Talks

Horizontal and vertical distributions of mesoscale eddy kinetic energy (EKE), the dominant reservoir of ocean kinetic energy, are influenced by both environmental and dynamical factors. Compared to partitioning across horizontal scales, distributions of EKE in the vertical have been relatively under-observed and under-studied. Using newly collected full-depth observations of horizontal velocity from four unique mooring sites and output from the NOAA GFDL CM2.6 suite, this work presents a characterization of eddy vertical structure and investigates the factorings controlling its spatio-temporal variability. Time series analysis and application of clustering tools reveal geographic patterns in vertical structure. These patterns indicate the role of latitude and bathymetry in moderating the vertical partitioning of EKE. These relationships are interpreted through the lens of theoretical expectation and considered in the context of techniques used to infer or impose vertical structure.

It is commonly believed that logical states of quantum error-correcting codes have to be highly entangled such that codes capable of correcting more errors require more entanglement to encode a qubit. Here we show that this belief may or may not be true depending on a particular code. To this end, we characterize a tradeoff between the code distance d quantifying the number of correctable errors, and geometric entanglement of logical states quantifying their maximal overlap with product states or more general ``topologically trivial" states. The maximum overlap is shown to be exponentially small in d for three families of codes: (1) low-density parity check (LDPC) codes with commuting check operators, (2) stabilizer codes, and (3) codes with a constant encoding rate. Equivalently, the geometric entanglement of any logical state of these codes grows at least linearly with d. On the opposite side, we also show that this distance-entanglement tradeoff does not hold in general. For any constant d and k (number of logical qubits), we show there exists a family of codes such that the geometric entanglement of some logical states approaches zero in the limit of large code length.

Entanglement in many-body quantum systems is notoriously hard to characterize due to the exponentially many parameters involved to describe the state. On the other hand, we are usually not interested in all the microscopic details of the entanglement attern but only some of its global features. It turns out, quantum circuits of different levels of complexity provide a useful way to establish a hierarchy among many-body entanglement structures. A circuit of a finite depth generates only short range entanglement which is in the same gapped phase as an unentangled product state. A linear depth circuit on the other hand can lead to chaos beyond thermal equilibrium. In this talk, we discuss how to reach the interesting regime in between that contains nontrivial gapped orders. This is achieved using the Sequential Quantum Circuit — a circuit of linear depth but with each layer acting only on one subregion in the system. We discuss how the Sequential Quantum Circuit can be used to generate nontrivial gapped states with long range correlation or long range entanglement, perform renormalization group transformation in foliated fracton order, and create defect excitations inside the bulk of a higher dimensional topological state.

Bayesian causal structure learning aims to learn a posterior distribution over directed acyclic graphs (DAGs), and the mechanisms that define the relationship between parent and child variables. By taking a Bayesian approach, it is possible to reason about the uncertainty of the causal model. The notion of modelling the uncertainty over models is particularly crucial for causal structure learning since the model could be unidentifiable when given only a finite amount of observational data. In this paper, we introduce a novel method to jointly learn the structure and mechanisms of the causal model using Variational Bayes, which we call Variational Bayes-DAG-GFlowNet (VBG). We extend the method of Bayesian causal structure learning using GFlowNets to learn not only the posterior distribution over the structure, but also the parameters of a linear-Gaussian model. Our results on simulated data suggest that VBG is competitive against several baselines in modelling the posterior over DAGs and mechanisms, while offering several advantages over existing methods, including the guarantee to sample acyclic graphs, and the flexibility to generalize to non-linear causal mechanisms.

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Two gapped ground states of lattice Hamiltonians are in the same quantum phase of matter, or topological phase, if they can be connected by a constant-depth circuit. It is conjectured that in two spatial dimensions, two gapped ground states with gappable boundary are in the same phase if and only if they have the same anyon contents, which are described by a unitary modular tensor category. We prove this conjecture for a class of states that obey a strict form of area law. Our main technical development is to transform these states into string-net wavefunctions using constant-depth circuits.

I will show the existence of a universal upper bound on the energy gap of topological states of matter, such as (integer and fractional) Chern insulators, quantum spin liquids and topological superconductors. This gap bound turns out to be fairly tight for the Chern insulator states that were predicted and observed in twisted bilayer transition metal dichalcogenides. Next, I will show a universal relation between the energy gap and dielectric constant of solids. These results are derived from fundamental principles of physics and therefore apply to all electronic materials. I will end by outlining new research directions involving topology, quantum geometry and energy.

The Bay of Bengal (bay) is a semi-enclosed tropical basin driven by seasonally reversing monsoon winds and a huge quantity of freshwater from rainfall and river runoff. The bay plays a fundamental role in controlling weather systems that make up the Asian summer monsoon system, including monsoon depressions and tropical cyclones. We have used a high resolution (~1 km) regional ocean model of the Bay of Bengal to explore the sub-mesoscale variability in the bay. Model simulations show that the East India Coastal Current (EICC) is extremely rich in submesoscale features compared to the open ocean and exhibit significant seasonal variations. Submesoscale activity over the EICC region is weakest during spring (March-May), slightly stronger during summer monsoon (June-September) and strongest during winter monsoon (November-January). Weak winds during spring and a huge fresh-water gain during summer monsoon tend to weaken submesoscale activity. Investigation of conversion rates of APE to KE...

Surface currents modify wind driven Ekman pumping in the ocean both by modifying the stress itself and by modifying the relationship between the stress and the Ekman transport. The former effect results in a strong mesoscale structure in the wind stress curl, such as is evident from scatterometer data. This mesoscale forcing is anti-correlated with surface vorticity and thus produces a strong damping effect on ocean eddies and currents. Recent work, however, suggests that this damping effect is over-represented in common parameterizations of the air-sea wind stress. The latter effect is referred to as nonlinear Ekman dynamics. These dynamics take the stress as given and add advective terms to the linear balance. Specifically, cross terms involving the Ekman and non-Ekman components of the flow are added to the linear Ekman balance. This is known to produce small scale (e.g., submesoscale) structures in the pumping velocity.

Here, we first review both the ocean surface velocity depen...

Surface currents modify wind driven Ekman pumping in the ocean both by modifying the stress itself and by modifying the relationship between the stress and the Ekman transport. The former effect results in a strong mesoscale structure in the wind stress curl, such as is evident from scatterometer data. This mesoscale forcing is anti-correlated with surface vorticity and thus produces a strong damping effect on ocean eddies and currents. Recent work, however, suggests that this damping effect is over-represented in common parameterizations of the air-sea wind stress. The latter effect is referred to as nonlinear Ekman dynamics. These dynamics take the stress as given and add advective terms to the linear balance. Specifically, cross terms involving the Ekman and non-Ekman components of the flow are added to the linear Ekman balance. This is known to produce small scale (e.g., submesoscale) structures in the pumping velocity.

Here, we first review both the ocean surface velocity depen...

Critical behaviour associated with the occurrence of tipping points is one of the key aspects of the dynamics of the Earth system. Criticality occurs in many different forms and with different characteristic spatial and temporal scales. Past critical transitions have sometimes been associated with mass extinction events, and the snowball/warm Earth dichotomy has played a major role in the emergence of multicellular life. Currently, anthropogenic forcing to the climate system seem to be bringing some multi stable subcomponents of the climate closer to a bifurcation point, as in the case of the Atlantic meridional overturning circulation and the Greenland ice sheet. We will present here a general mathematical framework to look into critical behaviour in the Earth system. We will connect the analysis of the response of the system to perturbation in connection to its global stability properties and discuss ideas for creating robust early warning signals.