arXiv subjects

Sonja Gombar

Publications and source records attributed to Sonja Gombar.

9 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

Hamiltonian dynamics of classical spins

We discuss the geometry behind classical Heisenberg model at the level suitable for third or fourth year students who did not have the opportunity to take a course on differential geometry. The arguments presented here rely solely on elementary algebraic concepts such as vectors, dual vectors and tensors, as well as Hamiltonian equations and Poisson brackets in their simplest form. We derive Poisson brackets for classical spins, along with the corresponding equations of motion for classical Heisenberg model, starting from the geometry of two-sphere, thereby demonstrating the relevance of standard canonical procedure in the case of Heisenberg model.

physics.ed-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↗

arXiv2024

Summation formulas generated by Hilbert space eigenproblem

We demonstrate that certain classes of Schl\" omilch-like infinite series and series that include generalized hypergeometric functions can be calculated in closed form starting from a simple quantum model of a particle trapped inside an infinite potential well and using principles of quantum mechanics. We provide a general framework based on the Hilbert space eigenproblem that can be applied to different exactly solvable quantum models. Obtaining series from normalization conditions in well-defined quantum problems secures their convergence.

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↗

arXiv2020

Influence of anharmonic convex interparticle potential and Shapiro steps in the opposite direction of driving force

The response function and largest Lyapunov exponent analysis were applied to the driven overdamped Frenkel-Kontorova model with two types of anharmonic convex interparticle potentials. In both cases model reduces to a single particle model for integer values of winding number. It is shown that the mirror image of the amplitude dependence of critical depinning force and largest Lyapunov exponent observed recently in the standard Frenkel-Kontorova model [Commun. Nonlinear Sci. Numer. Simul. 47, 100 (2017)] is not retained generally. Behaviour of systems with relatively strong interparticle force was examined and evidence for the appearance of mode-locking phenomenon in both directions of particles' motion is presented.

nlin.CD↗

arXiv2020

Correlation between quantum entanglement and quantum coherence in the case of XY spin chains with the Dzyaloshinskii-Moriya interaction

Recently, there has been an increased interest in studying quantum entanglement and quantum coherence. Since both of these properties are attributed to the existence of quantum superposition, it would be useful to determine if some type of correlation between them exists. Hence, the purpose of this paper is to explore the type of the correlation in several systems with different types of anisotropy. The focus will be on the XY spin chains with the Dzyaloshinskii-Moriya interaction and the type of the mentioned bond will be explored using the quantum renormalization group method.

cond-mat.str-el↗

arXiv2020

Exciton dynamics in different aromatic hydrocarbon systems

The exciton dispersion is examined in the case of four selected prototypical molecular solids: pentacene,tetracene,picene,chrysene. The model parameters are determined by fitting to experimental data obtained by inelastic electron scattering. Within the picture that relies on Frenkel-type excitons we obtain that theoretical dispersion curves along different directions in the Brillouin zone are in good agreement with the experimental data, suggesting that the influence of charge-transfer excitons on exciton dispersion of the analyzed organic solids is not as large as proposed. In reciprocal space directions where Davydov splitting is observed we employ the upgraded version of Hamiltonian used in Materials 11, 2219 (2018).

cond-mat.mtrl-sci↗

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↗