Glimmers of a Quantum KAM Theorem: Insights from Quantum Quenches in One Dimensional Bose Gases

Real-time dynamics in a quantum many-body system are inherently complicated and hence difficult to predict. There are, however, a special set of systems where these dynamics are theoretically tractable: integrable models. Such models possess non-trivial conserved quantities beyond energy and momentum. These quantities are believed to control dynamics and thermalization in low dimensional atomic gases as well as in quantum spin chains. But what happens when the special symmetries leading to the existence of the extra conserved quantities are broken? Is there any memory of the quantities if the breaking is weak? Here, in the presence of weak integrability breaking, we show that it is possible to construct residual quasi-conserved quantities, so providing a quantum analog to the KAM theorem and its attendant Nekhoreshev estimates. We demonstrate this construction explicitly in the context of quantum quenches in one-dimensional Bose gases and argue that these quasi-conserved quantities can be probed experimentally.Comment: 21 pages with appendices; 13 figures; version accepted by PR

Modal analysis of gravitational instabilities in nearly Keplerian, counter-rotating collisionless discs

We present a modal analysis of instabilities of counter-rotating, self-gravitating collisionless stellar discs, using the recently introduced modified WKB formulation of spiral density waves for collisionless systems (Gulati \& Saini). The discs are assumed to be axisymmetric and in coplanar orbits around a massive object at the common center of the discs. The mass in both discs is assumed to be much smaller than the mass of the central object. For each disc, the disc particles are assumed to be in near circular orbits. The two discs are coupled to each other gravitationally. The perturbed dynamics of the discs evolves on the order of the precession time scale of the discs, which is much longer than the Keplerian time scale. We present results for the azimuthal wave number $m=1$ and $m=2$, for the full range of disc mass ratio between the prograde and retrograde discs. The eigenspectra are in general complex, therefore all eigenmodes are unstable. Eigenfunctions are radially more compact for $m = 1$ as compared to $m = 2$. Pattern speed of eigenmodes is always prograde with respect to the more massive disc. The growth rate of unstable modes increases with increasing mass fraction in the retrograde disc, and decreases with $m$; therefore $m=1$ instability is likely to play the dominant role in the dynamics of such systems.Comment: 24 pages, 8 figures, 1 tabl

Phase Diagram for Magnon Condensate in Yttrium Iron Garnet Film

Recently, magnons, which are quasiparticles describing the collective motion of spins, were found to undergo Bose-Einstein condensation (BEC) at room temperature in films of Yttrium Iron Garnet (YIG). Unlike other quasiparticle BEC systems, this system has a spectrum with two degenerate minima, which makes it possible for the system to have two condensates in momentum space. Recent Brillouin Light scattering studies for a microwave-pumped YIG film of thickness d=5 $\mu$m and field H=1 kOe find a low-contrast interference pattern at the characteristic wavevector $Q$ of the magnon energy minimum. In this report, we show that this modulation pattern can be quantitatively explained as due to non-symmetric but coherent Bose-Einstein condensation of magnons into the two energy minima. Our theory predicts a transition from a high-contrast symmetric phase to a low-contrast non-symmetric phase on varying the $d$ and $H$, and a new type of collective oscillations.Comment: 6 figures. Accepted by Nature Scientific Report