arXiv subjects

Piotr Zdybel

Publications and source records attributed to Piotr Zdybel.

9 recordsLinked to original sources

arXiv2026

Nonequilibrium corrections to conserved Ising criticality in scalar active matter: Ward identities, spectrum, and long crossovers

We identify the slowest-decaying nonequilibrium perturbations near the three-dimensional conserved Ising critical point and determine their impact on finite-size observables. We study two classes of perturbations: a field-dependent noise-to-mobility ratio $Θ(ϕ)=D(ϕ)/M(ϕ)$ and the gradient activity of Active Model B+. Starting from the Martin-Siggia-Rose-Janssen-De Dominicis action, we compute the linearized flow using the functional renormalization group. The transport sector is block triangular, with leading odd eigenvalue $y_{Θ_1}=-Δ_ϕ$, where $Δ_ϕ=(d-2+η)/2$. In the gradient sector, removing the detailed-balance direction leaves two genuinely nonequilibrium modes, chemical and current-like. Two smooth regulators give $y_{Θ_1}\simeq-0.52$, $y_J\simeq-0.56$, and $y_{\rm ch}\simeq-0.89$. A translation Ward identity expresses the current operator as the divergence of the stress tensor. Together with conservation and Itô causality, this forbids chemical operators from generating the current mode, making the nonequilibrium stability matrix triangular; an independent two-loop calculation in $d=4-\varepsilon$ finds no additional current contact counterterm. Within the FRG truncation, $y_J-y_{Θ_1}=-η$; beyond it, this relation requires the absence of an additional contact anomaly. Using the 3D Ising value $η=0.0362978(20)$ [Kos et al., 2016] gives $y_{Θ_1}\simeq-0.5181$ and $y_J\simeq-0.5544$. Because these exponents nearly coincide, single-power fits yield amplitude-dependent apparent exponents and crossover lengths may exceed accessible system sizes. We derive the resulting finite-size scaling rules: odd block observables respond linearly to activity, while even observables receive only quadratic corrections.

cond-mat.stat-mech↗

arXiv2026

Exact solution for the motion of a rigid particle with $\boldsymbol{S_4}$ and $\boldsymbol{C_{2v}}$ symmetry settling under gravity in a viscous fluid

We provide an exact and complete solution for the dynamics of a rigid particle of uniform density with $C_{2v}$ and $S_4$ symmetry, settling under gravity in a viscous fluid at a Reynolds number much smaller than unity. The $S_4$ symmetry renders the problem exactly integrable, with all orbits labelled by a single conserved quantity $0\le C\le 1$. We show that, for $0<C<1$, there are two different time scales, which lead to quasi-periodic evolution, with a significant time-dependent horizontal displacement. We obtain the tilt $θ$ and spin $ψ$ Euler angles as periodic Jacobi elliptic functions of time, and the azimuthal angle $ϕ$ through an incomplete elliptic integral of the third kind with a complex characteristic, which splits $ϕ$ into a uniform drift and a strictly periodic modulation. The orientation period and the drift rate (corresponding to a constant angular velocity around the gravity direction) follow in a closed form. The vertical centre-of-mass displacement is obtained in terms of periodic in time incomplete elliptic integrals, and the periodic orbit-averaged settling velocity reduces to a single ratio of complete elliptic integrals. The horizontal component of the motion in the laboratory frame of reference is obtained exactly and algebraically in terms of all three Euler angles, so it is quasi-periodic. The horizontal component of the centre-of-mass position traces rosette-like, in general open curves confined by two concentric `envelope' circles. We determine very simple exact expressions for radii of both envelopes and demonstrate that they tend to infinity for a family of shapes with the rotation-translation coupling decreasing to zero. We also explain the origin of cusps at the rosette-like trajectory and provide a commensurability condition selecting strictly periodic rosettes.

physics.flu-dyn↗

arXiv2026

Experimental and numerical study of the dynamics of sedimenting pairs of semi-flexible fibers close to attractive `aligned' relative configuration

