arXiv subjects

Armen E. Allahverdyan

Publications and source records attributed to Armen E. Allahverdyan.

At least 19 recordsLinked to original sources

arXiv2026

Nonlocal Electrostatic Field Theory from Microscopic Description

The study of electric fields in soft materials converges either to the study of point-like particles (local) in nonlinear theories or to the use of particles with finite sizes in nonlocal linear theories. In this work we start from the microscopic equations of motion and construct a unified mean field Fokker-Planck equation that describes the non-equilibrium electrostatics of nonlocal nonlinear systems. We obtain a generalized Poisson-Boltzmann equation for such systems as well as their electrostatic free energy expression. In the linear approximation we obtain an anisotropic susceptibility in an isotropic fluid which allows for local linear response inversion in electrostatics.

cond-mat.soft↗

arXiv2026

Resonances in light scattering from nonequilibrium dipole pairs

We identify a fundamentally new class of resonances in light scattering from a pair of point-like electric dipoles. These resonances arise from multiple scattering response and correspond to poles of the two-particle Green function. The realization of exact resonances requires violation of the optical theorem, which holds in equilibrium systems but can be violated under nonequilibrium conditions, without violating causality. As a concrete example, we show that a pumped two-level atom can realize the required polarizability and access the exact resonance regime. Our results for one electric and one magnetic dipole show how resonances can amplify a weak magnetic response of a single dipole to the incident field. In equilibrium systems, only approximate resonances with finite amplification are possible. Using the Drude model for metallic nanoparticles, we show that while equilibrium resonances enhance the scattering, they never exceed the optimal single-dipole response.

physics.optics↗

arXiv2025

System-Bath Approach to Rotating Brownian Motion

Rotating equilibrated systems are widespread, but relatively little attention has been devoted to studying them from the first principles of statistical mechanics. We fill this gap by studying a Brownian particle coupled with a thermal bath made of rotating harmonic oscillators. We show that the Langevin equation that describes the dynamics of the Brownian particle contains (due to rotation) long-range correlated noise. In contrast to the usual situation of (non-rotating) equilibration, the rotating Gibbs distribution is recovered only for a weak coupling with the bath. In the presence of a uniform magnetic field, the stationary state is not Gibbsian, even under weak coupling. In this context, we clarify the applicability of the Bohr-van Leeuwen theorem to classical systems in rotating equilibrium, as well as the concept of work done by a changing magnetic field. We show that the Brownian particle under a rotationally symmetric potential reaches a stationary state that behaves as an effective equilibrium, characterized by a free energy. As a result, no work can be extracted via cyclic processes that respect the rotation symmetry. However, if the external potential exhibits asymmetry, then work extraction via slow cyclic processes is possible. This is illustrated by a general scenario involving a slow rotation of a non-rotation-symmetric potential. We study sedimentation equilibrium and show that centrifugal instability is prevented by a finite friction.

cond-mat.stat-mech↗

arXiv2025

Enhanced detection of time-dependent dielectric structure: Rayleigh's limit and quantum vacuum

Detection of scattered light can determine the susceptibility of dielectrics. Such imaging normally holds Rayleigh's limit: details finer than the wavelength of the incident light cannot be determined from the far-field zone. We show that time-modulation of an inhomogeneous dielectric can be used to determine its susceptibility. To this end, we focus on the inverse quantum optics problem for spatially and temporally modulated metamaterial, whose dielectric susceptibility is similar to moving dielectrics. We show that the vacuum contribution to the photodetection signal is non-zero due to the negative frequencies even in the far-field zone. Hence, certain dielectric features can be determined without radiating any incident field on the dielectric. When the incident light is scattered (or re-radiated), the determination of dielectric susceptibility is enhanced and overcomes Rayleigh's limit in the far-field zone. We study similar effects for an inhomogeneous dielectric moving with a constant speed, a problem we consider within relativistic optics. Now the vacuum contribution to the photodetection signal reflects dielectric features, can be long-range in space but is not a far-field effect.

quant-ph↗

arXiv2024

Unsupervised extraction of local and global keywords from a single text

We propose an unsupervised, corpus-independent method to extract keywords from a single text. It is based on the spatial distribution of words and the response of this distribution to a random permutation of words. As compared to existing methods (such as e.g. YAKE) our method has three advantages. First, it is significantly more effective at extracting keywords from long texts. Second, it allows inference of two types of keywords: local and global. Third, it uncovers basic themes in texts. Additionally, our method is language-independent and applies to short texts. The results are obtained via human annotators with previous knowledge of texts from our database of classical literary works (the agreement between annotators is from moderate to substantial). Our results are supported via human-independent arguments based on the average length of extracted content words and on the average number of nouns in extracted words. We discuss relations of keywords with higher-order textual features and reveal a connection between keywords and chapter divisions.

