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John Toner

Publications and source records attributed to John Toner.

At least 19 recordsLinked to original sources
arXiv2025

The Order-disorder Transition in Incompressible Polar Active Fluids with an Easy Axis

Dry active matter in an anisotropic medium is of experimental relevance, and the interplay between anisotropy and the dynamics of the active matter remains under-explored. Here, we derive the hydrodynamic equations of a generic dry polar active fluid that preferentially flows along a particular axis induced by the anisotropy of the medium. We then study its critical behavior at the order-disorder transition in which the symmetry between ``forward" and ``back" along the special axis is spontaneously broken. We obtain the critical static and dynamic exponents, mean velocity, and two point correlation functions exactly in three dimensions, and to two-loop level in two dimensions, by mapping our class of systems to the equilibrium Ising model with dipolar interactions.

cond-mat.soft↗
arXiv2025

Hydrodynamic Theory of Two-dimensional Chiral Malthusian Flocks

We study the hydrodynamic behavior of two-dimensional chiral dry Malthusian flocks; that is, chiral polar-ordered active matter with neither number nor momentum conservation. We show that, in the absence of fluctuations, such systems generically form a ``time cholesteric", in which the velocity of the entire system rotates uniformly at a fixed frequency b. Fluctuations about this state belong to the universality class of (2+1)-Kardar-Parisi-Zhang (KPZ) equation, which implies short-ranged orientational order in the hydrodynamic limit. We then show that, in the limit of weak chirality, the hydrodynamics of a system with reasonable size is expected to governed by the linear regime of the KPZ equation, exhibiting quasi-long-ranged orientational order. Our predictions for the velocity and number density correlations are testable in both simulations and experiments.

cond-mat.soft↗
arXiv2025

Only the Ambidextrous Can Flock: Two-dimensional Chiral Malthusian Flocks, Time Cholesterics, and the KPZ Equation

We study two-dimensional chiral dry Malthusian flocks; that is, chiral polar-ordered active matter with neither number nor momentum conservation. In the absence of fluctuations, these form a ``time cholesteric", in which the velocity rotates uniformly in time at a fixed frequency. Fluctuations are described by the (2+1)-Kardar-Parisi-Zhang (KPZ) equation, which implies short-ranged orientational order. For weak chirality, the system is in the linear regime of the KPZ equation for a wide range of length scales, over which it exhibits quasi-long-ranged orientational order. Our predictions for velocity and density correlations are testable in both simulations and experiments.

cond-mat.soft↗
arXiv2025

The inconvenient truth about flocks

We reanalyze the hydrodynamic theory of "flocks" that is, polar ordered "dry" active fluids in two dimensions. For "Malthusian" flocks, in which birth and death cause the density to relax quickly, thereby eliminating density as a hydrodynamic variable, we are able to obtain two exact scaling laws relating the three scaling exponents characterizing the long-distance properties of these systems. We also show that it is highly plausible that such flocks display long-range order in two dimensions. In addition, we demonstrate that for "immortal" flocks, in which the number of flockers is conserved, the extra non-linearities allowed by the presence of an extra slow variable (number density) make it impossible to obtain any exact scaling relations between the exponents. We thereby demonstrate that several past published claims of exact exponents for Malthusian and immortal flocks are all incorrect.

cond-mat.soft↗
arXiv2024

Birth, Death, and Horizontal Flight: Malthusian flocks with an easy plane in three dimensions

I formulate the theory of three dimensional "Malthusian flocks" -- i.e., coherently moving collections of self-propelled entities (such as living creatures) which are being "born" and "dying" during their motion -- whose constituents all have a preference for having their velocity vectors lie parallel to the same two-dimensional plane. I determine the universal scaling exponents characterizing such systems exactly, finding that the dynamical exponent $z=3/2$, the "anisotropy" exponent $\zeta=3/4$, and the "roughness" exponent $\chi=-1/2$. I also give the scaling laws implied by these exponents.

cond-mat.soft↗
arXiv2024

Phase separation in ordered polar active fluids: A new Universality class

We show that phase separation in ordered polar active fluids belongs to a new universality class. This describes large collections of self-propelled entities (``flocks"), all spontaneously moving in the same direction, in which attractive interactions (which can be caused by, e.g., autochemotaxis) cause phase separation: the system spontaneously separates into a high density band and a low density band, moving parallel to each other, and to the direction of mean flock motion, at different speeds. The upper critical dimension for this transition is $d_c=5$, in contrast to the well-known $d_c=4$ of equilibrium phase separation. We obtain the large-distance, long-time scaling laws of the velocity and density fluctuations, which are characterized by universal critical correlation length and order parameter exponents $\nu_\perp$, $\nu_\parallel$ and $\beta$ respectively. We calculate these to $\mathcal{O} (\epsilon)$ in a $d=5-\epsilon$ expansion.

