arXiv subjects

Vadood Adami

Publications and source records attributed to Vadood Adami.

5 recordsLinked to original sources

arXiv2026

Emergent Topological Complexity in the Barabasi-Albert Model with Higher-Order Interactions

We examine the homological structure of the Barabasi-Albert model, focusing on the time evolution of $\Delta$-dimensional simplices and topological holes as functions of time $t$ and the attachment parameter $m$ (the number of edges added by each incoming node). Numerical simulations reveal a non-trivial topological transition (TT) in the $(\Delta, m)$ plane, marking a change from a topologically trivial regime to non-trivial topology. This transition signals the emergence of topological complexity in the model, where higher-order structures develop self-similarly across scales. Beyond this transition, the network exhibits self-similar topological growth, evidenced by a power-law decay in the increments of $\Delta$-simplices with $m$-dependent exponents. An analogous transition occurs in the Betti numbers, which display self-similar behavior near the TT and an arctangent dependence farther from it. Based on simulation data, we propose explicit scaling relations describing the behavior of both $\Delta$-simplices and Betti numbers near the TT. Overall, the analysis reveals a rich, gapful topological transition structure, where topological quantities exhibit discrete jumps at the transition point.

cond-mat.stat-mech↗

arXiv2025

A Self-Organized Model for the Flicker Noise in Interacting Two-Dimensional Electron Gas

We investigate self-organized criticality in a two-dimensional electron gas (2DEG) by introducing a lattice-based model that incorporates electron-electron interactions through the concept of coherence length. Our numerical simulations demonstrate that in the strongly interacting regime, the system exhibits a distinct set of universal critical exponents, markedly different from those observed in the weakly interacting limit. This dichotomy aligns with experimental findings on the metal-insulator transition in 2DEGs, where high interaction strength (low carrier density) leads to qualitatively different behavior. The analysis includes scaling of the average electron density with temperature, the power spectral density, and the statistics of electronic avalanches - namely their size distributions and autocorrelation functions. In all cases, the extracted exponents differ significantly between the weak and strong interaction regimes, highlighting the emergence of two universality classes governed by interaction strength. These results underscore the critical role of electron correlations in the self-organized behavior of low-dimensional electronic systems.

cond-mat.stat-mech↗

arXiv2025

Quantum Geometry of Finite XY Chains: A Comparison of Neveu-Schwarz and Ramond Sectors

This paper presents a geometrical analysis of finite length XY quantum chains. We begin by examining the ground state and the first excited state of the model, emphasizing the impact of finite size effects under two distinct choices of the Jordan Wigner transformation: the Neveu Schwartz (NS) and Ramond (R) sectors. We explore the geometric features of the system by analyzing the quantum (Berry) curvature derived from the Fubini Study metric, which is intimately connected to the quantum Fisher information. This approach uncovers a rich interplay between boundary conditions and quantum geometry. In the gamma h parameter space, we identify distinct sign changing arcs of the curvature, confined to some region. These arcs mark transitions between the NS and R sectors, indicating fundamental changes in the structure of the fermionic ground state. Remarkably, the number of such transition lines increases with system size, hinting at an emergent continuum of topological boundary effects in the thermodynamic limit. Our findings highlight a novel mechanism where boundary conditions shape quantum geometric properties, offering new insights into finite size topology and the structure of low dimensional quantum systems.

quant-ph↗

arXiv2024

Topology of the Visibility Graph of Sandpiles

In this paper, we explore the higher- and lower-order connectivity aspects of the visibility graph representation of sandpile models, focusing on the Bak-Tang-Wiesenfeld (BTW) model. By converting the time series of avalanche events into visibility graphs, we investigate the structural properties that emerge at different scales of connectivity. Specifically, we utilize persistent homology and simplicial complex theory to identify higher-order topological features. Analyzing the statistics of degree and betweenness centralities reveal that the resulting graph is a scale-free network with the degree exponent of $\gamma_k=2.50\pm 0.02$ and betweenness exponent of $\gamma_b=1.585\pm 0.008$. The analysis of the simplexes show that the distribution function of one, two and three dimensional simplexes are power-law with the exponents of $\gamma_{\sigma_1}=0.795\pm 0.006$, $\gamma_{\sigma_2}=0.602\pm 0.009$ and $\gamma_{\sigma_3}=0.422\pm 0.008$ respectively. This power-law behavior is also seen in the homology group analysis, for the Betti numbers, the exponents of which are reported in the paper. The persistent entropy of life time of $d$ dimensional holes is analyzed indicating that it increases logarithmically in terms of the network size $N$ for $d=0,1$ and $2$.

cond-mat.stat-mech↗

arXiv2024

Eigenvalue Preferential Attachment Networks A Dandelion Structure

In this paper we introduce a new type of preferential attachment network, the growth of which is based on the eigenvalue centrality. In this network, the agents attach most probably to the nodes with larger eigenvalue centrality which represents that the agent has stronger connections. A new network is presented, namely a dandelion network, which shares some properties of star-like structure and also a hierarchical network. We show that this network, having hub-and-spoke topology is not generally scale free, and shows essential differences with respect to the Barab{\'a}si-Albert preferential attachment model. Most importantly, there is a super hub agent in the system (identified by a pronounced peak in the spectrum), and the other agents are classified in terms of the distance to this super-hub. We explore a plenty of statistical centralities like the nodes degree, the betweenness and the eigenvalue centrality, along with various measures of structure like the community and hierarchical structures, and the clustering coefficient. Global measures like the shortest path statistics and the self-similarity are also examined.

cond-mat.stat-mech↗