cs.CL↗

arXiv2024

Teaching ideal quantum measurement, from dynamics to interpretation

We present a graduate course on ideal measurements, analyzed as dynamical processes of interaction between the tested system S and an apparatus A, described by quantum statistical mechanics. The apparatus A=M+B involves a macroscopic measuring device M and a bath B. The requirements for ideality of the measurement allow us to specify the Hamiltonian of the isolated compound system S+M+B. The resulting dynamical equations may be solved for simple models. Conservation laws are shown to entail two independent relaxation mechanisms: truncation and registration. Approximations, justified by the large size of M and of B, are needed. The final density matrix $\hat{\cal D}(t_f)$ of S+A has an equilibrium form. It describes globally the outcome of a large set of runs of the measurement. The measurement problem, i.e., extracting physical properties of individual runs from $\hat{\cal D}(t_f)$, then arises due to the ambiguity of its splitting into parts associated with subsets of runs. To deal with this ambiguity, we postulate that each run ends up with a distinct pointer value $A_i$ of the macroscopic M. This is compatible with the principles of quantum mechanics. Born's rule then arises from the conservation law for the tested observable; it expresses the frequency of occurrence of the final indications $A_i$ of M in terms of the initial state of S. Von Neumann's reduction amounts to updating of information due to selection of $A_i$. We advocate the terms $q$-probabilities and $q$-correlations when analyzing measurements of non-commuting observables. These ideas may be adapted to different types of courses.

quant-ph↗

arXiv2024

Thermal transitions in a one-dimensional, finite-size Ising model

We revisit the one-dimensional ferromagnetic Ising spin-chain with a finite number of spins and periodic boundaries and derive analytically and verify numerically its various stationary and dynamical properties at different temperatures. In particular, we determine the probability distributions of magnetization, the number of domain walls, and the corresponding residence times for different chain lengths and magnetic fields. While we study finite systems at thermal equilibrium, we identify several temperatures similar to the critical temperatures for first-order phase transitions in the thermodynamic limit. We illustrate the utility of our results by their application to structural transitions in biopolymers having non-trivial intermediate equilibrium states.

cond-mat.stat-mech↗

arXiv2023

Ultimatum game: regret or fairness?

In the ultimatum game, the challenge is to explain why responders reject non-zero offers thereby defying classical rationality. Fairness and related notions have been the main explanations so far. We explain this rejection behavior via the following principle: if the responder regrets less about losing the offer than the proposer regrets not offering the best option, the offer is rejected. This principle qualifies as a rational punishing behavior and it replaces the experimentally falsified classical rationality (the subgame perfect Nash equilibrium) that leads to accepting any non-zero offer. The principle is implemented via the transitive regret theory for probabilistic lotteries. The expected utility implementation is a limiting case of this. We show that several experimental results normally prescribed to fairness and intent-recognition can be given an alternative explanation via rational punishment; e.g. the comparison between "fair" and "superfair", the behavior under raising the stakes etc. Hence we also propose experiments that can distinguish these two scenarios (fairness versus regret-based punishment). They assume different utilities for the proposer and responder. We focus on the mini-ultimatum version of the game and also show how it can emerge from a more general setup of the game.

econ.TH↗

arXiv2023

Regret theory, Allais' Paradox, and Savage's omelet

We study a sufficiently general regret criterion for choosing between two probabilistic lotteries. For independent lotteries, the criterion is consistent with stochastic dominance and can be made transitive by a unique choice of the regret function. Together with additional (and intuitively meaningful) super-additivity property, the regret criterion resolves the Allais' paradox including the cases were the paradox disappears, and the choices agree with the expected utility. This superadditivity property is also employed for establishing consistency between regret and stochastic dominance for dependent lotteries. Furthermore, we demonstrate how the regret criterion can be used in Savage's omelet, a classical decision problem in which the lottery outcomes are not fully resolved. The expected utility cannot be used in such situations, as it discards important aspects of lotteries.

