arXiv subjects

Artem Alexandrov

Publications and source records attributed to Artem Alexandrov.

13 recordsLinked to original sources

arXiv2026

Duck hunting with quantum mechanics

We bridge two sides of singular perturbation theory: the classical theory of slow-fast systems and the semi-classical approach to quantum mechanical systems. For a specific but physically important class of dynamical systems, we show that purely classical and exotic objects, so-called canard solutions, are shadows of instantons in the corresponding quantum system. We demonstrate that canard solutions exist in a domain of parameter space whose boundaries are determined by an instanton action. We illustrate our statements analytically for the relevant example, the overdamped Josephson junction, and confirm them numerically. For the Josephson junction, the canard window is the exponentially narrow gap between consecutive Shapiro steps.

nlin.PS↗

arXiv2026

Graphon Spin Systems as Exactly Solvable Models

Graphons are measurable functions used to describe the asymptotic behavior of convergent graph families. Originally motivated by problems in combinatorics and graph theory, graphons have found numerous applications in the modeling and analysis of dynamical processes on networks. In this work, we use graphons to formulate the Ising model on convergent graph sequences, which include many network topologies common in applications. We derive the mean-field limit for the resulting model and obtain exact results for phase transitions in such systems. Specifically, we show that the critical temperatures of the Ising model on graphons are determined by the eigenvalues of the Hilbert-Schmidt operator associated with the graph limit. For many important network topologies, these eigenvalues can be computed explicitly. We illustrate our results with three representative random network models: Erdős-Rényi, small-world, and power-law. In the small-world case, we demonstrate phase transitions to both ferromagnetic and antiferromagnetic phases, as well as coexistence of local minima of the free energy. The latter gives rise to multistability, as confirmed by Monte Carlo simulations. The results of this work demonstrate that the Ising model on graphons combines the analytical tractability of exactly solvable mean-field models with the ability to accommodate a broad range of network topologies. We expect that the use of graphons in spin models will lead to new insights into the statistical physics of interacting systems on complex networks.

cond-mat.dis-nn↗

arXiv2026

Three-Dimensional Kardar--Parisi--Zhang Scaling in Polariton Condensates

Kardar--Parisi--Zhang (KPZ) universality provides an example of macroscopic scaling generated by microscopic violation of detailed balance. While one- and two-dimensional realizations have been explored in driven condensates and growing interfaces, demonstrating KPZ scaling in three spatial dimensions remains a major challenge. Here we propose a three-dimensional exciton-polariton crystal as a platform for observation of 3D KPZ universality. Starting from a stochastic driven-dissipative Gross-Pitaevskii equation for a condensate formed in a three-dimensional photonic-crystal lower-polariton band, we eliminate the massive density and reservoir modes and obtain an effective $3+1$-dimensional KPZ equation for the condensate phase. Numerical simulations of both the KPZ equation and the full driven-dissipative polariton model show an intermediate-asymptotic regime in which the first-order coherence obeys $-\ln |\gone(0,Δt)|\propto |Δt|^{2β}$ and $-\ln |\gone(Δr,0)|\propto |Δr|^{2χ}$, with exponents consistent with the $3+1$ KPZ benchmarks $β= 0.1845$, $χ= 0.3135$. Our results identify three-dimensional polariton crystals as a controllable quantum fluid route to higher-dimensional nonequilibrium universality.

cond-mat.stat-mech↗

arXiv2025

Phase transitions in the Ising model on random graphs

We study phase transitions in the Ising model on random graphs using graph limits. We show that the critical temperatures are determined by the eigenvalues of the kernel operator associated with the graph limit. Bifurcation diagrams for Erdos-Renyi, small-world, and power-law graphs illustrate the theory. In the small-world case, we identify metastable behavior in both ferromagnetic and antiferromagnetic regimes.

math-ph↗

arXiv2025

Dynamical systems on torus related to general Heun equations: phase-lock areas and constriction breaking

The overdamped Josephson junction in superconductivity theory can be modeled by the family of dynamical systems on the torus, which is known as the RSJ model. This family admits an equivalent description by a family of second-order differential equations: special double confluent Heun equations. In the present paper, we construct two new families of dynamical systems on torus that can be equivalently described by a family of general Heun equations (GHE), with four singular points, and confluent Heun equations, with three singular points. The first family, related to GHE, is a deformation of the RSJ model, which will be denoted by dRSJ. The phase-lock areas of a family of dynamical systems on the torus are those level subsets of the rotation number function that have nonempty interiors. It is known that for the RSJ model, the rotation number quantization effect occurs: phase-lock areas exist only for integer rotation number values. Moreover, each phase-lock area is a chain of domains separated by points. Those separation points that do not lie on the abscissa axis are called constrictions. In the present paper, we study phase-lock areas in the new family dRSJ. The quantization effect remains valid in this family. On the other hand, we show that in the new family dRSJ the constrictions break down.

math.DS↗

arXiv2025

Phase-locking in dynamical systems and quantum mechanics

In this study, we discuss the Prufer transform that connects the dynamical system on the torus and the Hill equation, which is interpreted as either the equation of motion for the parametric oscillator or the Schrodinger equation with periodic potential. The structure of phase-locking domains in the dynamical system on torus is mapped into the band-gap structure of the Hill equation. For the parametric oscillator, we provide the relation between the non-adiabatic Hannay angle and the Poincare rotation number of the corresponding dynamical system. In terms of quantum mechanics, the integer rotation number is connected to the quantization number via the Milne quantization approach and exact WKB. Using recent results concerning the exact WKB approach in quantum mechanics, we discuss the possible non-perturbative effects in the dynamical systems on the torus and for parametric oscillator. The semiclassical WKB is interpreted in the framework of a slow-fast dynamical system. The link between the classification of the coadjoint Virasoro orbits and the Hill equation yields a classification of the phase-locking domains in the parameter space in terms of the classification of Virasoro orbits. Our picture is supported by numerical simulations for the model of the Josephson junction and Mathieu equation.