cond-mat.soft↗
arXiv2024

Coulomb universality

Motivated by a number of realizations of long-range interacting systems, including ultra-cold atomic and molecular gases, we study a neutral plasma with power-law interactions longer-ranged than Coulombic. We find that beyond a crossover length, such interactions are universally screened down to a standard Coulomb form in all spatial dimensions. This implies, counter-intuitively, that in two dimensions and below, such a "super-Coulombic" gas is asymptotically Coulombically confining at low temperatures. At higher temperatures, the plasma undergoes a deconfining transition that in two dimensions is the same Kosterlitz-Thouless transition that occurs in a conventional Coulomb gas, but at an elevated temperature that we calculate. We also predict that in contrast, above two dimensions, even when naively the bare potential is confining, there is no confined phase of the plasma at any nonzero temperature. In addition, the super-Coulomb to Coulomb crossover is followed at longer length scales by an unconventional "Debye-Huckel" screening, which leads to faster-than-Coulombic, power-law decay of the screened potential, in contrast to the usual exponentially decaying Yukawa potential. Furthermore, we show that power-law potentials, that fall off more rapidly than Coulomb, are screened down to a shorter-ranged power-law, rather than an exponential Debye-Huckel Yukawa form. We expect these prediction to be testable in simulations, and hope they will inspire experimental studies in various platforms.

cond-mat.stat-mech↗
arXiv2024

Spinodal decomposition and phase separation in polar active matter

We develop and study the hydrodynamic theory of flocking with autochemotaxis. This describes large collections of self-propelled entities all spontaneously moving in the same direction, each emitting a substance which attracts the others (e.g., ants). The theory combines features of the Keller-Segel model for autochemotaxis with the Toner-Tu theory of flocking. We find that sufficiently strong autochemotaxis leads to an instability of the uniformly moving state (the ``flock"), in which bands of different density form moving parallel to the mean flock velocity with different speeds. These bands, which are reminiscent of ant trails, coarsen over time to reach a phase-separated state, in which one high density and one low density band fill the entire system. The same instability, described by the same hydrodynamic theory, can occur in flocks phase separating due to any microscopic mechanism (e.g., sufficiently strong attractive interactions). Although in many ways analogous to equilibrium phase separation via spinodal decomposition, the two steady state densities here are determined not by a common tangent construction, as in equilibrium, but by an uncommon tangent construction very similar to that found for motility induced phase separation (MIPS) of disordered active particles. Our analytic theory agrees well with our numerical simulations of our equations of motion.

cond-mat.soft↗
arXiv2024

Following your nose: Autochemotaxis and other mechanisms for spinodal decomposition in flocks

We develop the hydrodynamic theory of dry, polar ordered, active matter (``flocking") with autochemotaxis; i.e., self-propelled entities moving in the same direction, each emitting a substance which attracts the others (e.g., ants). We find that sufficiently strong autochemotaxis leads to an instability to phase separation into one high and one low density band. This is very analogous to both equilibrium phase separation, and ``motility induced phase separation" (``MIPS") and can occur in flocks due to any microscopic mechanism (e.g., sufficiently strong attractive interactions) that makes the entities cohere.

cond-mat.soft↗
arXiv2023

Dynamics of packed swarms: time-displaced correlators of two dimensional incompressible flocks

We analytically calculate the scaling exponents of a two-dimensional KPZ-like system: coherently moving incompressible polar active fluids. Using three different renormalization group approximation schemes, we obtain values for the ``roughness" exponent $\chi$ and anisotropy exponent $\zeta$ that are extremely near the known exact results. This implies our prediction for the previously completely unknown dynamic exponent $z$ is quantitatively accurate.

cond-mat.soft↗
arXiv2022

Roughening of two-dimensional interfaces in nonequilibrium phase-separated systems

I show that non-equilibrium two-dimensional interfaces between three dimensional phase separated fluids exhibit a peculiar "sub-logarithmic" roughness. Specifically, an interface of lateral extent $L$ will fluctuate vertically (i.e., normal to the mean surface orientation) a typical RMS distance $w\equiv\sqrt{\langle |h(\br,t)|^2\rangle} \propto [\ln{(L/a)}]^{1/3}$ (where $a$ is a microscopic length, and $ h(\br,t)$ is the height of the interface at two dimensional position $\br$ at time $t$). In contrast, the roughness of equilibrium two-dimensional interfaces between three dimensional fluids, obeys $w \propto [\ln{(L/a)}]^{1/2}$. The exponent $1/3$ for the active case is exact. In addition, the characteristic time scales $\tau(L)$ in the active case scale according to $\tau(L)\propto L^3 [\ln{(L/a)}]^{1/3}$, in contrast to the simple $\tau(L)\propto L^3$ scaling found in equilibrium systems with conserved densities and no fluid flow.