Dynamics of two short semi-flexible fibers settling under gravity in a viscous fluid are investigated at Reynolds numbers Re << 1. We focus on fibers initially relatively close to each other, and we check if later they approach an aligned horizontal configuration, previously identified numerically (Bukowicki and Ekiel-Jezewska, Soft Matter 46 (2019) 9379) as attractive for symmetric initial conditions of moderately elastic filaments. In our experiments, two semi-flexible ball chains sediment in a highly viscous silicone oil. They are initially straight and close to a parallel horizontal relative configuration. Their motion and shape deformation are recorded using two synchronized cameras. For most of the trials, ball chains stay together, with damped oscillations around the symmetric aligned configuration. For a few initial conditions, the ball chains move away horizontally or vertically. To study the behavior over a longer time, we perform numerical simulations, modeling moderately elastic filaments as chains of identical beads, with the centers of consecutive beads connected by springs and with the fibers' elastic resistance to bending. Different initial positions and orientations are considered. Their dynamics are determined by the multipole expansion of the Stokes equations, implemented in the precise Hydromultipole numerical code. For short times, we observe the similar dynamics of semi-flexible ball chains and moderately elastic filaments. We provide examples of long-time numerical simulations illustrating that elastic filaments close to each other can move away horizontally or vertically, but after a long time, come back and perform damped oscillations while approaching the aligned configuration with almost touching filament ends. We confirm the attractive nature of the aligned configuration of very close semi-flexible sedimenting fibers, even if they are far away from each other.

physics.flu-dyn↗

arXiv2025

Sedimenting rigid particles of certain shapes approach a stationary orientation

This work investigates experimentally and numerically the dynamics of rigid particles settling under gravity in a highly viscous fluid. We demonstrate that certain shapes: cones, crescent moons, arrowheads, and open flat rings reorient and approach a stationary configuration. We determine the mobility coefficients and the characteristic reorientation times. We find out that the two rotational-translational mobility coefficients have opposite signs. Therefore, based on the equations of motion for rigid bodies with two orthogonal planes of symmetry, theoretically derived by Joshi and Govindarajan, Phys. Rev. Lett., 134, 2025, 014002 and Ekiel-Jezewska and Wajnryb, J. Phys. Condens. Matter, 21, 2009, 204102, we conclude that the approached stationary configurations are stable. Owing to the similarity principle, our experimental findings apply to micro-objects in water-based solutions. The reorientation of sedimenting rigid particles of certain shapes to a stationary stable configuration in a relatively short time might be used for biological, medical, or industrial applications.

cond-mat.soft↗

arXiv2024

Scaling law for a buckled elastic filament in a shear flow

We analyze the three-dimensional buckling of an elastic filament in a shear flow of a viscous fluid at low Reynolds number and high Peclet number. We apply the Euler-Bernoulli beam (elastica) theoretical model. We show the universal character of the full 3D spectral problem for the small perturbation of the thin filament from a straight position of arbitrary orientation. We use the eigenvalues and eigenfunctions for the linearized elastica equation in the shear plane, found earlier by [Liu et al., 2024] with the Chebyshev spectral collocation method, to solve the full 3D eigenproblem. We provide a simple analytic approximation to the eigenfunctions, represented as Gaussian wavepackets. As the main result of the paper, we derive square-root dependence of the eigenfunction wavenumber on the parameter $\tildeχ=-η\sin 2ϕ\sin^2θ$, where $η$ is the elastoviscous number, and the filament orientation is determined by the zenith angle $θ$ with respect to the vorticity direction and the azimuthal angle $ϕ$ relative to the flow direction. We also compare the eigenfunctions with shapes of slightly buckled elastic filaments with a non-negligible thickness with the same Young's modulus, using the bead model and performing numerical simulations with the precise Hydromultipole numerical codes.

physics.flu-dyn↗

arXiv2021

Stability of the Fulde-Ferrell-Larkin-Ovchinnikov states in anisotropic systems and critical behavior at thermal $m$-axial Lifshitz points

