arXiv subjects

Alexander Gorsky

Publications and source records attributed to Alexander Gorsky.

At least 19 recordsLinked to original sources

arXiv2026

Griffiths phase in clique percolation in random geometric graphs

In this study, we discuss the clique percolation in the ensembles of random geometric graphs with different kernels that quantify the geometrical constraints. For the sharp cut-off we find the wide Griffiths phase of extended criticality with the power-law behavior. One boundary of the Griffiths phase is the generalization of a percolation critical point for the ER ensemble when the percolation within the large but finite cluster emerges. The second boundary corresponds to the point in the parameter space when the percolation in the entire clustered system becomes available. For the power-law kernel, richer behavior with a clique-size-dependent boundary between the effective ER and geometric regimes has been identified. The Griffiths phase in this case exists as well. Finally, the pattern with the exponential kernel has been analyzed. We briefly discuss the possible applications of our findings.

cond-mat.dis-nn↗

arXiv2026

Composite worldline instantons and the nonperturbative particle decay in constant external electric and magnetic fields

In this paper, we discuss the validity of the composite worldline instanton approach for the nonperturbative decay of charged particles in constant electric and magnetic fields. It is shown that the instanton results in the leading exponential approximation in the different limits agree with the ones obtained by the imaginary part of the self-energy in the external field and by overlap of the wave functions. We comment on the possible application of our results for the estimation of the decay rate of the proton in the external electric and magnetic field in the leading exponential approximation. The effects of entanglement of the particles in the final state are briefly mentioned.

hep-th↗

arXiv2026

Exactly Solvable RD Model: RG Cycles Meet Fractality

We consider the Bethe ansatz integrable Russian Doll (RD) model of superconductivity with time-reversal symmetry breaking, which exhibits a cyclic renormalization group. By obtaining an exact solution for the renormalization group flows, we investigate the phase structure in the one-pair sector, which includes localized, fractal, and delocalized phases. We show that the quantum number Q, arising from the Bethe ansatz equations, counts the number of cycles and parametrizes the towers of states. Using the action of the renormalization group on the eigenstates, we demonstrate that Q serves as an order parameter, providing a new mechanism for the formation of the fractal phase in the deterministic systems and an example of the interplay between fractality and cyclic RG.

cond-mat.stat-mech↗

arXiv2026

Theta-term in Russian Doll Model: phase structure, quantum metric and BPS multifractality

We investigate the phase structure of the deterministic and disordered versions of the Russian Doll Model (RDM), which is a generalization of Richardson model of superconductivity in a finite system with time-reversal symmetry breaking parameter $θ$. It is one of the simplest examples of the cyclic RG where $\log N$ plays the role of the RG time. The deterministic model is integrable and shares the same Bethe Ansatz (BA) equations with the inhomogeneous twisted XXX spin chain. We analyze the quantum metric, the Berry curvature, and the fractal dimension in the sector with a single Cooper pair. A rich phase structure in the $(θ,γ)$ parameter plane is found, where $γ\log N$ quantifies the hopping term. For the deterministic RDM we clearly identify the extended domain of non-ergodic multifractal phase on the $(θ,γ)$ parameter plane supporting the reentrance transitions between the localized, ergodic, and multifractal phases. We find the pattern of phase transitions in the global charge $Q(θ,γ)$, which arises from the BA equation. In particular, in the multifractal phase in the deterministic model $Q(γ)$ exhibits the analogue of "charge concentration" and fortuity phenomena discussed in the context of black hole microstates at finite $N$. The BA equations in RDM exactly coincide with the equations defining the ground states in the theory on the worldvolume of the vortex strings in $N_F=2N_C$ ${\cal N}=2$ SQCD at a strong coupling point $\frac{1}{g_{YM}^2}=0$ with identification $θ_{RDM}= θ_{4D}-π$. We conjecture that the Hamiltonian of the RDM model describes the mixing in particular 2d-4d BPS sector of the Hilbert space. Our findings provide an example of the BPS multifractality regime for the probe operator in the sector of Hilbert space, and we comment on the possible application to dense QCD with $θ$ term.

hep-th↗

arXiv2026

Neural Receptive Fields, Stimulus Space Embedding and Effective Geometry of Scale-Free Networks

Understanding how receptive fields emerge and organize within brain networks and how neural dynamics couple with stimuli space is fundamental to neuroscience. Models often rely on fine-tuning connectivity to match empirical data, which may limit biological plausibility. Here we propose a physiologically grounded alternative where receptive fields and population-level attractor dynamics arise naturally from the effective hyperbolic geometry of scale-free networks. By associating stimulus space with the boundary of a hyperbolic embedding, we simulate neural dynamics using rate-based and spiking models, revealing localized activity patterns that reflect stimulus space structure without synaptic fine-tuning. The resulting receptive fields follow experimentally observed statistics and properties, and their sizes depends on neuron's connectivity degree. The model generalizes across stimuli dimensionalities and various modalities, such as orientation and place selectivity. Experimental analyses of hippocampal place fields recorded on a linear track support these findings. This framework offers a novel organizing principle linking network structure, stimulus space encoding, and neural dynamics, providing insights into receptive field formation across diverse brain areas.

q-bio.NC↗

arXiv2025

Consciousness via MIPT?

