Asymmetric spatial structure of zero modes for birefringent Dirac fermions

We study the zero energy modes that arise in an unusual vortex configuration involving both the kinetic energy and an appropriate mass term in a model which exhibits birefringent Dirac fermions as its low energy excitations. We find the surprising feature that the ratio of the length scales associated with states centered on vortex and anti-vortex topological defects can be arbitrarily varied but that fractionalization of quantum numbers such as charge is unaffected. We discuss this situation from a symmetry point of view and present numerical results for a specific lattice model realization of this scenario.Comment: 7 pages, 6 figure

Transport in a periodically--driven tilted lattice via the extended reservoir approach: Stability criterion for recovering the continuum limit

Extended reservoirs provide a framework for capturing macroscopic, continuum environments, such as metallic electrodes driving a current through a nanoscale contact, impurity, or material. We examine the application of this approach to periodically--driven systems, specifically in the context of quantum transport. As with non--equilibrium steady states in time--independent scenarios, the current displays a Kramers' turnover including the formation of a plateau region that captures the physical, continuum limit response. We demonstrate that a simple stability criteria identifies an appropriate relaxation rate to target this physical plateau. Using this approach, we study quantum transport through a periodically--driven tilted lattice coupled to two metallic reservoirs held at a finite bias and temperature. We use this model to benchmark the extended reservoir approach and assess the stability criteria. When the system and reservoir are weakly coupled, the approach recovers well--understood physical behavior in this limit. Extended reservoirs enable addressing strong coupling and non--linear response as well, where we analyze how transport responds to the dynamics inside the driven lattice. These results set the foundations for the use of extended reservoir approach for periodically-driven, quantum systems, such as many--body Floquet states

The confluence of fractured resonances at points of dynamical, many--body flare

Resonant transport occurs when there is a matching of frequencies across some spatial medium, increasing the efficiency of shuttling particles from one reservoir to another. We demonstrate that in a periodically driven, many--body titled lattice there are sets of spatially fractured resonances. These ``emanate'' from two essential resonances due to scattering off internal surfaces created when the driving frequency and many--body interaction strength vary, a scattering reminiscent of lens flare. The confluence of these fractured resonances dramatically enhances transport. At one confluence, the interaction strength is finite and the essential resonance arises due to the interplay of interaction with the counter--rotating terms of the periodic drive. The other forms where several paths split by the many--body interaction merge in the non--interacting limit. We discuss the origin and structure of the fractured resonances, as well as the scaling of the conductance on system parameters. These results furnish a new example of the richness of open, driven, many--body systems.Comment: comments welcome

On the flat cohomology of binary norm forms

Let $\mathcal{O}$ be an order of index $m$ in the maximal order of a quadratic number field $k=\mathbb{Q}(\sqrt{d})$. Let $\underline{\mathbf{O}}_{d,m}$ be the orthogonal $\mathbb{Z}$-group of the associated norm form $q_{d,m}$. We describe the structure of the pointed set $H^1_{\mathrm{fl}}(\mathbb{Z},\underline{\mathbf{O}}_{d,m})$, which classifies quadratic forms isomorphic (properly or improperly) to $q_{d,m}$ in the flat topology. Gauss classified quadratic forms of fundamental discriminant and showed that the composition of any binary $\mathbb{Z}$-form of discriminant $\Delta_k$ with itself belongs to the principal genus. Using cohomological language, we extend these results to forms of certain non-fundamental discriminants.Comment: 24 pages, submitted. Comments are welcom

Discrete molecular dynamics simulations of peptide aggregation

We study the aggregation of peptides using the discrete molecular dynamics simulations. At temperatures above the alpha-helix melting temperature of a single peptide, the model peptides aggregate into a multi-layer parallel beta-sheet structure. This structure has an inter-strand distance of 0.48 nm and an inter-sheet distance of 1.0 nm, which agree with experimental observations. In this model, the hydrogen bond interactions give rise to the inter-strand spacing in beta-sheets, while the Go interactions among side chains make beta-strands parallel to each other and allow beta-sheets to pack into layers. The aggregates also contain free edges which may allow for further aggregation of model peptides to form elongated fibrils.Comment: 15 pages, 8 figure

Investigative approaches: Lessons learned from the RaDonda Vaught case

Accidental patient harms occur frequently in healthcare, but their exact prevalence and interventions that will best prevent them are still poorly understood. In rare cases, healthcare providers who have contributed to accidental patient harm may be criminally prosecuted to obtain justice for the patient and family or to set an example, which theoretically prevents other providers from making similar mistakes due to fear of punishment. A recent case where this strategy was chosen is the RaDonda L. Vaught vs. Tennessee (2022) criminal case. The present article discusses this case and its ramifications, as well as provides concrete recommendations for actions that healthcare organizations should take to foster a safer and more resilient healthcare system. Recommendations include placing an emphasis on just culture; ensuring timely, systems-level investigations of all incidents; creating and facilitating participation in a national reporting system; incorporating Human Factors professionals at multiple levels of organizations; and establishing a national safety board for medicine

Theory of interacting electrons on the honeycomb lattice

The low-energy theory of electrons interacting via repulsive short-range interactions on graphene's honeycomb lattice at half filling is presented. The exact symmetry of the Lagrangian with local quartic terms for the Dirac field dictated by the lattice is D_2 x U_c(1) x (time reversal), where D_2 is the dihedral group, and U_c(1) is a subgroup of the SU_c(2) "chiral" group of the non-interacting Lagrangian, that represents translations in Dirac language. The Lagrangian describing spinless particles respecting this symmetry is parameterized by six independent coupling constants. We show how first imposing the rotational, then Lorentz, and finally chiral symmetry to the quartic terms, in conjunction with the Fierz transformations, eventually reduces the set of couplings to just two, in the "maximally symmetric" local interacting theory. We identify the two critical points in such a Lorentz and chirally symmetric theory as describing metal-insulator transitions into the states with either time-reversal or chiral symmetry being broken. In the site-localized limit of the interacting Hamiltonian the low-energy theory describes the continuous transitions into the insulator with either a finite Haldane's (circulating currents) or Semenoff's (staggered density) masses, both in the universality class of the Gross-Neveu model. The picture of the metal-insulator transition on a honeycomb lattice emerges at which the residue of the quasiparticle pole at the metallic and the mass-gap in the insulating phase both vanish continuously as the critical point is approached. We argue that the Fermi velocity is non-critical as a consequence of the dynamical exponent being fixed to unity by the emergent Lorentz invariance. Effects of long-range interaction and the critical behavior of specific heat and conductivity are discussed.Comment: 16 revtex pages, 4 figures; typos corrected, new and updated references; published versio