cond-mat.soft↗
arXiv2022

Broken living layers: dislocations in active smectics

We show that dislocations in active 2d smectics with underlying rotational symmetry are always unbound in the presence of noise, meaning the active smectic phase does not exist for non-zero noise in $d=2$. The active smectic phase can, like equilibrium smectics in 2d, be stabilized by applying rotational symmetry breaking fields; however, even in the presence of such fields, active smectics are still much less stable against noise than equilibrium ones, when the symmetry breaking field(s) are weak.

cond-mat.soft↗
arXiv2022

Hydrodynamic theory of two-dimensional incompressible polar active fluids with quenched and annealed disorder

We study the moving phase of two-dimensional (2D) incompressible polar active fluids in the presence of both quenched and annealed disorder. We show that long-range polar order persists even in this defect-ridden two-dimensional system. We obtain the large-distance, long-time scaling laws of the velocity fluctuations using three distinct dynamic renormalization group schemes. These are an uncontrolled one-loop calculation in exactly two dimensions, and two $d=(d_c-ε)$-expansions to $O(ε)$, obtained by two different analytic continuations of our 2D model to higher spatial dimensions: a ``hard" continuation which has $d_c={7\over 3}$, and a ``soft" continuation with $d_c={5\over 2}$. Surprisingly, the quenched and annealed parts of the velocity correlation function have the same anisotropy exponent and the relaxational and propagating parts of the dispersion relation have the same dynamic exponent in the nonlinear theory even though they are distinct in the linearized theory. This is due to anomalous hydrodynamics. Furthermore, all three renormalization schemes yield very similar values for the universal exponents, and, therefore, we expect the numerical values we predict for them to be highly accurate.

cond-mat.soft↗
arXiv2022

Packed swarms on dirt: two-dimensional incompressible flocks with quenched and annealed disorder

We show that incompressible polar active fluids can exhibit an ordered, coherently moving phase even in the presence of quenched disorder in two dimensions. Unlike such active fluids with annealed (i.e., time-dependent) disorder only, which behave like equilibrium ferromagnets with long-range interactions, this robustness against quenched disorder is a fundamentally non-equilibrium phenomenon. The ordered state belongs to a new universality class, whose scaling laws we calculate using three different renormalization group schemes, which all give scaling exponents within 0.02 of each other, indicating that our results are quite accurate. Our predictions can be quantitatively tested in readily available artificial active systems, and imply that biological systems such as cell layers can move coherently in vivo, where disorder is inevitable.

cond-mat.soft↗
arXiv2022

Incompressible polar active fluids with quenched disorder in dimensions $d> 2$

We present a hydrodynamic theory of incompressible polar active fluids with quenched disorder. This theory shows that such fluids can overcome the disruption caused by the quenched disorder and move coherently, in the sense of having a non-zero mean velocity in the hydrodynamic limit. However, the scaling behavior of this class of active systems cannot be described by linearized hydrodynamics in spatial dimensions between 2 and 5. Nonetheless, we obtain the exact dimension-dependent scaling exponents in these dimensions.

cond-mat.soft↗
arXiv2022

Susceptibility of Polar Flocks to Spatial Anisotropy

We consider the effect of spatial anisotropy on polar flocks by investigating active $q$-state clock models in two dimensions. In contrast to what happens in equilibrium, we find that, in the large-size limit, any amount of anisotropy changes drastically the phenomenology of the rotationally-invariant case, destroying long-range correlations, pinning the direction of global order, and transforming the traveling bands of the coexistence phase into a single moving domain. All this happens beyond a lengthscale that diverges in the $q\to\infty$ limit. A phenomenology akin to that of the Vicsek model can thus be observed in a finite system for large enough values of $q$. We provide a scaling argument which rationalizes why anisotropy has so different effects in the passive and active cases.

cond-mat.stat-mech↗
arXiv2021

Long-ranged order and flow alignment in sheared $p-$atic liquid crystals

We formulate a hydrodynamic theory of $p-$atic liquid crystals, namely two-dimensional anisotropic fluids endowed with generic $p-$fold rotational symmetry. Our approach, based on an order parameter tensor that directly embodies the discrete rotational symmetry of $p-$atic phases, allows us to unveil several unknown aspects of flowing $p-$atics, that previous theories, characterized by ${\rm O(2)}$ rotational symmetry, could not account for. This includes the onset of long-ranged orientational order in the presence of a simple shear flow of arbitrary shear rate, as opposed to the standard quasi-long-ranged order of two-dimensional liquid crystals, and the possibility of flow alignment at large shear rates.

cond-mat.soft↗