First law and quantum correction for holographic entanglement contour

Entanglement entropy satisfies a first law-like relation, which equates the first order perturbation of the entanglement entropy for the region AA to the first order perturbation of the expectation value of the modular Hamiltonian, \delta S_{A}=\delta \langle K_A \rangleδSA=δ⟨KA⟩. We propose that this relation has a finer version which states that, the first order perturbation of the entanglement contour equals to the first order perturbation of the contour of the modular Hamiltonian, i.e. \delta s_{A}(\textbf{x})=\delta \langle k_{A}(\textbf{x})\rangleδsA(𝐱)=δ⟨kA(𝐱)⟩. Here the contour functions s_{A}(\textbf{x})sA(𝐱) and k_{A}(\textbf{x})kA(𝐱) capture the contribution from the degrees of freedom at \textbf{x}𝐱 to S_{A}SA and K_AKA respectively. In some simple cases k_{A}(\textbf{x})kA(𝐱) is determined by the stress tensor. We also evaluate the quantum correction to the entanglement contour using the fine structure of the entanglement wedge and the additive linear combination (ALC) proposal for partial entanglement entropy (PEE) respectively. The fine structure picture shows that, the quantum correction to the boundary PEE can be identified as a bulk PEE of certain bulk region. While the shows that the quantum correction to the boundary PEE comes from the linear combination of bulk entanglement entropy. We focus on holographic theories with local modular Hamiltonian and configurations of quantum field theories where the applies.

Holographic quantum tasks with input and output regions

Quantum tasks are quantum computations with inputs and outputs occurring at specified spacetime locations. Considering such tasks in the context of AdS/CFT has led to novel constraints relating bulk geometry and boundary entanglement. In this article we consider tasks where inputs and outputs are encoded into extended spacetime regions, rather than the points previously considered. We show that this leads to stronger constraints than have been derived in the point based setting. In particular we improve the connected wedge theorem, appearing earlier in arXiv:1912.05649, by finding a larger bulk region whose existence implies large boundary correlation. As well, we show how considering extended input and output regions leads to non-trivial statements in Poincaré-AdS2+1, a setting where the point-based connected wedge theorem is always trivial.

Gauge invariant target space entanglement in D-brane holography

It has been suggested in arXiv:2004.00613 that in Dp-brane holography, entanglement in the target space of the D-brane Yang-Mills theory provides a precise notion of bulk entanglement in the gravity dual. We expand on this discussion by providing a gauge invariant characterization of operator sub-algebras corresponding to such entanglement. This is achieved by finding a projection operator which imposes a constraint characterizing the target space region of interest. By considering probe branes in the Coloumb branch we provide motivation for why the operator sub-algebras we consider are appropriate for describing a class of measurements carried out with low-energy probes in the corresponding bulk region of interest. We derive expressions for the corresponding Renyi entropies in terms of path integrals which can be directly used in numerical calculations.

Investigation of the Ionic Liquid Graphene Electric Double Layer in Supercapacitors Using Constant Potential Simulations

In this work, we investigate the effect of the cation structure on the structure and dynamics of the electrode–electrolyte interface using molecular dynamics simulations. A constant potential method is used to capture the behaviour of 1-ethyl-3-methylimidazolium bis (trifluoromethane)sulfonimide ([C2mim][NTf2]) and butyltrimethylammonium bis(trifluoromethane) sulfonimide ([N4,1,1,1][NTf2]) ionic liquids at varying potential differences applied across the supercapacitor. We find that the details of the structure in the electric double layer and the dynamics differ significantly, yet the charge profile and capacitance do not vary greatly. For the systems considered, charging results in the rearrangement and reorientation of ions within ∼1 nm of the electrode rather than the diffusion of ions to/from the bulk region. This occurs on timescales of O(10 ns) for the ionic liquids considered, and depends on the viscosity of the fluid.

Near wall Prandtl number effects on velocity gradient invariants and flow topologies in turbulent Rayleigh–Bénard convection

