Albion Lawrence

When atmospheric storms pass over the ocean, they resonantly force near-inertial waves (NIWs), internal waves with a frequency close to the local Coriolis frequency $f$. It has long been recognised that the evolution of NIWs is modulated by the ocean's mesoscale eddy field. This can result in NIWs being concentrated into anticyclones which provide an efficient pathway for NIW propagation to depth. Here we analyse the eigenmodes of NIWs in the presence of mesoscale eddies and heavily draw on parallels with quantum mechanics. Whether the eddies are effective at modulating the behaviour of NIWs depends on the wave dispersiveness $\varepsilon ^2 = f\lambda ^2/\varPsi$, where $\lambda$ is the deformation radius and $\varPsi$ is a scaling for the eddy streamfunction. If $\varepsilon \gg 1$, NIWs are strongly dispersive, and the waves are only weakly affected by the eddies. We calculate the perturbations away from a uniform wave field and the frequency shift away from $f$. If $\varepsilon \ll 1$, NIWs are weakly dispersive, and the wave evolution is strongly modulated by the eddy field. In this weakly dispersive limit, the Wentzel–Kramers–Brillouin approximation, from which ray tracing emerges, is a valid description of the NIW evolution even if the large-scale atmospheric forcing apparently violates the requisite assumption of a scale separation between the waves and the eddies. The large-scale forcing excites many wave modes, each of which varies on a short spatial scale and is amenable to asymptotic analysis analogous to the semi-classical analysis of quantum systems. The strong modulation of weakly dispersive NIWs by eddies has the potential to modulate the energy input into NIWs from the wind, but we find that this effect should be small under oceanic conditions.

A bulge surface, on a time reflection-symmetric Cauchy slice of a holographic spacetime, is a non-minimal extremal surface that occurs between two locally minimal surfaces homologous to a given boundary region. According to the python’s lunch conjecture of Brown et al., the bulge’s area controls the complexity of bulk reconstruction, in the sense of the amount of post-selection that needs to be overcome for the reconstruction of the entanglement wedge beyond the outermost extremal surface. We study the geometry of bulges in a variety of classical spacetimes, and discover a number of surprising features that distinguish them from more familiar extremal surfaces such as Ryu-Takayanagi surfaces: they spontaneously break spatial isometries, both continuous and discrete; they are sensitive to the choice of boundary infrared regulator; they can self-intersect; and they probe entanglement shadows, orbifold singularities, and compact spaces such as the sphere in AdS _p× S^q p × S q . These features imply, according to the python’s lunch conjecture, novel qualitative differences between complexity and entanglement in the holographic context. We also find, surprisingly, that extended black brane interiors have a non-extensive complexity; similarly, for multi-boundary wormhole states, the complexity pleateaus after a certain number of boundaries have been included.

We construct an infinite family of microstates for black holes in Minkowski spacetime which have effective semiclassical descriptions in terms of collapsing dust shells in the black hole interior. Quantum mechanical wormholes cause these states to have exponentially small, but universal, overlaps. We show that these overlaps imply that the microstates span a Hilbert space of log dimension equal to the event horizon area divided by four times the Newton constant, explaining the statistical origin of the Bekenstein-Hawking entropy.

Final technical report for he DOE QuantISED grant "Structure and Dynamics of Entanglement in Large Quantum Systems", awarded to Profs. Albion Lawrence and Matthew Headrick a Brandeis University. The work on this grant included entanglement in "matrix quantum mechanics", a system wih large numbers of degrees of freedom; the dynamics of a system coupled to a large environment; and the formulation of he "bit threads" picture of entanglement in quantum systems which are equivalent to a theory of quantum gravity.

Along-track wavenumber spectral densities of sea surface height (SSH) are estimated from Jason-2 altimetry data as a function of spatial location and calendar month, to understand the seasonality of meso- and submesoscale balanced dynamics across the global ocean. Regions with significant mode-1 and mode-2 baroclinic tides are rejected, restricting the analysis to the extratropics. Where balanced motion dominates, the SSH spectral density is averaged over all pass segments in a region for each calendar month, and is fit to a 4-parameter model consisting of a flat plateau at low wavenumbers, a transition at wavenumber k0 to a red power law spectrum k−s, and a white spectrum at high wavenumbers that models the altimeter noise. The monthly time series of the model parameters are compared to the evolution of the mixed layer. The annual mode of the spectral slope s reaches a minimum after the mixed layer deepens, and the annual mode of the bandpassed kinetic energy in the ranges [2k0,4k0] and [k0,2k0] peak ∼2 and ∼4 months, respectively, after the maximum of the annual mode of the mixed layer depth. This analysis is consistent with an energization of the submesoscale by a winter mixed layer instability followed by an inverse cascade of kinetic energy to the mesoscale, in agreement with prior modeling studies and in situ measurements. These results are compared to prior modeling, in situ, and satellite investigations of specific regions, and are broadly consistent with them within measurement uncertainties.

We study target space entanglement in gauged multi-matrix models as models of entanglement between groups of D-branes separated by a planar entangling surface, paying close attention to the implementation of gauge invariance. We open with a review of target space entanglement between identical particles, which shares some important features (specifically a gauged permutation symmetry) with our main problem. For our matrix models, we implement a gauge fixing well-adapted to the entangling surface. In this gauge, we map the matrix model problem to that of entanglement of a U(1) gauge theory on a complete or all-to-all lattice. Matrix elements corresponding to open strings stretching across the entangling surface in the target space lead to interesting contributions to the entanglement entropy.

We present a family of consistent quantum field theories of monodromy quintessence in strong coupling, which can serve as benchmarks in modeling dark energy different from the cosmological constant. These theories have discrete gauge symmetries that can protect them from quantum field theory and quantum gravity corrections, both perturbative and nonperturbative. The strong coupling effects, at scales ≳
mm
−
1
, flatten the potential and activate operators with higher powers of derivatives. The predicted equation of state is close to, but not exactly equal to,
−
1
. Thus testing the model may be within reach of the (near) future programs to explore the nature of dark energy.

We consider the reduced density matrix for a disk in the ground state of the interacting fixed points of the large-N O(N) vector model in 2 + 1 dimensions. Using the map to the free energy on H-2 x S-1, we show that there is an instability in the Renyi entropies at n = 1 in the N ->infinity limit, indicating a phase transition at or near this Renyi parameter. We close with a discussion of the finite-N case.