Abstract We study the hydrodynamics of fluids composed self-spinning objects such as chiral grains or colloidal particles subject to torques. These active break both parity and time-reversal symmetries in their non-equilibrium steady states. As a result, constitutive relations media display dissipationless linear-response coefficient called odd (or equivalently, Hall) viscosity. This viscosity does not lead energy dissipation, but gives rise flow perpendicular applied pressure. show how...

We compute electromagnetic, gravitational and mixed linear response functions of two- dimensional free fermions in external quantizing magnetic field at an integer filling factor. The results are presented the form effective action as expansion currents stresses wave-vectors frequencies probing electromagnetic metric fields. identify terms coming from geometric Chern-Simons, Wen-Zee, Chern-Simons action. derive expressions for Hall conductivity, viscosity find current charge density...

We consider the geometric part of effective action for Fractional Quantum Hall Effect (FQHE). It is shown that accounting framing anomaly quantum Chern-Simons theory essential to obtain correct gravitational linear response functions. In lowest order in gradients generating functional includes Chern-Simons, Wen-Zee and Chern- Simons terms. The latter term has a contribution from which fixes value thermal conductivity contributes viscosity FQH states on sphere. also discuss effects responses...

We formulate a geometric framework that allows us to study momentum and energy transport in nonrelativistic systems. It amounts coupling of the system Newton-Cartan (NC) geometry with torsion. The approach generalizes classic Luttinger's formulation thermal transport. In particular, we clarify meaning fields conjugated current. These describe background nonvanishing temporal use developed formalism construct equilibrium partition function coupled NC 2+1 dimensions derive various...

We study constraints imposed by the Galilean invariance on linear electromagnetic and elastic responses of two-dimensional gapped systems in a background magnetic field. Exact relations between response functions following from Ward identities are derived. In addition to viscosity-conductivity known literature, we find new density-curvature thermal Hall response.

A dense system of vortices can be treated as a fluid and itself could described in terms hydrodynamics. We develop the hydrodynamics vortex fluid. This captures characteristics flows averaged over fast circulations intervortex space. The features anomalous stress absent Euler's yields number interesting effects. Some them are deflection streamlines, correction to Bernoulli law, an accumulation regions with high curvature curved origin stresses is divergence interactions at microscale which...

We study collisions between two strongly interacting atomic Fermi gas clouds. observe exotic nonlinear hydrodynamic behavior, distinguished by the formation of a very sharp and stable density peak as clouds collide subsequent evolution into box-like shape. model dynamics these using quasi-1D equations. Our simulations time-dependent profiles agree well with data provide clear evidence shock wave in this universal quantum system.

We consider quantum Hall states on a space with boundary, focusing the aspects of edge physics which are completely determined by symmetries problem. There four distinct terms Chern-Simons type that appear in low-energy effective action state. Two these protect gapless modes. They describe conductance and, some provisions, thermal conductance. The remaining two, including Wen-Zee term, contributes to viscosity, do not modes but instead related local boundary response fixed symmetries....

We propose to describe correlations in classical and quantum systems terms of full counting statistics a suitably chosen discrete observable. The method is illustrated with two exactly solvable examples: the one-dimensional Ising model spin-1/2 $XY$ chain. For model, our results phase diagram phases distinguishable by long-distance behavior Jordan-Wigner strings. anisotropic chain transverse magnetic field, we compute magnetization use it classify method, this case, reproduces previously...

Floquet spin chains have been a venue for understanding topological states of matter that are qualitatively different from their static counterparts by, example, hosting $\pi$ edge modes show stable period-doubled dynamics. However the stability these to interactions has traditionally required system be many-body localized in order suppress heating. In contrast, here we even absence disorder, and presence bulk heating, long lived. Their lifetime is extracted exact diagonalization found...

Using the Calogero model as an example, we show that transport in interacting nondissipative electronic systems is essentially nonlinear and unstable. Nonlinear effects are due to curvature of spectrum near Fermi energy. As typical for systems, a propagating semiclassical wave packet develops shock at finite time. A collapses into oscillatory features which further evolve regularly structured localized pulses carrying fractionally quantized charge. The can be used describe fractional quantum...