cond-mat.stat-mech↗

arXiv2024

Penrose method for Kuramoto model with inertia and noise

Using the Penrose method of instability analysis, we consider the synchronization transition in the Kuramoto model with inertia and noise with all-to-all couplings. Analyzing the Penrose curves, we identify the appearance of cluster and chimera states in the presence of noise. We observe that noise can destroy chimera and biclusters states. The critical coupling describing bifurcation from incoherent to coherent state is found analytically. To confirm our propositions based on the Penrose method, we perform numerical simulations.

nlin.AO↗

arXiv2023

On out-of-equilibrium phenomena in pseudogap phase of complex SYK+U model

In this Letter we consider the out-of-equilibrium phenomena in the complex Sachdev-Ye-Kitaev (SYK) model supplemented with the attractive Hubbard interaction (SYK+U). This model provides the clear-cut transition from non-Fermi liquid phase in pure SYK to the superconducting phase through the pseudogap phase with non-synchronized Cooper pairs. We investigate the quench of the phase soft mode in this model and the relaxation to the equilibrium state. Using the relation with Hamiltonian mean field (HMF) model we show that the SYK+U model enjoys the several interesting phenomena, like violent relaxation, quasi-stationary long living states, out-of-equilibrium finite time phase transitions, non-extensivity and tower of condensates. We comment on the holographic dual gravity counterparts of these phenomena.

cond-mat.str-el↗

arXiv2023

Information geometry and synchronization phase transition in Kuramoto model

We discuss the recently proposed description of Kuramoto model in terms of hyperbolic space and relate it to the information geometry. In particular the dynamical equation in Kuramoto all-to-all model is identified with the gradient flow of the Kullback-Leibner divergence on the statistical manifold. The Fisher information metric is evaluated for the Kuramoto and Kuramoto-Shakagichi models. We argue that the components of Fisher metric diverge at the critical point hence it can be used as an alternative order parameter for the synchronization phase transition.

cond-mat.stat-mech↗

arXiv2022

Synchronization on star graph with noise

We investigate synchronization in the Kuramoto model with noise on a star graph. By revising the case of a complete graph, we propose a closed form of self-consistency equation for the conventional order parameter and generalize it for a star graph. Using the obtained self-consistency equation, we demonstrate that there is a crossover between the abrupt synchronization at small noise and the continuous phase transition for quite large noise. We probe this crossover numerically and analytically.

cond-mat.dis-nn↗

arXiv2022

Synchronization on star-like graphs and emerging $\mathbb{Z}_{p}$ symmetries at strong coupling

We discuss the aspects of synchronization on inhomogeneous star-like graphs with long rays in Kuramoto model framework. We assume the positive correlation between internal frequencies and degrees for all nodes which supports the abrupt first order synchronization phase transition. It is found that different ingredients of the graph get synchronized at different critical couplings. Combining numerical and analytic tools we evaluate all critical couplings for the long star graph. Surprisingly it is found that at strong coupling there are discrete values of coupling constant which support the synchronized states with emerging $\mathbb{Z}_{p}$ symmetries. The stability of synchronized phase is discussed and the interpretation of phase with emerging $\mathbb{Z}_{p}$ symmetry for the Josephson array on long star graph is mentioned.

cond-mat.dis-nn↗

arXiv2020

Zilch Vortical Effect for Fermions

We consider the notion of zilch current that was recently discussed in the literature as an alternative helicity measure for photons. Developing this idea, we suggest the generalization of the zilch for the systems of fermions. We start with the definition of the photonic zilch current in chiral kinetic theory framework and work out field-theoretical definition of the fermionic zilch using the Wigner function formalism. This object has similar properties to the photonic zilch and is conserved in the non-interacting theory. We also show that, in full analogy with a case of photons, the fermionic zilch acquires a non-trivial contribution due to the medium rotation - zilch vortical effect (ZVE) for fermions. Combined with a previously studied ZVE for photons, these results form a wider set of chiral effects parameterized by the spin of the particles and the spin of the current. We briefly discuss the origin of the ZVE, its possible relation to the anomalies in the underlying microscopic theory and possible application for studying the spin polarization in chiral media.

hep-th↗

arXiv2019

Tunneling anomalous Hall effect in a ferroelectric tunnel junction

We report on a theoretical study on the tunneling anomalous Hall effect (TAHE) in a ferroelectric tunnel junction (FTJ), resulting from spin-orbit coupling (SOC) in the ferroelectric barrier. For ferroelectric barriers with large SOC, such as orthorhombic HfO2 and BiInO3, we predict values of the tunneling anomalous Hall conductivity (TAHC) measurable experimentally. We demonstrate strong anisotropy in TAHC depending on the type of SOC. For the SOC with equal Rashba and Dresselhaus parameters, we predict the perfect anisotropy with zero TAHC for certain magnetization orientations. The TAHC changes sign with ferroelectric polarization reversal providing a new functionality of FTJs. Conversely, measuring the TAHC as a function of magnetization orientation offers an efficient way to quantify the type of SOC in the insulating barrier. Our results provide a new insight into the TAHE and open avenues for potential device applications.

cond-mat.mes-hall↗