econ.TH↗

arXiv2022

Lasting effects of static magnetic field on classical Brownian motion

The Bohr-Van Leeuwen theorem states that an external static magnetic field does not influence the state of a classical equilibrium system: there is no equilibrium classical magnetism, since the magnetic field does not do work. We revisit this famous no-go result and consider a classical charged Brownian particle interacting with an equilibrium bath. We confirm that the Bohr-Van Leeuwen theorem holds for the long-time (equilibrium) state of the particle. But the external static, homogeneous magnetic field does influence the long-time state of the thermal bath, which is described via the Caldeira-Leggett model. In particular, the magnetic field induces an average angular momentum for the (uncharged!) bath, which separates into two sets rotating in opposite directions. The effect relates to the bath going slightly out of equilibrium under the influence of the Brownian particle and persists for arbitrarily long times. In this context we studied the behavior of the two other additive integrals of motion, energy and linear momentum. The situation with linear momentum is different, because it is dissipated away by (and from) the bath modes. The average energy of the bath mode retains the magnetic field as a small correction. Thus, only the bath angular momentum really feels the magnetic field for long times.

cond-mat.stat-mech↗

arXiv2022

Optimal alphabet for single text compression

A text written using symbols from a given alphabet can be compressed using the Huffman code, which minimizes the length of the encoded text. It is necessary, however, to employ a text-specific codebook, i.e. the symbol-codeword dictionary, to decode the original text. Thus, the compression performance should be evaluated by the full code length, i.e. the length of the encoded text plus the length of the codebook. We studied several alphabets for compressing texts -- letters, n-grams of letters, syllables, words, and phrases. If only sufficiently short texts are retained, an alphabet of letters or two-grams of letters is optimal. For the majority of Project Gutenberg texts, the best alphabet (the one that minimizes the full code length) is given by syllables or words, depending on the representation of the codebook. Letter 3 and 4-grams, having on average comparable length to syllables/words, perform noticeably worse than syllables or words. Word 2-grams also are never the best alphabet, on the account of having a very large codebook. We also show that the codebook representation is important -- switching from a naive representation to a compact one significantly improves the matters for alphabets with large number of symbols, most notably the words. Thus, meaning-expressing elements of the language (syllables or words) provide the best compression alphabet.

cs.IT↗

arXiv2022

Dissipative search of an unstructured database

The search of an unstructured database amounts to finding one element having a certain property out of $N$ elements. The classical search with an oracle checking one element at a time requires on average $N/2$ steps. The Grover algorithm for the quantum search, and its unitary Hamiltonian evolution analogue, accomplish the search asymptotically optimally in $\mathcal{O} (\sqrt{N})$ time steps. We reformulate the search problem as a dissipative Markov process acting on an $N$-level system weakly coupled to a thermal bath. Assuming that the energy levels of the system represent the database elements, we show that, with a proper choice of the spectrum and physically admissible, long-range transition rates between the energy levels, the system relaxes to the ground state, corresponding to the sought element, in time $\mathcal{O} (\ln N)$.

quant-ph↗

arXiv2022

Non-equilibrium, weak-field induced magnetism: a mechanism for magnetobiology

There is a long-time quest for understanding physical mechanisms of weak magnetic field interaction with biological matter. Two factors impeded the development of such mechanisms: first, a high (room) temperature of a cellular environment, where a weak, static magnetic field induces a (classically) zero equilibrium response. Second, the friction in the cellular environment is large, preventing a weak field to alter non-equilibrium processes such as a free diffusion of charges. Here we study a class of non-equilibrium steady states of a cellular ion in a confining potential, where the response to a (weak, homogeneous, static) magnetic field survives strong friction and thermal fluctuations. The magnetic field induces a rotational motion of the ion that proceeds with the cyclotron frequency. Such non-equilibrium states are generated by a white noise acting on the ion additionally to the non-local (memory-containing) friction and noise generated by an equilibrium thermal bath. The intensity of this white noise can be weak, i.e. much smaller than the thermal noise intensity.

cond-mat.stat-mech↗

arXiv2021

Dynamical symmetrization of the state of identical particles

We propose a dynamical model for state symmetrization of two identical particles produced in spacelike-separated events by independent sources. We adopt the hypothesis that the pair of non-interacting particles can initially be described by a tensor product state since they are in principle distinguishable due to their spacelike separation. As the particles approach each other, a quantum jump takes place upon particle collision, which erases their distinguishability and projects the two-particle state onto an appropriately (anti)symmetrized state. The probability density of the collision times can be estimated quasi-classically using the Wigner functions of the particles' wavepackets, or derived from fully quantum mechanical considerations using an appropriately adapted time-of-arrival operator. Moreover, the state symmetrization can be formally regarded as a consequence of the spontaneous measurement of the collision time. We show that symmetric measurements performed on identical particles can in principle discriminate between the product and symmetrized states. Our model and its conclusions can be tested experimentally.

