arXiv subjects

Dima L. Shepelyansky

Publications and source records attributed to Dima L. Shepelyansky.

At least 19 recordsLinked to original sources

arXiv2026

Time reversal of complex evolution on a quantum computer

The Boltzmann-Loschmidt dispute in 1876-1877 discussed the problem of time reversal of ther- malization from time reversible classical equations of motion. Here, 150 years later, we highlight this problem in the frame of quantum computing. A quantum protocol is proposed that allows to perform a time reversal of complex evolution in the regime of many-body quantum chaos with many qubits. The system represents an evolution of qubits on a square lattice with inter-qubit next-nearest static couplings with a driven pulsed magnetic field. The system entropy grows rapidly to maximal values but returns to initial small values after time reversal. This time reversal is shown to be stable with respect to quantum gate imperfections. However, similar to the Lorenz butterfly effect, there is the butterfly effect of qubit when inversion of only one qubit breaks time reversibility of the whole system. It is argued that this protocol is accessible to nowadays quantum computers and annealers with hundreds of qubits.

cond-mat.stat-mech↗

arXiv2026

Thermodynamic statistics of given names in USA and France

Using official government data sets of USA and France we analyze the occurrence/frequency/popularity distributions of given names on a time scale of more than 100 years. These distributions are characterized through the Lorenz and Pareto curves broadly used in the analysis of wealth inequality in the world. These curves remain stable during the considered time period with the Gini coefficient remaining in the narrow range 0.85-0.95. As for the case of wealth inequality, we show that the distributions of names are well described by the Rayleigh-Jeans (RJ) thermalization and condensation phenomenon well studied in various physical systems. The RJ thermalization results from two integrals of motion being analogous to energy and probability norm conservation in physical systems with energy states corresponding to popularity levels of names. Time correlations between names are also determined showing their stability until the middle of the twentieth century and a significant change after that.

cond-mat.stat-mech↗

arXiv2026

Thermodynamic theory of voting and EU elections

We introduce a thermodynamic theory of voting and show that it provides a good description of distribution of party votes in EU elections. The theory traces parallels between system energies of coupled nonlinear oscillators and party vote fractions. Such a classical system evolution is characterized by the conservation of total energy and probability norm that leads to the Rayleigh-Jeans (RJ) thermalization and condensation at low energy states. A similar thermalization also describes the wealth inequality in society. This feature belongs to the phenomena of constraint driven condensation known in statistical mechanics. We show that the RJ theory well depicts the Lorenz and Pareto curves obtained from the EU vote results. The theory also recovers the dispersion of votes between candidates of first round presidential elections in France.

cond-mat.stat-mech↗

arXiv2026

Thermodynamic description of worldwide distribution of energy and carbon emission

Based on public data, we analyze the distributions of energy and carbon emission over world countries on a scale of the last 40-50 years using their presentation via Lorenz and Pareto curves. These curves in rescaled format remain remarkably stable on this time period being characterized by high values of the Gini coefficient indicating a strong inequality of energy distribution. To explain these distributions, we introduce the ENergy Thermalization Hypothesis (ENTH) according to which these distributions result from the Rayleigh-Jeans (RJ) thermalization and condensation of agents representing different countries. We show that this hypothesis provides an excellent description of Lorenz and Pareto curves obtained from data on the above time period. It also gives natural grounds for inequality relating it to the RJ condensation at low energy states. We additionally trace parallels with the wealth inequality in the world.

cond-mat.stat-mech↗

arXiv2026

Thermodynamic description of wealth inequality in the world

According to the recent Wealth Thermalization Hypothesis (WTH) the wealth inequality in the world is described by the Rayleigh-Jeans (RJ) thermal distribution of interacting agents in a society with social stratification. In this concept, the wealth layers of society are associated with energy levels from a nonlinear dynamical system conserving two integrals of motion being total energy and probability norm. This leads to RJ condensation and the formation of a huge poverty phase of low wealth and a tiny oligarchic phase that captures a main part of total society wealth. This RJ phenomenon has similarities with self cleaning in multimode optical fibers and constraint driven condensation in various physical systems. We analyze real Lorenz and Pareto curves for wealth of households in countries and the world, Gross Domestic Product of countries, market capitalization of companies at stock exchange of Hong Kong, Shanghai, London, bitcoin transactions, world trade between countries and show that the WTH theory gives a good description of these curves. On the basis of this comparison we argue that the RJ thermal distribution provides a universal description of wealth inequality in the world.

