Talks

In this talk, we develop a systematic framework for understanding symmetries in topological phases in \(2+1\) dimensions using the string-net model, encompassing both gauge symmetries that preserve anyon types and global symmetries permuting anyon types, including both invertible symmetries describable by groups and noninvertible symmetries described by categories. As an archetypal example, we reveal the first noninvertible categorical gauge symmetry of topological orders in \(2+1\) dimensions: the Fibonacci gauge symmetry of the doubled Fibonacci topological order, described by the Fibonacci fusion \(2\)-category. Our approach involves two steps: first, establishing duality between different string-net models with Morita equivalent input UFCs that describe the same topological order; and second, constructing symmetry transformations within the same string-net model when the dual models have isomorphic input UFCs, achieved by composing duality maps with isomorphisms of degrees of freedom between the dual models.

We present a tensorization algorithm for constructing tensor train representations of functions, drawing on sketching and cross interpolation ideas. The method only requires black-box access to the target function and a small set of sample points defining the domain of interest. Thus, it is particularly well-suited for machine learning models, where the domain of interest is naturally defined by the training dataset. We show that this approach can be used to enhance the privacy and interpretability of neural network models. Specifically, we apply our decomposition to (i) obfuscate neural networks whose parameters encode patterns tied to the training data distribution, and (ii) estimate topological phases of matter that are easily accessible from the tensor train representation. Additionally, we show that this tensorization can serve as an efficient initialization method for optimizing tensor trains in general settings, and that, for model compression, our algorithm achieves a superior trade-off between memory and time complexity compared to conventional tensorization methods of neural networks.

The question of the long-time behavior of quantum trajectories has been recently solved in the finite-dimensional case. In infinite dimension, the problem is still open. In this talk, we consider the particular model of the "one-atom maser," an infinite-dimensional system with many applications in quantum mechanics. We completely describe its long-time behavior by comparing it with a classical birth-and-death process. This is a joint work with T. Benoist and L. Bruneau.

Hundred years ago Stern and Gerlach demonstrated that spin-1/2 particles moving through a very high magnetic field gradient showed spin-path entanglement. Here, we show there that one can describe the emergence of the spin state and path variable’s entanglement as a dynamical feature in Stern-Gerlach experiments using open quantum system approach. This novel approach also gives broadening of the spots on the detector as well as the collapse of the wavefunction.

Reference: 

Das, G., & Bhattacharyya, R. (2024). Irreversibility of a Stern-Gerlach experiment. Physical Review A, 110(6), 062211. (DOI: https://doi.org/10.1103/PhysRevA.110.062211)