Collective field theory for the Calogero model represents particles with fractional statistics in terms of hydrodynamic modes---density and velocity fields. We show that quantum hydrodynamics this can be written as a single evolution equation on real holomorphic Bose field---the integrable Benjamin-Ono equation. It renders tools systems to studies nonlinear dynamics 1D liquids.

The excitation spectrum of an $S=1∕2$ two-dimensional triangular quantum antiferromagnet is studied using $1∕S$ expansion. Due to the noncollinearity classical ground state significant and nontrivial corrections spin-wave appear already in first order contrast square lattice antiferromagnet. resulting magnon dispersion almost flat a substantial portion Brillouin zone. Our results are quantitative agreement with recent series expansion studies by Zheng et al. [Phys. Rev. Lett. 96, 057201...

We develop a hydrodynamic description of the classical Calogero–Sutherland liquid: model with an infinite number particles and non-vanishing density particles. The equations, being written for velocity fields liquid, are shown to be bidirectional analog Benjamin–Ono equation. latter is known describe internal waves deep stratified fluids. show that equation appears as real reduction modified KP hierarchy. derive chiral nonlinear which conventional degeneration at large density. construct...

We consider free surface dynamics of a two-dimensional incompressible fluid with odd viscosity. The viscosity is peculiar part the tensor which does not result in dissipation and allowed when parity symmetry broken. For case fluids, manifests itself through (no stress) boundary conditions. first find wave solutions hydrodynamics linear approximation study dispersion such waves. As expected, waves are chiral even exist absence gravity vanishing shear In this limit, we derive effective...

Results are presented for the dynamics of an almost strong edge mode which is quasi-stable Majorana occurring in non-integrable spin chains. The studied using exact diagonalization, and compared with time-evolution respect to effective semi-infinite model Krylov space obtained from recursion method. Hamiltonian found resemble a spatially inhomogeneous SSH where hopping amplitude increases linearly distance into bulk, typical thermalizing systems, but also has staggered or dimerized structure...

Almost strong edge-mode operators arising at the boundaries of certain interacting one-dimensional symmetry protected topological phases with Z_{2} have infinite temperature lifetimes that are nonperturbatively long in integrability breaking terms, making them promising as bits for quantum information processing. We extract lifetime these small system sizes well thermodynamic limit. For latter, a Lanczos scheme is employed to map operator dynamics tight-binding model single particle Krylov...

We propose a new data representation method based on Quantum Cognition Machine Learning and apply it to manifold learning, specifically the estimation of intrinsic dimension sets. The idea is learn each point as quantum state, encoding both local properties well its relation with entire data. Inspired by ideas from geometry, we then construct states cloud equipped metric. metric exhibits spectral gap whose location corresponds proposed estimator detection this gap. When tested synthetic...

We revisit the problem of finding probability distribution a fermionic number one-dimensional spinless free fermions on segment given length. The generating function for this can be expressed as determinant Toeplitz matrix. use recently proven generalized Fisher--Hartwig conjecture asymptotic behavior such determinants to find full counting statistics line segment. Unlike method bosonization, formula correctly takes into account discreteness charge. Furthermore, we check numerically...

In everyday fluids, viscosity is resistance to flow and dissipative, but a quantum Hall (QH) fluid at zero temperature has nondissipative (``odd'' viscosity). Using exact results we theoretically study observable consequences of odd in incompressible fluids two dimensions.

A semiclassical wave-packet propagating in a dissipationless Fermi gas inevitably enters "gradient catastrophe" regime, where an initially smooth front develops large gradients and undergoes dramatic shock wave phenomenon. The non-linear effects electronic transport are due to the curvature of spectrum at surface. They can be probed by sudden switching local potential. In equilibrium, this process produces number particle-hole pairs, phenomenon closely related Orthogonality Catastrophe. We...

We present here a classical hydrodynamic model of two-dimensional fluid which has many properties Fractional Quantum Hall effect. This incorporates the FQHE relation between vorticity and density exhibits viscosity conductivity found in liquids. describe to Chern-Simons-Ginzburg-Landau theory show how Laughlin's wave function is annihilated by quantum velocity operator.