cond-mat.stat-mech↗

arXiv2026

Boltzmann-Loschmidt dispute reloaded quantum 150 years later

The Boltzmann-Loschmidt dispute of 1876 questioned the possibility of a statistical irreversible description by time reversible classical equations of motion of atoms. Here we show analytically and numerically that the quantum chaos diffusion of cold atoms, or ions, in a harmonic trap and pulsed optical lattice can be inverted back in time with up to 100\% efficiency. This is in sharp contrast to classical evolution where exponentially small errors break time reversibility. We argue that the existing experimental skills allow highlighting the Boltzmann-Loschmidt dispute from a quantum perspective.

cond-mat.stat-mech↗

arXiv2026

Dynamical thermalization and turbulence in social stratification models

We study the nonlinear chaotic dynamics in a system of linear oscillators coupled by social network links with an additional stratification of oscillator energies, or frequencies, and supplementary nonlinear interactions. It is argued that this system can be viewed as a model of social stratification in a society with nonlinear interacting agents with energies playing a role of wealth states of society. The Hamiltonian evolution is characterized by two integrals of motion being energy and probability norm. Above a certain chaos border the chaotic dynamics leads to dynamical thermalization with the Rayleigh-Jeans (RJ) distribution over states with given energy or wealth. At low energies, this distribution has RJ condensation of norm at low energy modes. We point out a similarity of this condensation with the wealth inequality in the world countries where about a half of population owns only a couple of percent of the total wealth. In the presence of energy pumping and absorption, the system reveals features of the Kolmogorov-Zakharov turbulence of nonlinear waves.

cond-mat.stat-mech↗

arXiv2025

Kicked fluxonium with quantum strange attractor

The quantum dissipative time evolution of a fluxonium under a pulsed field (kicks) is studied numerically and analytically. In the classical limit the system dynamics is converged to a strange chaotic attractor. The quantum properties of this system are studied for the density matrix in the frame of Lindblad equation. In the case of dissipative quantum evolution the steady-state density matrix is converged to a quantum strange attractor being similar to the classical one. It is shown that depending on the dissipation strength there is a regime when the eigenstates of density matrix are localized at a strong or moderate dissipation. At a weak dissipation the eigenstates are argued to be delocalized being linked to the Ehrenfest explosion of quantum wave packet. This phenomenon is related with the Lyapunov exponent and Ehrenfest time for the quantum strange attractor. Possible experimental realisations of this quantum strange attractor with fluxonium are discussed.

quant-ph↗

arXiv2025

Thermodynamic description of world GDP distribution over countries

We apply the concept of Rayleigh-Jeans thermalization of classical fields for a description of the world Gross Domestic Product (GDP) distribution over countries. The thermalization appears due to a variety of interactions between countries with conservation of two integrals being total GDP and probability (norm). In such a case there is an emergence of Rayleigh-Jeans condensation at states with low GDP. This phenomenon has been studied theoretically and experimentally in multimode optical fibers and we argue that it is at the origin of emergence of poverty and oligarchic phases for GDP of countries. A similar phenomenon has been discussed recently in the framework of the Wealth Thermalization Hypothesis to explain the high inequality of wealth distribution in human society and companies at Stock Exchange markets. We show that the Rayleigh-Jeans thermalization well describes the GDP distribution during the last 50 years.

cond-mat.stat-mech↗

arXiv2025

Opinion formation at Ising social networks

We study the process of opinion formation in an Ising social network of scientific collaborations. The network is undirected. An Ising spin is associated with each network node being oriented up (red) or down (blue). Certain nodes carry fixed, opposite opinions whose influence propagates over the other spins, which are flipped according to the majority-influence opinion of neighbors of a given spin during the asynchronous Monte Carlo process. The amplitude influence of each spin is self-consistently adapted, and a flip occurs only if this majority influence exceeds a certain conviction threshold. All non-fixed spins are initially randomly distributed, with half of them oriented up and half down. Such a system can be viewed as a model of elite influence, coming from the fixed spins, on the opinions of the crowd of non-fixed spins. We show that a phase transition occurs as the amplitude influence of the crowd spins increases: the dominant opinion shifts from that of the elite nodes to a phase in which the crowd spins' opinion becomes dominant and the elite can no longer impose their views.

physics.soc-ph↗

arXiv2025

Dynamical thermalization, Rayleigh-Jeans condensate, vortexes and wave collapse in quantum chaos fibers and fluid of light

