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Abstract
Many familiar notions of classical physics are supplanted by new concepts and intuition in quantum mechanics. This goes doubly so for open quantum systems, where coupling to an external environment leads to the irreversible loss of quantum information. In this thesis, we investigate how non-reciprocity, symmetries and diagonalization procedures in open quantum systems are different than their classical or closed-system counterparts.
We first show that non-reciprocity, the tendency for particles to propagate in a preferred direction, can be used to build a quantum sensor whose signal-to-noise ratio grows exponentially with the size of the sensor. Non-reciprocity also has a marked effect on the quantum steady state of tight-binding models; we find for a representative model that the steady state occupation is characterized by a surprising macroscopically-large length scale.
Shifting gears, we then demonstrate how to diagonalize a large class of Lindbladians, the open quantum system equivalent of a Hamiltonian. We first reformulate third quantization, a technique that is used to diagonalize quadratic Lindbladians. Not only do we make the procedure more physically transparent, but we show that is naturally related to Keldysh field theory, a much more widely-used tool. Finally, we use this technique to show how so-called weak symmetries can be used to diagonalize strongly-interacting dissipative quantum models, despite there being no associated conserved quantities.