphs for enumerating the contractible HC's. Given the impression which the computational data for $m \leq 9$ convey, we conjecture that the asymptotic domination of the contractible HC's versus the non-contractible HC's, among the total number of HC's, depends on the parity of $m$.}

math.CO↗

arXiv2021

Using quantum mechanics for calculation of different infinite sums

We demonstrate that certain class of infinite sums can be calculated analytically starting from a specific quantum mechanical problem and using principles of quantum mechanics. For simplicity we illustrate the method by exploring the problem of a particle in a box. Twofold calculation of the mean value of energy for the polynomial wave function inside the well yields even argument $p$ ($p>2$) of Riemann zeta and related functions. This method can be applied to a wide class of exactly solvable quantum mechanical problems which may lead to different infinite sums. Besides, the analysis performed here provides deeper understanding of superposition principle and presents useful exercise for physics students.

quant-ph↗

arXiv2018

Dynamics of Frenkel excitons in pentacene

The dispersion relation for noninteracting excitons and the influence of perturbative correction is examined in the case of pentacene structure. The values of exchange integrals are determined by the nonlinear fits to the experimental dispersion data obtained by inelastic electron scattering in Phys. Rev. Lett. \textbf{98}, 037402 (2007). We obtain theoretical dispersion curves along four different directions in the Brillouin zone which possess the same periodicity as the experimental data. We also showed that perturbative corrections are negligible since the exciton gap in dispersion relation is huge in comparison to exchange integrals.

cond-mat.str-el↗