17,246 research outputs found
Presentations for monoids of finite partial isometries
In this paper we give presentations for the monoid of all
partial isometries on and for its submonoid
of all order-preserving partial isometries.Comment: 11 pages, submitte
Spin-Driven Nematic Instability of the Multi-Orbital Hubbard Model: Application to Iron-Based Superconductors
Nematic order resulting from the partial melting of density-waves has been
proposed as the mechanism to explain nematicity in iron-based superconductors.
An outstanding question, however, is whether the microscopic electronic model
for these systems -- the multi-orbital Hubbard model -- displays such an
ordered state as its leading instability. In contrast to usual electronic
instabilities, such as magnetic and charge order, this fluctuation-driven
phenomenon cannot be captured by the standard RPA method. Here, by including
fluctuations beyond RPA in the multi-orbital Hubbard model, we derive its
nematic susceptibility and contrast it with its ferro-orbital order
susceptibility, showing that its leading instability is the spin-driven nematic
phase. Our results also demonstrate the primary role played by the
orbital in driving the nematic transition, and reveal that high-energy magnetic
fluctuations are essential to stabilize nematic order in the absence of
magnetic order.Comment: 8 pages, 6 figure
On the Modeling of Droplet Evaporation on Superhydrophobic Surfaces
When a drop of water is placed on a rough surface, there are two possible
extreme regimes of wetting: the one called Cassie-Baxter (CB) with air pockets
trapped underneath the droplet and the one characterized by the homogeneous
wetting of the surface, called the Wenzel (W) state. A way to investigate the
transition between these two states is by means of evaporation experiments, in
which the droplet starts in a CB state and, as its volume decreases, penetrates
the surface's grooves, reaching a W state. Here we present a theoretical model
based on the global interfacial energies for CB and W states that allows us to
predict the thermodynamic wetting state of the droplet for a given volume and
surface texture. We first analyze the influence of the surface geometric
parameters on the droplet's final wetting state with constant volume, and show
that it depends strongly on the surface texture. We then vary the volume of the
droplet keeping fixed the geometric surface parameters to mimic evaporation and
show that the drop experiences a transition from the CB to the W state when its
volume reduces, as observed in experiments. To investigate the dependency of
the wetting state on the initial state of the droplet, we implement a cellular
Potts model in three dimensions. Simulations show a very good agreement with
theory when the initial state is W, but it disagrees when the droplet is
initialized in a CB state, in accordance with previous observations which show
that the CB state is metastable in many cases. Both simulations and theoretical
model can be modified to study other types of surface.Comment: 23 pages, 7 figure
Interplay between superconductivity and itinerant magnetism in underdoped BaKFeAs ( 0.2) probed by the response to controlled point-like disorder
The response of superconductors to controlled introduction of point-like
disorder is an important tool to probe their microscopic electronic collective
behavior. In the case of iron-based superconductors (IBS), magnetic
fluctuations presumably play an important role in inducing high temperature
superconductivity. In some cases, these two seemingly incompatible orders
coexist microscopically. Therefore, understanding how this unique coexistence
state is affected by disorder can provide important information about the
microscopic mechanisms involved. In one of the most studied pnictide family,
hole-doped BaKFeAs (BaK122), this coexistence occurs over a
wide range of doping levels, 0.16~~0.25. We used
relativistic 2.5 MeV electrons to induce vacancy-interstitial (Frenkel) pairs
that act as efficient point-like scattering centers. Upon increasing dose of
irradiation, the superconducting transition temperature decreases
dramatically. In the absence of nodes in the order parameter this provides a
strong support for a sign-changing pairing. Simultaneously, in the
normal state, there is a strong violation of the Matthiessen's rule and a
decrease (surprisingly, at the same rate as ) of the magnetic transition
temperature , which indicates the itinerant nature of the long-range
magnetic order. Comparison of the hole-doped BaK122 with electron-doped
Ba(FeCo)As (FeCo122) with similar 110~K,
0.02, reveals significant differences in the normal states, with no
apparent Matthiessen's rule violation above on the electron-doped
side. We interpret these results in terms of the distinct impact of impurity
scattering on the competing itinerant antiferromagnetic and
superconducting orders
On semigroups of endomorphisms of a chain with restricted range
Let be a finite or infinite chain and let be the monoid of all
endomorphisms of . In this paper, we describe the largest regular
subsemigroup of and Green's relations on . In fact, more
generally, if is a nonempty subset of and the subsemigroup of
of all elements with range contained in , we characterize the largest
regular subsemigroup of and Green's relations on . Moreover,
for finite chains, we determine when two semigroups of the type are
isomorphic and calculate their ranks.Comment: To appear in Semigroup Foru
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