arXiv subjects

Thomas H. Seligman

Publications and source records attributed to Thomas H. Seligman.

At least 19 recordsLinked to original sources

arXiv2025

Lithium Adsorbtion on Polyacenes $\&$ Zig-zag-edge Graphene Strips

The effect of increased electron-density (from adsorbed Li atoms) in polyacenes and in nano-ribbons with zig-zag edge is discussed in terms of resonance theoretical considerations and in terms edge-localized frontier molecular orbitals. The argumentation from simple pictures is finally using the density functional theory (DFT) for anthracene, polyacene polymer and graphene strips. Some discussion is made for zig-zag edge graphene.

physics.chem-ph↗

arXiv2025

From sectorial coarse graining to extreme coarse graining of S&P 500 correlation matrices

Starting from the Pearson Correlation Matrix of stock returns and from the desire to obtain a reduced number of parameters relevant for the dynamics of a financial market, we propose to take the idea of a sectorial matrix, which would have a large number of parameters, to the reduced picture of a real symmetric $2 \times 2$ matrix, extreme case, that still conserves the desirable feature that the average correlation can be one of the parameters. This is achieved by averaging the correlation matrix over blocks created by choosing two subsets of stocks for rows and columns and averaging over each of the resulting blocks. Averaging over these blocks, we retain the average of the correlation matrix. We shall use a random selection for two equal block sizes as well as two specific, hopefully relevant, ones that do not produce equal block sizes. The results show that one of the non-random choices has somewhat different properties, whose meaning will have to be analyzed from an economy point of view.

q-fin.ST↗

arXiv2024

COVID anomaly in the correlation analysis of S&P 500 market states

Analyzing market states of the S&P 500 components on a time horizon January 3, 2006 to August 10, 2023, we found the appearance of a new market state not previously seen and we shall discuss its possible implications as an isolated state or as a beginning of a new general market condition. We study this in terms of the Pearson correlation matrix and relative correlation with respect to the S&P 500 index. In both cases the anomaly shows strongly.

stat.AP↗

arXiv2023

Dynamics of market states and risk assessment

Previous research explored various conditions of financial markets based on the similarity of correlation structures and classified as market states. We introduce modifications to previous selection criteria for these market states, mainly due to increased attention to the transition matrix between the states. Clustering and thus market states are fixed by the optimization of two parameters -- number of clusters and noise suppression, but in similar conditions, we give preference to the clustering which avoids large jumps in the transition matrix. We found statistically significant results applying this model to the SP 500 and Nikkei 225 markets for the pre-COVID-19 pandemic era (2006-2019). Retaining the epoch length of 20 trading days but reducing the shift of the epoch to a single trading day we are led to the concept of a trajectory of the market in the space of correlation matrices. We may visualize these states after dimensional scaling to two or three dimensions. This approach, using dynamics, improves the options of risk assessment, opens the door to dynamical treatments of markets (e.g. hedging), and shows noise suppression in a new light.

q-fin.ST↗

arXiv2023

A dynamical Interpretation of Sequential Decay in Reactive Scattering

The topic of this article is a dynamical explanation of the sequential decay in rearrangement scattering. The essential observation is the behaviour of trajectories close to the basin boundary of the breakup channel. As a most simplistic example of demonstration, we use a version of the perturbed three particle Calogero-Moser system in a 1-dimensional position space.

nlin.CD↗

arXiv2021

Random Matrix Ensembles For Many-Body Quantum Systems

Classical random matrix ensembles were originally introduced in physics to approximate quantum many-particle nuclear interactions. However, there exists a plethora of quantum systems whose dynamics is explained in terms of few-particle (predominantly two-particle) interactions. The random matrix models incorporating the few-particle nature of interactions are known as embedded random matrix ensembles. In the present paper, we provide a brief overview of these two ensembles and illustrate how the embedded ensembles can be successfully used to study decoherence of a qubit interacting with an environment, both for fermionic and bosonic embedded ensembles. Numerical calculations show the dependence of decoherence on the nature of the environment.

quant-ph↗

arXiv2021

Dynamics of the market states in the space of correlation matrices with applications to financial markets

The concept of states of financial markets based on correlations has gained increasing attention during the last 10 years. We propose to retrace some important steps up to 2018, and then give a more detailed view of recent developments that attempt to make the use of this more practical. Finally, we try to give a glimpse to the future proposing the analysis of trajectories in correlation matrix space directly or in terms of symbolic dynamics as well as attempts to analyze the clusters that make up the states in a random matrix context.

q-fin.ST↗

arXiv2020

Photonic realization of the kappa-deformed Dirac equation

We show an implementation of a kappa-deformed Dirac equation in tight-binding arrays of photonic waveguides. This is done with a special configuration of couplings extending to second nearest neighbors. Geometric manipulations can control these evanescent couplings. A careful study of wave packet propagation is presented, including the effects of deformation parameters on Zitterbewegung or trembling motion. In this way, we demonstrate how to recreate the effects of a flat noncommutative spacetime -i.e., kappa-Minkowski spacetime -in simple experimental setups. We touch upon elastic realizations in the section of Conclusions.

