SciPost Phys. Core 3, 003 (2020) ·
published 20 August 2020

· pdf
We study quantum dynamics on noncommutative spaces of negative curvature,
focusing on the hyperbolic plane with spatial noncommutativity in the presence
of a constant magnetic field. We show that the synergy of noncommutativity and
the magnetic field tames the exponential divergence of operator growth caused
by the negative curvature of the hyperbolic space. Their combined effect
results in a firstorder transition at a critical value of the magnetic field
in which strong quantum effects subdue the exponential divergence for {\it all}
energies, in stark contrast to the commutative case, where for high enough
energies operator growth always diverge exponentially. This transition
manifests in the entanglement entropy between the `left' and `right' Hilbert
spaces of spatial degrees of freedom. In particular, the entanglement entropy
in the lowest Landau level vanishes beyond the critical point. We further
present a nonlinear solvable bosonic model that realizes the underlying
algebraic structure of the noncommutative hyperbolic plane with a magnetic
field.
SciPost Phys. 5, 010 (2018) ·
published 27 July 2018

· pdf
We consider free surface dynamics of a twodimensional incompressible fluid
with odd viscosity. The odd viscosity is a peculiar part of the viscosity
tensor which does not result in dissipation and is allowed when parity symmetry
is broken. For the case of incompressible fluids, the odd viscosity manifests
itself through the free surface (no stress) boundary conditions. We first find
the free surface wave solutions of hydrodynamics in the linear approximation
and study the dispersion of such waves. As expected, the surface waves are
chiral and even exist in the absence of gravity and vanishing shear viscosity.
In this limit, we derive effective nonlinear Hamiltonian equations for the
surface dynamics, generalizing the linear solutions to the weakly nonlinear
case. Within the small surface angle approximation, the equation of motion
leads to a new class of nonlinear chiral dynamics governed by what we dub the
{\it chiral} Burgers equation. The chiral Burgers equation is identical to the
complex Burgers equation with imaginary viscosity and an additional analyticity
requirement that enforces chirality. We present several exact solutions of the
chiral Burgers equation. For generic multiple pole initial conditions, the
system evolves to the formation of singularities in a finite time similar to
the case of an ideal fluid without odd viscosity. We also obtain a periodic
solution to the chiral Burgers corresponding to the nonlinear generalization
of small amplitude linear waves.
Submissions
Submissions for which this Contributor is identified as an author:
Prof. Ganeshan: "**The referee writes:** In thi..."
in Submissions  report on Lyapunov exponents and entanglement entropy transition on the noncommutative hyperbolic plane