2,084 research outputs found
How viscous bubbles collapse: topological and symmetry-breaking instabilities in curvature-driven hydrodynamics
The duality between the mechanical equilibrium of elastic bodies and
non-inertial flow in viscous liquids has been a guiding principle in decades of
research. However, this duality is broken whenever the Gaussian curvature of
viscous films evolves rapidly in time. In such a case the film evolves through
a non-inertial yet geometrically nonlinear surface dynamics, which has remained
largely unexplored. We reveal the driver of such dynamics as the flow of
currents of Gaussian curvature of the evolving surface, rather than the
existence of an energetically favored target metric, as in the elastic
analogue. Focusing on the prototypical example of a bubble collapsing after
rapid depressurization, we show that the spherically-shaped viscous film
evolves via a topological instability, whose elastic analogue is forbidden by
the existence of an energy barrier. The topological transition brings about
compression within the film, triggering another, symmetry breaking instability
and radial wrinkles that grow in amplitude and invade the flattening film.
Building on an analogy between surface currents of Gaussian curvature and
polarization in electrostatic conductors, we obtain quantitative predictions
for the evolution of the flattening film. We propose that this classical
dynamics has ramifications in the emerging field of viscous hydrodynamics of
strongly correlated electrons in two-dimensional materials.Comment: 17 pages (10 pages of appendices). A demonstration video is included
as an ancillary fil
Dynamical susceptibility near a long-wavelength critical point with a nonconserved order parameter
We study the dynamic response of a two-dimensional system of itinerant
fermions in the vicinity of a uniform () Ising nematic quantum
critical point of wave symmetry. The nematic order parameter is not a
conserved quantity, and this permits a nonzero value of the fermionic
polarization in the wave channel even for vanishing momentum and finite
frequency: . For weak coupling between the
fermions and the nematic order parameter (i.e. the coupling is small compared
to the Fermi energy), we perturbatively compute over a parametrically broad range of frequencies where the fermionic
self-energy is irrelevant, and use Eliashberg theory to
compute in the non-Fermi liquid regime at
smaller frequencies, where . We find that
is a constant, plus a frequency dependent correction
that goes as at high frequencies, crossing over to
at lower frequencies. The scaling holds also in a non-Fermi
liquid regime. The non-vanishing of gives rise to
additional structure in the imaginary part of the nematic susceptibility
at , in marked contrast to the
behavior of the susceptibility for a conserved order parameter. This additional
structure may be detected in Raman scattering experiments in the wave
geometry
Dynamical susceptibility of a near-critical non-conserved order parameter and B2g Raman response in Fe-based superconductors
We analyze the dynamical response of a two-dimensional system of itinerant
fermions coupled to a scalar boson , which undergoes a continuous
transition towards nematic order with wave form-factor. We consider two
cases: (a) when is a soft collective mode of fermions near a Pomeranchuk
instability, and (b) when it is an independent critical degree of freedom, such
as a composite spin order parameter near an Ising-nematic transition. In both
cases, the order-parameter is not a conserved quantity and the wave
fermionic polarization remains finite even at . The
polarization has similar behavior in the two cases, but the
relations between and the bosonic susceptibility are different, leading to different forms of , as measured by Raman scattering. We compare our results with
polarization-resolved Raman data for the Fe-based superconductors
FeSeS, NaFeCoAs and BaFeAs. We argue that the
data for FeSeS are well described within Pomeranchuk scenario,
while the data for NaFeCoAs and BaFeAs are better described
within the "independent" scenario involving a composite spin order
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