Related papers: Contact non-squeezing at large scale via generatin…
We generalize the familiar notions of overtwistedness and Giroux torsion in 3-dimensional contact manifolds, defining an infinite hierarchy of local filling obstructions called planar torsion, whose integer-valued order $k \ge 0$ can be…
Understanding the nanoscale effects controlling the dynamics of a contact line -- defined as the line formed at the junction of two fluid phases and a solid -- has been a longstanding problem in fluid mechanics pushing experimental and…
We show how mapping techniques inherent to $N^{2}$-dimensional discrete phase spaces can be used to treat a wide family of spin systems which exhibits squeezing and entanglement effects. This algebraic framework is then applied to the…
Analytical expressions of some of the spin-spin correlation functions up to eight lattice sites for the spin-1/2 anti-ferromagnetic Heisenberg chain at zero temperature without magnetic field are obtained. The key object of our method is…
Squeezing of collective atomic spins has been shown to improve the sensitivity of atomic clocks and magnetometers to levels significantly below the standard quantum limit. In most cases the requisite atom-atom entanglement has been…
We revisit the classic problem of an elastic solid with a two-dimensional wavy surface squeezed against an elastic flat half-space from infinitesimal to full contact. Through extensive numerical calculations and analytic derivations, we…
We carry out a statistically meaningful study on self-affine rough surfaces in elastic frictionless non-adhesive contact. We study the evolution of the true contact area under increasing squeezing pressure. Rough surfaces are squeezed from…
We construct examples in any odd dimension of contact manifolds with finite and non-zero algebraic torsion (in the sense of Latschev-Wendl), which are therefore tight and do not admit strong symplectic fillings. We prove that Giroux torsion…
We extend the classical theory of sphere theorems to the transverse geometry of Riemannian foliations. In this setting, we establish transverse analogues of the Grove-Shiohama diameter sphere theorem and of the Berger-Klingenberg…
This article is devoted problems of electromagnetic interaction in curved spacetime. Such problems exist, in particular, when we investigate electromagnetic quantum processes near black holes. The generalization of reduction formalism…
For a closed connected manifold N, we establish the existence of geometric structures on various subgroups of the contactomorphism group of the standard contact jet space J^1N, as well as on the group of contactomorphisms of the standard…
We study the generation of metrologically useful entanglement in a three-level (spin-1) system naturally realized in arrays of dipole-interacting Rydberg atoms confined in optical tweezers. In the spin-quadrupolar operator basis, the…
We prove one deformation theoretic extension of the Gromov non-squeezing phenomenon to $lcs$ structures, or locally conformally symplectic structures, which suitably generalize both symplectic and contact structures. We also conjecture an…
This sequel to our previous paper [MS11b] continues the study of topological contact dynamics and applications to contact dynamics and topological dynamics. We provide further evidence that the topological automorphism groups of a contact…
We explore the relationship between contact forms on $\mathbb S^3$ defined by Finsler metrics on $\mathbb S^2$ and the theory developed by H. Hofer, K. Wysocki and E. Zehnder in \cite{HWZ,HWZ1}. We show that a Finsler metric on $\mathbb…
Generalizing Weyl's tube formula and building on Chern's work, Alesker reinterpreted the Lipschitz-Killing curvature integrals as a family of valuations (finitely-additive measures with good analytic properties), attached canonically to any…
We prove that on overtwisted contact manifolds there can be no positive loops of contactomorphisms that are generated by a $C^0$-small Hamiltonian function.
The papers by Janszky and Adam [Phys. Rev. A {\bf 46}, 6091 (1992)] and Chen \textit{et al.} [Phys. Rev. Lett. {\bf 104}, 063002 (2010)] are examples of works where one can find the following equivalences: belonging to the following class:…
Using Floer-theoretic methods, we prove that the non-existence of an exotic symplectomorphism on the standard symplectic ball, $\mathbb{B}^{2n},$ implies a rather strict topological condition on the free contact circle actions on the…
I study the entanglement entropy (EE) across a deformed sphere in conformal field theories (CFTs). I show that the sphere (locally) minimizes the universal term in EE among all shapes. In arXiv:1407.7249 it was derived that the sphere is a…