13 research outputs found
Convergence of Derivative Expansion in Supersymmetric Functional RG Flows
We confirm the convergence of the derivative expansion in two supersymmetric
models via the functional renormalization group method. Using pseudo-spectral
methods, high-accuracy results for the lowest energies in supersymmetric
quantum mechanics and a detailed description of the supersymmetric analogue of
the Wilson-Fisher fixed point of the three-dimensional Wess-Zumino model are
obtained. The superscaling relation proposed earlier, relating the relevant
critical exponent to the anomalous dimension, is shown to be valid to all
orders in the supercovariant derivative expansion and for all
Holographic quenches and anomalous transport
We study the response of the chiral magnetic effect due to continuous
quenches induced by time dependent electric fields within holography.
Concretely, we consider a holographic model with dual chiral anomaly and
compute the electric current parallel to a constant, homogeneous magnetic field
and a time dependent electric field in the probe approximation. We explicitly
solve the PDEs by means of pseudospectral methods in spatial and time
directions and study the transition to an universal "fast" quench response.
Moreover, we compute the amplitudes, i.e.,~residues of the quasi normal modes,
by solving the (ODE) Laplace transformed equations. We investigate the
possibility of considering the asymptotic growth rate of the amplitudes as a
well defined notion of initial time scale for linearized systems. Finally, we
highlight the existence of Landau level resonances in the electrical
conductivity parallel to a magnetic field at finite frequency and show
explicitly that these only appear in presence of the anomaly. We show that the
existence of these resonances induces, among others, a long-lived AC electric
current once the electric field is switched off.Comment: 34 pages, 10 figure
Pseudospectrum and binary black hole merger transients
The merger phase of binary black hole coalescences is a transient between an
initial oscillating regime (inspiral) and a late exponentially damped phase
(ringdown). In spite of the non-linear character of Einstein equations, the
merger dynamics presents a surprisingly simple behaviour consistent with
effective linearity. On the other hand, energy loss through the event horizon
and by scattering to infinity renders the system non-conservative. Hence, the
infinitesimal generator of the (effective) linear dynamics is a non-selfadjoint
operator. Qualitative features of transients in linear dynamics driven by
non-selfadjoint (in general, non-normal) operators are captured by the
pseudospectrum of the time generator. We propose the pseudospectrum as a
unifying framework to thread together the phases of binary black hole
coalescences, from the inspiral-merger transition up to the late quasinormal
mode ringdown.Comment: 18 pages, 1 figur