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Award ID contains: 2407290

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  1. ; ; (, Journal of Mathematical Physics)
    Single-mode squeezed states exhibit a direct correspondence with points on the Poincaré disk. In this study, we delve into this correspondence and describe the motions of the disk generated by a quadratic Hamiltonian. This provides a geometric representation of squeezed states and their evolution. We discuss applications in bang-bang and adiabatic control problems involving squeezed states. 
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    Free, publicly-accessible full text available June 1, 2026
  2. ; ; ; (, Reviews in Mathematical Physics)
    In this study, we examine the quantization of Hall conductance in an infinite plane geometry. We consider a microscopic charge-conserving system with a pure, gapped infinite-volume ground state. While Hall conductance is well-defined in this scenario, existing proofs of its quantization have relied on assumptions of either weak interactions, or properties of finite volume ground state spaces, or invertibility. Here, we assume that the conditions necessary to construct the braided [Formula: see text]-tensor category which describes anyonic excitations are satisfied, and we demonstrate that the Hall conductance is rational if the tensor category is finite. 
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    Free, publicly-accessible full text available May 6, 2026