We revisit the question concerning stability of nonuniform superfluid states of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type to thermal and quantum fluctuations. Invoking the properties of the putative phase diagram of two-component Fermi mixtures, on general grounds we argue, that for isotropic, continuum systems the phase diagram hosting a long-range-ordered FFLO-type phase envisaged by the mean-field theory cannot be stable to fluctuations at any temperature $T>0$ in any dimensionality $d<4$. In contrast, in layered unidirectional systems the lower critical dimension for the onset of FFLO-type long-range order accompanied by a Lifshitz point at $T>0$ is $d=5/2$. In consequence, its occurrence is excluded in $d=2$, but not in $d=3$. We propose a relatively simple method, based on nonperturbative renormalization group to compute the critical exponents of the thermal $m$-axial Lifshitz point continuously varying $m$, spatial dimensionality $d$ and the number of order parameter components $N$. We point out the possibility of a robust, fine-tuning free occurrence of a quantum Lifshitz point in the phase diagram of imbalanced Fermi mixtures.

cond-mat.quant-gas↗

arXiv2020

Quantum Lifshitz points and fluctuation-induced first-order phase transitions in imbalanced Fermi mixtures

We perform a detailed analysis of the phase transition between the uniform superfluid and normal phases in spin- and mass-imbalanced Fermi mixtures. At mean-field level we demonstrate that at temperature $T\to 0$ the gradient term in the effective action can be tuned to zero for experimentally relevant sets of parameters, thus providing an avenue to realize a quantum Lifshitz point. We subsequently analyze damping processes affecting the order-parameter field across the phase transition. We show that, in the low energy limit, Landau damping occurs only in the symmetry-broken phase and affects exclusively the longitudinal component of the order-parameter field. It is however unavoidably present in the immediate vicinity of the phase transition at temperature $T=0$. We subsequently perform a renormalization-group analysis of the system in a situation, where, at mean-field level, the quantum phase transition is second order (and not multicritical). We find that, at $T$ sufficiently low, including the Landau damping term in a form derived from the microscopic action destabilizes the renormalization group flow towards the Wilson-Fisher fixed point. This signals a possible tendency to drive the transition weakly first-order by the coupling between the order-parameter fluctuations and fermionic excitations effectively captured by the Landau damping contribution to the order-parameter action.

cond-mat.quant-gas↗

arXiv2019

Damping of the Anderson-Bogolyubov mode by spin and mass imbalance in Fermi mixtures

We study the temporally nonlocal contributions to the gradient expansion of the pair fluctuation propagator for spin- and mass-imbalanced Fermi mixtures. These terms are related to damping processes of sound-like (Anderson-Bogolyubov) collective modes and are relevant for the structure of the complex pole of the pair fluctuation propagator. We derive conditions under which damping occurs even at zero temperature for large enough mismatch of the Fermi surfaces. We compare our analytical results with numerically computed damping rates of the Anderson-Bogolyubov mode.

cond-mat.quant-gas↗

arXiv2018

Effective potential and quantum criticality for imbalanced Fermi mixtures

We study the analytical structure of the effective action for spin- and mass-imbalanced Fermi mixtures at the onset of the superfluid state. Of our particular focus is the possibility of suppressing the tricritical temperature to zero, so that the transition remains continuous down to $T=0$ and the phase diagram hosts a quantum critical point. At mean-field level we analytically identify such a possibility in a regime of parameters in dimensionality $d=3$. In contrast, in $d=2$ we demonstrate that the occurrence of a quantum critical point is (at the mean-field level) excluded. We show that the Landau expansion of the effective potential remains well-defined in the limit $T\to 0^+$ except for a subset of model parameters which includes the standard BCS limit. We calculate the mean-field asymptotic shape of the transition line. Employing the functional renormalization group framework we go beyond the mean field theory and demonstrate the stability of the quantum critical point in $d=3$ with respect to fluctuations.

cond-mat.quant-gas↗