299 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
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.
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
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
Topology protects chiral edge currents in stochastic systems
Constructing systems that exhibit time-scales much longer than those of the
underlying components, as well as emergent dynamical and collective behavior,
is a key goal in fields such as synthetic biology and materials self-assembly.
Inspiration often comes from living systems, in which robust global behavior
prevails despite the stochasticity of the underlying processes. Here, we
present two-dimensional stochastic networks that consist of minimal motifs
representing out-of-equilibrium cycles at the molecular scale and support
chiral edge currents in configuration space. These currents arise in the
topological phase due to the bulk-boundary correspondence and dominate the
system dynamics in the steady-state, further proving robust to defects or
blockages. We demonstrate the topological properties of these networks and
their uniquely non-Hermitian features such as exceptional points and vorticity,
while characterizing the edge state localization. As these emergent edge
currents are associated to macroscopic timescales and length scales, simply
tuning a small number of parameters enables varied dynamical phenomena
including a global clock, dynamical growth and shrinkage, and synchronization.
Our construction provides a novel topological formalism for stochastic systems
and fresh insights into non-Hermitian physics, paving the way for the
prediction of robust dynamical states in new classical and quantum platforms.Comment: 14 pages, with appendices and 3 supplementary video
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