Related papers: Katok's special representation theorem for multidi…
The Euler equation of an ideal (i.e. inviscid incompressible) fluid can be regarded, following V.Arnold, as the geodesic flow of the right-invariant $L^2$-metric on the group of volume-preserving diffeomorphisms of the flow domain. In this…
Within the smooth category, an intertwining is exhibited between the global rigidity of irreducible higher rank abelian Anosov actions on the n-torus and the classification of equilibrium-free flows on the n-torus that possess nontrivial…
We prove a new automorphy lifting theorem for l-adic representations where we impose a new condition at l, which we call `potential diagonalizability'. This result allows for `change of weight' and seems to be substantially more flexible…
We recast superfluid hydrodynamics as the hydrodynamic theory of a system with an emergent anomalous higher-form symmetry. The higher-form charge counts the winding planes of the superfluid -- its constitutive relation replaces the…
We present a general solution of relativistic (1+1)-dimensional hydrodynamics for a perfect fluid flowing along the longitudinal direction as a function of time, uniformly in transverse space. The Khalatnikov potential is expressed as a…
In this paper we address the problem of representing solutions of a system of scalar linear partial difference equations akin to state space equations of 1-D systems theory. We first obtain a representation formula for a special class of…
The hard-disk model plays a role of touchstone for testing and developing the transport theory. By large scale molecular dynamics simulations of this model, three important autocorrelation functions, and as a result the corresponding…
For manifolds with geodesic flow that is ergodic on the unit tangent bundle, the quantum ergodicity theorem implies that almost all Laplacian eigenfunctions become equidistributed as the eigenvalue goes to infinity. For a locally symmetric…
We develop a unified kinetic theory for ordered fluids, which systematically extends the phase space with the appropriate generalized angular momenta. Our theory yields a uniquely determined mesoscopic model for any continuum with…
We establish expansion of every order for the correlation function of sufficiently regular observables of $\mathbb Z^d$ extensions of some hyperbolic flows. Our examples include the $\mathbb Z^2$ periodic Lorentz gas and geodesic flows on…
We consider a $C^{1,\alpha}$ smooth flow in $\mathbb{R}^n$ which is "strongly monotone" with respect to a cone $C$ of rank $k$, a closed set that contains a linear subspace of dimension $k$ and no linear subspaces of higher dimension. We…
In this paper, we investigate the embeddings for topological flows. We prove an embedding theorem for discrete topological system. Our results apply to suspension flows via constant function, and for this case we show an embedding theorem…
New elementary, self-contained proofs are presented for the topological and the smooth classification theorems of linear flows on finite-dimensional normed spaces. The arguments, and the examples that accompany them, highlight the…
We study the ergodic properties of eigenfunctions of Schr\"odinger operators on a closed connected Riemannian manifold $M$ in case that the underlying Hamiltonian system possesses certain symmetries. More precisely, let $M$ carry an…
The contribution presents a brief summary of the Gauge/Gravity approach to the study of hydrodynamic flow of the quark-gluon plasma formed in heavy-ion collisions, in a boost-invariant setting (Bjorken flow). Considering the ideal case of a…
Carroll hydrodynamics arises in the $c\to 0$ limit of relativistic hydrodynamics. Instances of its relevance include the Bjorken and Gubser flow models of heavy-ion collisions, where the ultrarelativistic nature of the flow makes the…
We investigate superfluidity, and the mechanism for creation of quantized vortices, in the relativistic regime. The general framework is a nonlinear Klein-Gordon equation in curved spacetime for a complex scalar field, whose phase dynamics…
We prove a model-theoretic representation theorem for the distribution of an ergodic exchangeable $k$-uniform hypergraph: every such measure arises as the pushforward of the countably-iterated Morley product of a global Borel-definable…
The superfluid fraction $f$ of a quantum fluid is defined in terms of the response of the system to a weak and constant drag. Notably, Leggett long ago derived two simple expressions providing a rigorous upper bound and a heuristic lower…
An alternative representation of an exact statistical field theory for simple fluids, based on the method of collective variables, is presented. The results obtained are examined from the point of another version of theory that was…