hep-lat↗

arXiv2020

Market states: A new understanding

We present the clustering analysis of the financial markets of S&P 500 (USA) and Nikkei 225 (JPN) markets over a period of 2006-2019 as an example of a complex system. We investigate the statistical properties of correlation matrices constructed from the sliding epochs. The correlation matrices can be classified into different clusters, named as market states based on the similarity of correlation structures. We cluster the S&P 500 market into four and Nikkei 225 into six market states by optimizing the value of intracluster distances. The market shows transitions between these market states and the statistical properties of the transitions to critical market states can indicate likely precursors to the catastrophic events. We also analyze the same clustering technique on surrogate data constructed from average correlations of market states and the fluctuations arise due to the white noise of short time series. We use the correlated Wishart orthogonal ensemble for the construction of surrogate data whose average correlation equals the average of the real data.

q-fin.CP↗

arXiv2020

Hidden duality and accidental degeneracy in cycloacene and Möbius cycloacene

The accidental degeneracy appearing in cycloacenes as triplets and quadruplets is explained with the concept of segmentation, introduced here with the aim of describing the effective disconnection of $π$ orbitals on these organic compounds. For periodic systems with time reversal symmetry, the emergent nodal domains are shown to divide the atomic chains into simpler carbon structures analog to benzene rings, diallyl chains, anthracene (triacene) chains and tetramethyl-naphtalene skeletal forms. The common electronic levels of these segments are identified as members of degenerate multiplets of the global system. The peculiar degeneracy of Möbius cycloacene is also explained by segmentation. In the last part, it is shown that the multiplicity of energies for cycloacene can be foreseen by studying the continuous limit of the tight-binding model; the degeneracy conditions are put in terms of Chebyshev polynomials. The results obtained in this work have important consequences on the physics of electronic transport in organic wires, together with their artificial realizations.

physics.chem-ph↗

arXiv2020

Current vortices in aromatic carbon molecules

The local current flow through three small aromatic carbon molecules, namely benzene, naphthalene and anthracene, is studied. Applying density functional theory and the non-equilibrium Green's function method for transport, we demonstrate that pronounced current vortices exist at certain electron energies for these molecules. The intensity of these circular currents, which appear not only at the anti-resonances of the transmission but also in vicinity of its maxima, can exceed the total current flowing through the molecular junction and generate considerable magnetic fields. The $π$ electron system of the molecular junctions is emulated experimentally by a network of macroscopic microwave resonators. The local current flows in these experiments confirm the existence of current vortices as a robust property of ring structures. The circular currents can be understood in terms of a simple nearest-neighbor tight-binding Hückel model. Current vortices are caused by the interplay of the complex eigenstates of the open system which have energies close-by the considered electron energy. Degeneracies, as observed in benzene and anthracene, can thus generate strong circular currents, but also non-degenerate systems like naphthalene exhibit current vortices. Small imperfections and perturbations can couple otherwise uncoupled states and induce circular currents.

cond-mat.mes-hall↗

arXiv2018

Complex market dynamics in the light of random matrix theory

We present a brief overview of random matrix theory (RMT) with the objectives of highlighting the computational results and applications in financial markets as complex systems. An oft-encountered problem in computational finance is the choice of an appropriate epoch over which the empirical cross-correlation return matrix is computed. A long epoch would smoothen the fluctuations in the return time series and suffers from non-stationarity, whereas a short epoch results in noisy fluctuations in the return time series and the correlation matrices turn out to be highly singular. An effective method to tackle this issue is the use of the power mapping, where a non-linear distortion is applied to a short epoch correlation matrix. The value of distortion parameter controls the noise-suppression. The distortion also removes the degeneracy of zero eigenvalues. Depending on the correlation structures, interesting properties of the eigenvalue spectra are found. We simulate different correlated Wishart matrices to compare the results with empirical return matrices computed using the S&P 500 (USA) market data for the period 1985-2016. We also briefly review two recent applications of RMT in financial stock markets: (i) Identification of "market states" and long-term precursor to a critical state; (ii) Characterization of catastrophic instabilities (market crashes).

q-fin.ST↗

arXiv2018

Identifying long-term precursors of financial market crashes using correlation patterns

The study of the critical dynamics in complex systems is always interesting yet challenging. Here, we choose financial market as an example of a complex system, and do a comparative analyses of two stock markets - the S&P 500 (USA) and Nikkei 225 (JPN). Our analyses are based on the evolution of crosscorrelation structure patterns of short time-epochs for a 32-year period (1985-2016). We identify "market states" as clusters of similar correlation structures, which occur more frequently than by pure chance (randomness). The dynamical transitions between the correlation structures reflect the evolution of the market states. Power mapping method from the random matrix theory is used to suppress the noise on correlation patterns, and an adaptation of the intra-cluster distance method is used to obtain the "optimum" number of market states. We find that the USA is characterized by four market states and JPN by five. We further analyze the co-occurrence of paired market states; the probability of remaining in the same state is much higher than the transition to a different state. The transitions to other states mainly occur among the immediately adjacent states, with a few rare intermittent transitions to the remote states. The state adjacent to the critical state (market crash) may serve as an indicator or a "precursor" for the critical state and this novel method of identifying the long-term precursors may be very helpful for constructing the early warning system in financial markets, as well as in other complex systems.

