Talks

Topological phases of matter offer a promising platform for quantum computation and quantum error correction. Nevertheless, unlike its counterpart in pure states, descriptions of topological order in mixed states remain relatively under-explored. We will give various definitions for replica topological order in mixed states. Similar to the replica trick, our definitions also involve n copies of density matrix of the mixed state. Within this framework, we categorize topological orders in mixed states as either quantum, classical, or trivial, depending on the type of information they encode.

For the case of the toric code model in the presence of decoherence, we associate for each phase a quantum channel and describes the structure of the code space. We show that in the quantum-topological phase, there exists a postselection-based error correction protocol that recovers the quantum information, while in the classical-topological phase, the quantum information has decohere and cannot be fully recovered. We accomplish this by describing the mixed state as a projected entangled pairs state (PEPS) and identifying the symmetry-protected topological order of its boundary state to the bulk topology.

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Atmosphere and ocean dynamics are dictated by balanced flows, such as mesoscale eddies, but determining a precise balanced state remains challenging in the presence of its nonlinear coupling with the unbalanced flows, such as internal gravity waves. The spontaneous loss of balance, resulting in nonlinear internal wave generation, challenges the existence of an invariant balanced state from a mathematical perspective, and at the same time has physical implications for the energy cycle of the atmosphere and ocean.

In this talk, I will discuss the recent progress in deriving and quantifying the balanced state in geophysical flows from nonlinear flow decomposition as well as the comparison of balanced states from different mathematical approaches: higher order balance and optimal balance . This decomposition is applied to varied oceanic regimes in a suite of idealized models to quantify spontaneous wave generation and assess its role in the energy cycle relative to other mechanisms. To ...

Covariant Formalism. Perturbation theory. Gauge fixing. Becchi Rouet Stora Tyutin symmetry and diffeomorphism invariance. One loop and two loop ultraviolet divergencies. Renormalization problems. Euclidean gravity. Gravitational instantons.