Acoustic characterization of Hofstadter butterfly with resonant scatterers

We are interested in the experimental characterization of the Hofstadter butterfly by means of acoustical waves. The transmission of an acoustic pulse through an array of 60 variable and resonant scatterers periodically distribued along a waveguide is studied. An arbitrary scattering arrangement is realized by using the variable length of each resonator cavity. For a periodic modulation, the structures of forbidden bands of the transmission reproduce the Hofstadter butterfly. We compare experimental, analytical, and computational realizations of the Hofstadter butterfly and we show the influence of the resonances of the scatterers on the structure of the butterfly

Butterfly Velocities for Holographic Theories of General Spacetimes

The butterfly velocity characterizes the spread of correlations in a quantum system. Recent work has provided a method of calculating the butterfly velocity of a class of boundary operators using holographic duality. Utilizing this and a presumed extension of the canonical holographic correspondence of AdS/CFT, we investigate the butterfly velocities of operators with bulk duals living in general spacetimes. We analyze some ubiquitous issues in calculating butterfly velocities using the bulk effective theory, and then extend the previously proposed method to include operators in entanglement shadows. We explicitly compute butterfly velocities for bulk local operators in the holographic theory of flat Friedmann-Robertson-Walker spacetimes and find a universal scaling behavior for the spread of operators in the boundary theory, independent of dimension and fluid components. This result may suggest that a Lifshitz field theory with z = 4 is the appropriate holographic dual for these spacetimes.Comment: 14 pages, 3 figures; fixed calculational error, removed the associated erroneous discussions on monotonicit

Criticality in Third Order Lovelock Gravity and the Butterfly effect

We study third order Lovelock Gravity in $D=7$ at the critical point which three (A)dS vacua degenerate into one. We see there is not propagating graviton at the critical point. And also we compute the butterfly velocity for this theory at the critical point by considering the shock wave solutions near horizon, this is important to note that although there is no propagating graviton at the critical point, due to boundary gravitons the butterfly velocity is non-zero. Finally we observe that the butterfly velocity for third order Lovelock Gravity at the critical point in $D=7$ is less than the butterfly velocity for Einstein-Gauss-Bonnet Gravity at the critical point in $D=7$ which is less than the butterfly velocity in D = 7 for Einstein Gravity, $v_{B}^{E.H}>v_{B}^{E.G.B}>v_{B}^{3rd\,\,Lovelock}$. Maybe we can conclude that by adding higher order curvature corrections to Einstein Gravity the butterfly velocity decreases.Comment: 10 pages, No figure, Minor correction

On Butterfly effect in Higher Derivative Gravities

We study butterfly effect in $D$-dimensional gravitational theories containing terms quadratic in Ricci scalar and Ricci tensor. One observes that due to higher order derivatives in the corresponding equations of motion there are two butterfly velocities. The velocities are determined by the dimension of operators whose sources are provided by the metric. The three dimensional TMG model is also studied where we get two butterfly velocities at generic point of the moduli space of parameters. At critical point two velocities coincide.Comment: 16 pages, references adde

Phase Diagram for the Hofstadter butterfly and integer quantum Hall effect in three dimensions

We give a perspective on the Hofstadter butterfly (fractal energy spectrum in magnetic fields), which we have shown to arise specifically in three-dimensional(3D) systems in our previous work. (i) We first obtain the `phase diagram' on a parameter space of the transfer energies and the magnetic field for the appearance of Hofstadter's butterfly spectrum in anisotropic crystals in 3D. (ii) We show that the orientation of the external magnetic field can be arbitrary to have the 3D butterfly. (iii) We show that the butterfly is beyond the semiclassical description. (iv) The required magnetic field for a representative organic metal is estimated to be modest ($\sim 40$ T) if we adopt higher Landau levels for the butterfly. (v) We give a simpler way of deriving the topological invariants that represent the quantum Hall numbers (i.e., two Hall conductivity in 3D, $\sigma_{xy}, \sigma_{zx}$, in units of $e^2/h$).Comment: 8 pages, 8 figures, eps versions of the figures will be sent on request to [email protected]

Garden varieties: how attractive are recommended garden plants to butterflies?

One way the public can engage in insect conservation is through wildlife gardening, including the growing of insect-friendly flowers as sources of nectar. However, plant varieties differ in the types of insects they attract. To determine which garden plants attracted which butterflies, we counted butterflies nectaring on 11 varieties of summer-flowering garden plants in a rural garden in East Sussex, UK. These plants were all from a list of 100 varieties considered attractive to British butterflies, and included the five varieties specifically listed by the UK charity Butterfly Conservation as best for summer nectar. A total of 2659 flower visits from 14 butterfly and one moth species were observed. We performed a principal components analysis which showed contrasting patterns between the species attracted to Origanum vulgare and Buddleia davidii. The “butterfly bush” Buddleia attracted many nymphalines, such as the peacock, Inachis io, but very few satyrines such as the gatekeeper, Pyronia tithonus, which mostly visited Origanum. Eupatorium cannibinum had the highest Simpson’s Diversity score of 0.75, while Buddleia and Origanum were lower, scoring 0.66 and 0.50 respectively. No one plant was good at attracting all observed butterfly species, as each attracted only a subset of the butterfly community. We conclude that to create a butterfly-friendly garden, a variety of plant species are required as nectar sources for butterflies. Furthermore, garden plant recommendations can probably benefit from being more precise as to the species of butterfly they attract