304 research outputs found
Interaction effects on 1D fermionic symmetry protected topological phases
In free fermion systems with given symmetry and dimension, the possible
topological phases are labeled by elements of only three types of Abelian
groups, Z_1, Z_2, or Z. For example non-interacting 1D fermionic
superconducting phases with S_z spin rotation and time-reversal symmetries are
classified by Z. We show that with weak interactions, this classification
reduces to Z_4. Using group cohomology, one can additionally show that there
are only four distinct phases for such 1D superconductors even with strong
interactions. Comparing their projective representations, we find all these
four symmetry protected topological phases can be realized with free fermions.
Further, we show that 1D fermionic superconducting phases with Z_n discrete S_z
spin rotation and time-reversal symmetries are classified by Z_4 when n=even
and Z_2 when n=odd; again, all these strongly interacting topological phases
can be realized by non-interacting fermions. Our approach can be applied to
systems with other symmetries to see which 1D topological phases can be
realized by free fermions
Low-energy behavior of spin-liquid electron spectral functions
We calculate the electron spectral function for a spin-liquid with a spinon
Fermi surface and a Dirac spin-liquid. Calculations are based upon the
slave-rotor mean-field theory. We consider the effect of gauge fluctuations
using a simple model and find the behavior is not strongly modified. The
results, distinct from conventional Mott insulator or band theory predictions,
suggest that measuring the spectral function e.g. via ARPES could help in the
experimental verification and characterization of spin liquids.Comment: 7 pages, 7 figure
Quantifying configurational information for a stochastic particle in a flow-field
Flow-fields are ubiquitous systems that are able to transport vital
signalling molecules necessary for system function. While information regarding
the location and transport of such particles is often crucial, it is not
well-understood how to quantify the information in such stochastic systems.
Using the framework of nonequilibrium statistical physics, we develop
theoretical tools to address this question. We observe that rotation in a
flow-field does not explicitly appear in the generalized potential that governs
the rate of system entropy production. Specifically, in the neighborhood of a
flow-field, rotation contributes to the information content only in the
presence of strain -- and then with a comparatively weaker contribution than
strain and at higher orders in time. Indeed, strain and especially the flow
divergence, contribute most strongly to transport properties such as particle
residence time and the rate of information change. These results shed light on
how information can be analyzed and controlled in complex artificial and living
flow-based systems.Comment: 12 pages, 5 figure
A topological mechanism for robust and efficient global oscillations in biological networks
Long and stable timescales are often observed in complex biochemical
networks, such as in emergent oscillations. How these robust dynamics persist
remains unclear, given the many stochastic reactions and shorter time scales
demonstrated by underlying components. We propose a topological model with
parsimonious parameters that produces long oscillations around the network
boundary, effectively reducing the system dynamics to a lower-dimensional
current. Using this to model KaiC, which regulates the circadian rhythm in
cyanobacteria, we compare the coherence of oscillations to that in other KaiC
models. Our topological model localizes currents on the system edge for an
efficient regime with simultaneously increased precision and decreased cost.
Further, we introduce a new predictor of coherence from the analysis of
spectral gaps, and show that our model saturates a global thermodynamic bound.
Our work presents a new mechanism for emergent oscillations in complex
biological networks utilizing dissipative cycles to achieve robustness and
efficient performance
The hierarchical structure of a firm: a geometric approach
This paper develops a novel, geometric approach to modelling a firm's hierarchical structure. We model the firm''s hierarchy as the sector of a circle, in which the radius represents the height of the hierarchy and the angle of the sector represents the width of the hierarchy. The firm then chooses the height and angle in order to maximise profit. We analyse the impacts of changes in economies of scale, input substitutability and labour productivity on the firm''s hierarchical structure. We find that the firm will unambiguously become more hierarchical as specialisation of its workers increases or as its output price increases. The effect of changes in scale economies is contingent on the level of task specialisation and output price.
Topological phases in discrete stochastic systems
Topological invariants have proved useful for analyzing emergent function as
they characterize a property of the entire system, and are insensitive to local
details, disorder, and noise. They support edge states, which reduce the system
response to a lower dimensional space and offer a mechanism for the emergence
of global cycles within a large phase space. Topological invariants have been
heavily studied in quantum electronic systems and been observed in other
classical platforms such as mechanical lattices. However, this framework
largely describes equilibrium systems within an ordered crystalline lattice,
whereas biological systems are often strongly non-equilibrium with stochastic
components. We review recent developments in topological states in discrete
stochastic models in 1d and 2d systems, and initial progress in identifying
testable signature of topological states in molecular systems and ecology.
These models further provide simple principles for targeted dynamics in
synthetic systems or in the engineering of reconfigurable materials. Lastly, we
describe novel theoretical properties of these systems such as the necessity
for non-Hermiticity in permitting edge states, as well as new analytical tools
to reveal these properties. The emerging developments shed light on fundamental
principles for non-equilibrium systems and topological protection enabling
robust biological function.Comment: Invited review for Reports on Progress in Physics, submitted.
Comments welcom
Collaborative Practices in Special Education: An Exploratory Study
Objective: This exploratory survey study examined collaborative practices of professionals working in special education. The basis for the survey was the Conceptual Model of Collaboration (CMC), created by Hess and colleagues (2017).
Methods: 27 professionals who work in special education participated. Cross tabulation tests and Pearson\u27s correlation tests were run to determine relationships between the variables.
Results: The findings indicated that the majority of participants value collaboration for student outcomes and professional development. Most participants agreed on common facilitators and barriers to collaboration. Collaboration primarily takes place in IEP meetings, through email and text messaging and is frequent in all classroom types and age ranges. Frequent collaboration has supported prioritization of sensory-motor programming for both the student and the classroom equally
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