The measurement-induced phase transition (MIPT) is a recently formulated phenomenon in out-of-equilibrium systems. The competition between unitary evolutions and measurement-induced non-unitaries leads to the transition between the entangled and disentangled phases at some critical measurement rate. We conjecture that self-organized MIPT plays a key role in the generative model of cognitive networks and the formation of the state of consciousness in the "newborn-adult" transition. To this aim, we formulate the probe-target picture for the brain and suggest that MIPT interpreted as learnability transition takes place in the mental part of the target where the sites in the cognitive networks of semantic memory are concepts. Comparison with the synchronization phase transitions in the probe is made.

q-bio.NC↗

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

Hilbert space geometry and quantum chaos

The quantum geometric tensor (QGT) characterizes the Hilbert space geometry of the eigenstates of a parameter-dependent Hamiltonian. In recent years, the QGT and related quantities have found extensive theoretical and experimental utility, in particular for quantifying quantum phase transitions both at and out of equilibrium. Here we consider the symmetric part (quantum Riemannian metric) of the QGT for various multi-parametric random matrix Hamiltonians and discuss the possible indication of ergodic or integrable behaviour. We found for a two-dimensional parameter space that, while the ergodic phase corresponds to the smooth manifold, the integrable limit marks itself as a singular geometry with a conical defect. Our study thus provides more support for the idea that the landscape of the parameter space yields information on the ergodic-nonergodic transition in complex quantum systems, including the intermediate phase.

cond-mat.stat-mech↗

arXiv2024

Refined cyclic renormalization group in Russian Doll model

Focusing on Bethe-ansatz integrable models, robust to both time-reversal symmetry breaking and disorder, we consider the Russian Doll Model (RDM) for finite system sizes and energy levels. Suggested as a time-reversal-symmetry breaking deformation of Richardson's model, the well-known and simplest model of superconductivity, RDM revealed an unusual cyclic renormalization group (RG) over the system size $N$, where the energy levels repeat themselves, shifted by one after a finite period in $\ln N$, supplemented by a hierarchy of superconducting condensates, with the superconducting gaps following the so-called Efimov (exponential) scaling. The equidistant single-particle spectrum of RDM made the above Efimov scaling and cyclic RG to be asymptotically exact in the wideband limit of the diagonal potential. Here, we generalize this observation in various respects. We find that, beyond the wideband limit, when the entire spectrum is considered, the periodicity of the spectrum is not constant, but appears to be energy-dependent. Moreover, we resolve the apparent paradox of shift in the spectrum by a single level after the RG period, despite the disappearance of a finite fraction of energy levels. We also analyze the effects of disorder in the diagonal potential on the above periodicity and show that it survives only for high energies beyond the energy interval of the disorder amplitude. Our analytic analysis is supported with exact diagonalization.

cond-mat.dis-nn↗

arXiv2024

KPZ scaling from the Krylov space

Recently, a superdiffusion exhibiting the Kardar-Parisi-Zhang (KPZ) scaling in late-time correlators and autocorrelators of certain interacting many-body systems has been reported. Inspired by these results, we explore the KPZ scaling in correlation functions using their realization in the Krylov operator basis. We focus on the Heisenberg time scale, which approximately corresponds to the ramp--plateau transition for the Krylov complexity in systems with a large but finite number degrees of freedom. Two frameworks are under consideration: i) the system with growing Lanczos coefficients and an artificial cut-off, and ii) the system with the finite Hilbert space. In both cases via numerical analysis, we observe the transition from Gaussian to KPZ-like scaling at the critical Euclidean time $t_{E}^*=c_{cr}K$, for the Krylov chain of finite length $K$, and $c_{cr}=O(1)$. In particular, we find a scaling $\sim K^{1/3}$ for fluctuations in the one-point correlation function and a dynamical scaling $\sim K^{-2/3}$ associated with the return probability (Loschmidt echo) corresponding to autocorrelators in physical space. In the first case, the transition is of the 3rd order and can be considered as an example of dynamical quantum phase transition (DQPT), while in the second, it is a crossover. For case ii), utilizing the relationship between the spectrum of tridiagonal matrices at the spectral edge and the spectrum of the stochastic Airy operator, we demonstrate analytically the origin of the KPZ scaling for the particular Krylov chain using the results of the probability theory. We argue that there is some outcome of our study for the double scaling limit of matrix models. For the case of topological gravity, the white noise $O(\frac{1}{N})$ term is identified, which should be taken into account in the controversial issue of ensemble averaging in 2D/1D holography.

hep-th↗

arXiv2024

Metric structural human connectomes: localization and multifractality of eigenmodes