The statistical behaviours of the invariants of the velocity gradient tensor and flow topologies for Rayleigh–Bénard convection of Newtonian fluids in cubic enclosures have been analysed using Direct Numerical Simulations (DNS) for a range of different values of Rayleigh (i.e. $$Ra=10^7-10^9$$ R a = 10 7 - 10 9 ) and Prandtl (i.e. $$Pr=1$$ P r = 1 and 320) numbers. The behaviours of second and third invariants of the velocity gradient tensor suggest that the bulk region of the flow at the core of the domain is vorticity-dominated whereas the regions in the vicinity of cold and hot walls, in particular in the boundary layers, are found to be strain rate-dominated and this behaviour has been found to be independent of the choice of Ra and Pr values within the range considered here. Accordingly, it has been found that the focal topologies S1 and S4 remain predominant in the bulk region of the flow and the volume fraction of nodal topologies increases in the vicinity of the active hot and cold walls for all cases considered here. However, remarkable differences in the behaviours of the joint probability density functions (PDFs) between second and third invariants of the velocity gradient tensor (i.e. Q and R) have been found in response to the variations of Pr. The classical teardrop shape of the joint PDF between Q and R has been observed away from active walls for all values of Pr, but this behavior changes close to the heated and cooled walls for high values of Pr (e.g. $$Pr=320$$ P r = 320 ) where the joint PDF exhibits a shape mirrored at the vertical Q-axis. It has been demonstrated that the junctions at the edges of convection cells are responsible for this behaviour for $$Pr=320$$ P r = 320 , which also increases the probability of finding S3 topologies with large negative magnitudes of Q and R. By contrast, this behaviour is not observed in the $$Pr=1$$ P r = 1 case and these differences between flow topology distributions in Rayleigh–Bénard convection in response to Pr suggest that the modelling strategy for turbulent natural convection of gaseous fluids may not be equally well suited for simulations of turbulent natural convection of liquids with high values of Pr.

Localised signalling compartments in 2D coupled by a bulk diffusion field: Quorum sensing and synchronous oscillations in the well-mixed limit

We analyse oscillatory instabilities for a coupled partial-ordinary differential equation (PDE-ODE) system modelling the communication between localised spatially segregated dynamically active signalling compartments that are coupled through a passive extracellular bulk diffusion field in a bounded 2D domain. Each signalling compartment is assumed to secrete a chemical into the extracellular medium (bulk region), and it can also sense the concentration of this chemical in the region around its boundary. This feedback from the bulk region, resulting from the entire collection of cells, in turn modifies the intracellular dynamics within each cell. In the limit where the signalling compartments are circular discs with a small common radius ɛ ≪ 1 and where the bulk diffusivity is asymptotically large, a matched asymptotic analysis is used to reduce the dimensionless PDE–ODE system into a nonlinear ODE system with global coupling. For Sel’kov reaction kinetics, this ODE system for the intracellular dynamics and the spatial average of the bulk diffusion field are then used to investigate oscillatory instabilities in the dynamics of the cells that are triggered due to the global coupling. In particular, numerical bifurcation software on the ODEs is used to study the overall effect of coupling defective cells (cells that behave differently from the remaining cells) to a group of identical cells. Moreover, when the number of cells is large, the Kuramoto order parameter is computed to predict the degree of phase synchronisation of the intracellular dynamics. Quorum sensing behaviour, characterised by the onset of collective behaviour in the intracellular dynamics as the number of cells increases above a threshold, is also studied. Our analysis shows that the cell population density plays a dual role of triggering and then quenching synchronous oscillations in the intracellular dynamics.

Energy production and self-sustained turbulence at the Kolmogorov scale in Couette flow

Several recent studies have reported that there exists a self-similar form of invariant solutions down to the Kolmogorov microscale in the bulk region of turbulent Couette flow. While their role in a fully developed turbulent flow is yet to be identified, here we report that there exists a related mechanism of turbulence production at the Kolmogorov microscale in the bulk region of turbulent Couette flow by performing a set of minimal-span direct numerical simulations up to friction Reynolds number $Re_{\unicode[STIX]{x1D70F}}\simeq 800$. This mechanism is found to essentially originate from the non-zero mean shear in the bulk region of the Couette flow, and involves eddy turn-over dynamics remarkably similar to the so-called self-sustaining process (SSP) and/or vortex–wave interaction (VWI). A numerical experiment that removes all other motions except in the core region is also performed, which demonstrates that the eddies at a given wall-normal location in the bulk region are sustained in the absence of other motions at different wall-normal locations. It is proposed that the self-sustaining eddies at the Kolmogorov microscale correspond to those in uniform shear turbulence at transitional Reynolds numbers, and a quantitative comparison between the eddies in uniform shear and near-wall turbulence is subsequently made. Finally, it is shown that turbulence production by the self-sustaining eddies at the Kolmogorov microscale is much smaller than that of full-scale simulations, and that the difference between the two increases with Reynolds number.

Green’s functions theory for an interstitial magnetic impurity in a transverse Ising ferromagnet

A Green’s function formalism is used to calculate the spectrum of localized states associated with an interstitial magnetic impurity in a semi-infinite ferromagnet described by the transverse Ising model. The nonresonant and resonant excitations of the system due to the impurity (i.e. the defect modes outside and inside, respectively, the region of the bulk and surface spin waves (SW)) are calculated numerically for the high-temperature phase. Two situations are analyzed, depending on the position of the interstitial impurity: the impurity is in the surface ([Formula: see text]) and the impurity is in the bulk region ([Formula: see text]).