We study analytically and numerically the time evolution of a nonlinear field described by the nonlinear Schrödinger equation in a chaotic $D$-shape billiard. In absence of nonlinearity the system has standard properties of quantum chaos. This model describes a longitudinal light propagation in a multimode D-shape optical fiber and also those in a Kerr nonlinear medium of atomic vapor. We show that, above a certain chaos border of nonlinearity, chaos leads to dynamical thermalization with the Rayleigh-Jeans thermal distribution and the formation of the Rayleigh-Jeans condensate in a vicinity of the ground state accumulating in it about 80-90\% of total probability. Certain similarities of this phenomenon with the Fröhlich condensate are discussed. Below the chaos border the dynamics is quasi-integrable corresponding to the Kolmogorov-Arnold-Moser integrability. We describe also the time evolution during the process of relaxation to the thermal state and the time dependence of quantum von Neumann and classical Boltzmann entropies during this process. At a strong focusing nonlinearity we show that the wave collapse can take place even at sufficiently high positive energy being very different from the open space case. Finally for the defocusing case we establish the superfluid regime for vortex dynamics at strong nonlinearity. System parameters for optical fiber experimental studies of these effects are also discussed.

cond-mat.stat-mech↗

arXiv2025

Opinion formation in Wikipedia Ising networks

We study properties of opinion formation on Wikipedia Ising Networks. Each Wikipedia article is represented as a node and links are formed by citations of one article to another generating a directed network of a given language edition with millions of nodes. Ising spins are placed at each node and their orientation up or down is determined by a majority vote of connected neighbors. At the initial stage there are only a few nodes from two groups with fixed competing opinions up and down while other nodes are assumed to have no initial opinion with no effect on the vote. The competition of two opinions is modeled by an asynchronous Monte Carlo process converging to a spin polarized steady-state phase. This phase remains stable with respect to small fluctuations induced by an effective temperature of the Monte Carlo process. The opinion polarization at the steady-state provides opinion (spin) preferences for each node. In the framework of this Ising Network Opinion Formation model we analyze the influence and competition between political leaders, world countries and social concepts. This approach is also generalized to the competition between three groups of different opinions described by three colors, for example Donald Trump, Vladimir Putin, Xi Jinping or USA, Russia, China within English, Russian and Chinese editions of Wikipedia of March 2025. We argue that this approach provides a generic description of opinion formation in various complex networks.

cs.SI↗

arXiv2025

Confrontation of capitalism and socialism in Wikipedia networks

We introduce the Ising Network Opinion Formation (INOF) model and apply it for the analysis of networks of 6 Wikipedia language editions. In the model, Ising spins are placed at network nodes/articles and the steady-state opinion polarization of spins is determined from the Monte Carlo iterations in which a given spin orientation is determined by in-going links from other spins. The main consideration is done for opinion confrontation between {\it capitalism, imperialism} (blue opinion) and {\it socialism, communism} (red opinion). These nodes have fixed spin/opinion orientation while other nodes achieve their steady-state opinions in the process of Monte Carlo iterations. We find that the global network opinion favors {\it socialism, communism} for all 6 editions. The model also determines the opinion preferences for world countries and political leaders, showing good agreement with heuristic expectations. We also present results for opinion competition between {\it Christianity} and {\it Islam}, and USA Democratic and Republican parties. We argue that the INOF approach can find numerous applications for directed complex networks.

cs.SI↗

arXiv2025

Wealth Thermalization Hypothesis and Social Networks

In 1955 Fermi, Pasta, Ulam and Tsingou performed first numerical studies with the aim to obtain the thermalization in a chain of nonlinear oscillators from dynamical equations of motion. This model happend to have several specific features and the dynamical thermalization was established only later in other studies. In this work we study more generic models based on Random Matrix Theory and social networks with a nonlinear perturbation leading to dynamical thermalization above a certain chaos border. These systems have two integrals of motion being total energy and norm so that the theoretical Rayleigh-Jeans thermal distribution depends on temperature and chemical potential. We introduce the wealth thermalization hypothesis according to which the society wealth is associated with energy in the Rayleigh-Jeans distribution. At relatively small values of total wealth or energy there is a formation of the Rayleigh-Jeans condensate, well studied in physical systems such as multimode optical fibers. This condensation leads to a huge fraction of poor households at low wealth and a small oligarchic fraction which monopolizes a dominant fraction of total wealth thus generating a strong inequality in human society. We show that this thermalization gives a good description of real data of Lorenz curves of US, UK, the whole world and capitalization of companies at Stock Exchange of New York SE (NYSE), London and Hong Kong. It is also shown that above a chaos border the dynamical Rayleigh-Jeans thermalization takes place also in social networks with the Lorenz curves being similar to those of wealth distribution in world countries. Possible actions for inequality reduction are briefly discussed.