In this study, we explore the fundamental principles behind the architecture of the human brain's structural connectome, from the perspective of spectral analysis of Laplacian and adjacency matrices. Building on the idea that the brain strikes a balance between efficient information processing and minimizing wiring costs, we aim to understand the impact of the metric properties of the connectome and how they relate to the existence of an inherent scale. We demonstrate that a simple generative model, combining nonlinear preferential attachment with an exponential penalty for spatial distance between nodes, can effectively reproduce several key characteristics of the human connectome, including spectral density, edge length distribution, eigenmode localization and local clustering properties. We also delve into the finer spectral properties of the human structural connectomes by evaluating the inverse participation ratios ($\text{IPR}_q$) across various parts of the spectrum. Our analysis reveals that the level statistics in the soft cluster region of the Laplacian spectrum deviate from a purely Poisson distribution due to interactions between clusters. Additionally, we identified scar-like localized modes with large IPR values in the continuum spectrum. We identify multiple fractal eigenmodes distributed across different parts of the spectrum, evaluate their fractal dimensions and find a power-law relationship in the return probability, which is a hallmark of critical behavior. We discuss the conjectures that a brain operates in the Griffiths or multifractal phases.

q-bio.NC↗

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↗

arXiv2024

Robust extended states in Anderson model on partially disordered random regular graphs

In this work we analytically explain the origin of the mobility edge in the partially disordered random regular graphs of degree d, i.e., with a fraction $β$ of the sites being disordered, while the rest remain clean. It is shown that the mobility edge in the spectrum survives in {a certain range of parameters} $(d,β)$ at infinitely large uniformly distributed disorder. The critical curve separating extended and localized states is derived analytically and confirmed numerically. The duality in the localization properties between the sparse and extremely dense RRG has been found and understood.

cond-mat.dis-nn↗

arXiv2023

On Schwinger-like pair production of baryons and new non-perturbative processes in electric field

We consider the Schwinger production of baryons in an external electric field in the worldline instanton approach. The process occurs in the confinement regime hence the holographic QCD and the Chiral Lagrangian are used as the tools. The new exponentially suppressed processes in a constant electric field involving the composite worldline instantons are suggested. These include the non-perturbative decay of a neutron into a proton and charged meson and the spontaneous production of $p\bar{n}π^{-}$ and $n\bar{p}π^{+}$ states.

hep-th↗

arXiv2023

Calogero-Moser eigenfunctions modulo $p^s$

In this note we use the Matsuo-Cherednik duality between the solutions to KZ equations and eigenfunctions of Calogero-Moser Hamiltonians to get the polynomial $p^s$-truncation of the Calogero-Moser eigenfunctions at a rational coupling constant. The truncation procedure uses the integral representation for the hypergeometric solutions to KZ equations. The $s\rightarrow \infty$ limit to the pure $p$-adic case has been analyzed in the $n=2$ case

hep-th↗

arXiv2023

Unconventional critical behavior of polymers at sticky boundaries

We discuss the generalization of a classical problem involving an $N$-step ideal polymer adsorption at a sticky boundary (potential well of depth $U$). It is known that as $N$ approaches infinity, the path undergoes a 2nd-order localization transition at a certain value of $U_{\text{tr}}$. By considering the random walk on a half-line with a sticky boundary (Model I), we demonstrate that the order of the phase transition can be altered by adjusting the scaling of the first return probability to the boundary. Additionally, we present a model of a random path on a discrete 1D lattice with non-uniform local hopping amplitudes and a potential well at the boundary (Model II). We illustrate that one can tailor such amplitudes so that the polymer undergoes a 3rd-order phase transition.

cond-mat.stat-mech↗

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

Generalized Devil's staircase and RG flows

We discuss a two-parameter renormalization group (RG) flow when parameters are organized in a single complex variable, $τ$, with modular properties. Throughout the work we consider a special limit when the imaginary part of $τ$ characterizing the disorder strength tends to zero. We argue that generalized Riemann-Thomae (gRT) function and the corresponding generalized Devil's staircase emerge naturally in a variety of physical models providing a universal behavior. In 1D we study the Anderson-like probe hopping in a weakly disordered lattice, recognize the origin of the gRT function in the spectral density of the probe and formulate specific RG procedure which gets mapped onto the discrete flow in the fundamental domain of the modular group $SL(2,Z)$. In 2D we consider the generalization of the phyllotaxis crystal model proposed by L. Levitov and suggest the explicit form of the effective potential for the probe particle propagating in the symmetric and asymmetric 2D lattice of defects. Analyzing the structure of RG flow equations in the vicinity of saddle points we claim emergence of BKT-like transitions at ${\rm Im}\,τ\to 0$. We show that the RG-like dynamics in the fundamental domain of $SL(2,Z)$ for asymmetric lattices asymptotically approaches the "Silver ratio". For a Hubbard model of particles on a ring interacting via long-ranged potentials we investigate the dependence of the ground state energy on the potential and demonstrate by combining numerical and analytical tools the emergence of the generalized Devil's staircase. Also we conjecture a bridge between a Hubbard model and a phyllotaxis.

cond-mat.stat-mech↗