quant-ph↗

arXiv2020

Two halves of a meaningful text are statistically different

Which statistical features distinguish a meaningful text (possibly written in an unknown system) from a meaningless set of symbols? Here we answer this question by comparing features of the first half of a text to its second half. This comparison can uncover hidden effects, because the halves have the same values of many parameters (style, genre {\it etc}). We found that the first half has more different words and more rare words than the second half. Also, words in the first half are distributed less homogeneously over the text in the sense of of the difference between the frequency and the inverse spatial period. These differences hold for the significant majority of several hundred relatively short texts we studied. The statistical significance is confirmed via the Wilcoxon test. Differences disappear after random permutation of words that destroys the linear structure of the text. The differences reveal a temporal asymmetry in meaningful texts, which is confirmed by showing that texts are much better compressible in their natural way (i.e. along the narrative) than in the word-inverted form. We conjecture that these results connect the semantic organization of a text (defined by the flow of its narrative) to its statistical features.

cs.CL↗

arXiv2019

Polymorphism in rapidly-changing cyclic environment

Selection in a time-periodic environment is modeled via the continuous-time two-player replicator dynamics, which for symmetric pay-offs reduces to the Fisher equation of mathematical genetics. For a sufficiently rapid and cyclic [fine-grained] environment, the time-averaged population frequencies are shown to obey a replicator dynamics with a non-linear fitness that is induced by environmental changes. The non-linear terms in the fitness emerge due to populations tracking their time-dependent environment. These terms can induce a stable polymorphism, though they do not spoil the polymorphism that exists already without them. In this sense polymorphic populations are more robust with respect to their time-dependent environments. The overall fitness of the problem is still given by its time-averaged value, but the emergence of polymorphism during genetic selection can be accompanied by decreasing mean fitness of the population. The impact of the uncovered polymorphism scenario on the models of diversity is examplified via the rock-paper-scissors dynamics, and also via the prisoner's dilemma in a time-periodic environment.

q-bio.PE↗

arXiv2018

Adaptive Decision Making via Entropy Minimization

An agent choosing between various actions tends to take the one with the lowest cost. But this choice is arguably too rigid (not adaptive) to be useful in complex situations, e.g., where exploration-exploitation trade-off is relevant in creative task solving or when stated preferences differ from revealed ones. Here we study an agent who is willing to sacrifice a fixed amount of expected utility for adaptation. How can/ought our agent choose an optimal (in a technical sense) mixed action? We explore consequences of making this choice via entropy minimization, which is argued to be a specific example of risk-aversion. This recovers the $ε$-greedy probabilities known in reinforcement learning. We show that the entropy minimization leads to rudimentary forms of intelligent behavior: (i) the agent assigns a non-negligible probability to costly events; but (ii) chooses with a sizable probability the action related to less cost (lesser of two evils) when confronted with two actions with comparable costs; (iii) the agent is subject to effects similar to cognitive dissonance and frustration. Neither of these features are shown by entropy maximization.

physics.data-an↗

arXiv2018

Relating Zipf's law to textual information

Zipf's law is the main regularity of quantitative linguistics. Despite of many works devoted to foundations of this law, it is still unclear whether it is only a statistical regularity, or it has deeper relations with information-carrying structures of the text. This question relates to that of distinguishing a meaningful text (written in an unknown system) from a meaningless set of symbols that mimics statistical features of a text. Here we contribute to resolving these questions by comparing features of the first half of a text (from the beginning to the middle) to its second half. This comparison can uncover hidden effects, because the halves have the same values of many parameters (style, genre, author's vocabulary {\it etc}). In all studied texts we saw that for the first half Zipf's law applies from smaller ranks than in the second half, i.e. the law applies better to the first half. Also, words that hold Zipf's law in the first half are distributed more homogeneously over the text. These features do allow to distinguish a meaningful text from a random sequence of words. Our findings correlate with a number of textual characteristics that hold in most cases we studied: the first half is lexically richer, has longer and less repetitive words, more and shorter sentences, more punctuation signs and more paragraphs. These differences between the halves indicate on a higher hierarchic level of text organization that so far went unnoticed in text linguistics. They relate the validity of Zipf's law to textual information. A complete description of this effect requires new models, though one existing model can account for some of its aspects.

cs.CL↗