q-fin.ST↗

arXiv2018

Correlation networks from random walk time series

Stimulated by the growing interest in the applications of complex networks framework on time series analysis, we devise a network model in which each of $N$ nodes is associated with a random walk of length $L$. Connectivity between any two nodes is established when the Pearson correlation coefficient(PCC) of the corresponding time series is greater than or equal to a threshold $H$, resulting in similarity networks with interesting properties. In particular, these networks can have high average clustering coefficients, "small world" property, and their degree distribution can vary from scale-free to quasi-constant depending on $H$. A giant component of size $N$ exists until a critical threshold $H_c$ is crossed, at which point relatively rare walks begin to detach from it, and remain isolated. This model can be used as a first step for building a null hypothesis for networks constructed from time series.

physics.soc-ph↗

arXiv2018

Characterization of catastrophic instabilities: Market crashes as paradigm

Catastrophic events, though rare, do occur and when they occur, they have devastating effects. It is, therefore, of utmost importance to understand the complexity of the underlying dynamics and signatures of catastrophic events, such as market crashes. For deeper understanding, we choose the US and Japanese markets from 1985 onward, and study the evolution of the cross-correlation structures of stock return matrices and their eigenspectra over different short time-intervals or "epochs". A slight non-linear distortion is applied to the correlation matrix computed for any epoch, leading to the emerging spectrum of eigenvalues. The statistical properties of the emerging spectrum display: (i) the shape of the emerging spectrum reflects the market instability, (ii) the smallest eigenvalue may be able to statistically distinguish the nature of a market turbulence or crisis -- internal instability or external shock, and (iii) the time-lagged smallest eigenvalue has a statistically significant correlation with the mean market cross-correlation. The smallest eigenvalue seems to indicate that the financial market has become more turbulent in a similar way as the mean does. Yet we show features of the smallest eigenvalue of the emerging spectrum that distinguish different types of market instabilities related to internal or external causes. Based on the paradigmatic character of financial time series for other complex systems, the capacity of the emerging spectrum to understand the nature of instability may be a new feature, which can be broadly applied.

q-fin.GN↗

arXiv2017

Protecting coherence by environmental decoherence: A solvable paradigmatic model

We consider a particularly simple exactly solvable model for a qubit coupled to sequentially nested environments. The purpose is to exemplify the coherence conserving effect of a central system, that has been reported as a result of increasing the coupling between near and far environment. The paradigmatic example is the Jaynes-Cummings Hamiltonian, which we introduce into a Kossakowski-Lindblad master equation using alternatively the lowering operator of the oscillator or its number operator as Lindblad operators. The harmonic oscillator is regarded as the near environment of the qubit, while effects of a far environment are accounted for by the two options for the dissipative part of the master equation. The exact solution allows us to cover the entire range of coupling strength from the perturbative regime to strong coupling analytically. The coherence conserving effect of the coupling to the far environment is confirmed throughout.

quant-ph↗

arXiv2017

Chains of benzenes with lithium-atom adsorption: Vibrations and spontaneous symmetry breaking

We study effects of different configurations of adsorbates on the vibrational modes as well as symmetries of polyacenes and poly-p-phenylenes focusing on lithium atom adsorption. We found that the spectra of the vibrational modes distinguish the different configurations. For more regular adsorption schemes the lowest states are bending and torsion modes of the skeleton, which are essentially followed by the adsorbate. On poly-p-phenylenes we found that lithium adsorption reduces and often eliminates the torsion between rings thus increasing symmetry. There is spontaneous symmetry breaking in poly-p-phenylenes due to double adsorption of lithium atoms on alternating rings.

physics.chem-ph↗

arXiv2017

Transport gap engineering by contact geometry in graphene nanoribbons: Experimental and theoretical studies on artificial materials

Electron transport in small graphene nanoribbons is studied by microwave emulation experiments and tight-binding calculations. In particular, it is investigated under which conditions a transport gap can be observed. Our experiments provide evidence that armchair ribbons of width $3m+2$ with integer $m$ are metallic and otherwise semiconducting, whereas zigzag ribbons are metallic independent of their width. The contact geometry, defining to which atoms at the ribbon edges the source and drain leads are attached, has strong effects on the transport. If leads are attached only to the inner atoms of zigzag edges, broad transport gaps can be observed in all armchair ribbons as well as in rhomboid-shaped zigzag ribbons. All experimental results agree qualitatively with tight-binding calculations using the nonequilibrium Green's function method.

cond-mat.mes-hall↗