cond-mat.stat-mech↗

arXiv2024

Relations of society concepts and religions from Wikipedia networks

We analyze the Google matrix of directed networks of Wikipedia articles related to 8 recent Wikipedia language editions representing different cultures (English, Arabic, German, Spanish, French, Italian, Russian, Chinese). Using the reduced Google matrix algorithm we determine relations and interactions of 23 society concepts and 17 religions represented by their respective articles for each of the 8 editions. The effective Markov transitions are found to be more intense inside the two blocks of society concepts and religions while transitions between the blocks are significantly reduced. We establish 5 poles of influence for society concepts (Law, Society, Communism, Liberalism, Capitalism) as well as 5 poles for religions (Christianity, Islam, Buddhism, Hinduism, Chinese folk religion) and determine how they affect other entries. We compute inter edition correlations for different key quantities providing a quantitative analysis of the differences or the proximity of views of the 8 cultures with respect to the selected society concepts and religions.

physics.soc-ph↗

arXiv2024

Random matrix model of Kolmogorov-Zakharov turbulence

We introduce and study a random matrix model of Kolmogorov-Zakharov turbulence in a nonlinear purely dynamical finite size system with many degrees of freedom. For the case of a direct cascade the energy and norm pumping takes place at low energy scales with absorption at high energies. For a pumping strength above a certain chaos border a global chaotic attractor appears with a stationary energy flow through a Hamiltonian inertial energy interval. In this regime, the steady-state norm distribution is described by an algebraic decay with an exponent in agreement with the Kolmogorov-Zakharov theory. Below the chaos border the system is located in the quasi-integrable regime similar to the Kolmogorov-Arnold-Moser theory and the turbulence is suppressed. For the inverse cascade the system rapidly enters a strongly nonlinear regime where the weak turbulence description is invalid. We argue that such a dynamical turbulence is generic showing that it is present in other lattice models with disorder and Anderson localization. We point out that such dynamical models can be realized in multimode optical fibers.

cond-mat.stat-mech↗

arXiv2024

Opinion formation in the world trade network

We extend the opinion formation approach to probe the world influence of economical organizations. Our opinion formation model mimics a battle between currencies within the international trade network. Based on the United Nations Comtrade database, we construct the world trade network for the years of the last decade from 2010 to 2020. We consider different core groups constituted by countries preferring to trade in a specific currency. We will consider principally two core groups, namely, 5 Anglo-Saxon countries which prefer to trade in US dollar and the 11 BRICS+ which prefer to trade in a hypothetical currency, hereafter called BRI, pegged to their economies. We determine the trade currency preference of the other countries via a Monte Carlo process depending on the direct transactions between the countries. The results obtained in the frame of this mathematical model show that starting from year 2014 the majority of the world countries would have preferred to trade in BRI than USD. The Monte Carlo process reaches a steady state with 3 distinct groups: two groups of countries preferring, whatever is the initial distribution of the trade currency preferences, to trade, one in BRI and the other in USD, and a third group of countries swinging as a whole between USD and BRI depending on the initial distribution of the trade currency preferences. We also analyze the battle between USD, EUR and BRI, and present the reduced Google matrix description of the trade relations between the Anglo-Saxon countries and the BRICS+.

q-fin.TR↗

arXiv2023

Goal quest for an intelligent surfer moving in a chaotic flow

We consider a model of an intelligent surfer moving on the Ulam network generated by a chaotic dynamics in the Chirikov standard map. This directed network is obtained by the Ulam method with a division of the phase space in cells of fixed size forming the nodes of a Markov chain. The goal quest for this surfer is to determine the network path from an initial node A to a final node B with minimal resistance given by the sum of inverse transition probabilities. We develop an algorithm for the intelligent surfer that allows to perform the quest in a small number of transitions which grows only logarithmically with the network size. The optimal path search is done on a fractal intersection set formed by nodes with small Erdös numbers of the forward and inverted networks. The intelligent surfer exponentially outperforms a naive surfer who tries to minimize its phase space distance to the target B. We argue that such an algorithm provides new hints for motion control in chaotic flows.

physics.soc-ph↗