Presented By: Applied Interdisciplinary Mathematics (AIM) Seminar  Department of Mathematics
AIM Seminar: On the Positive Definiteness of Response Functions in the Time Domain
Emanuel Gull, University of Michigan, Department of Physics
Response functions of quantum systems, such as electron Greenâ€™s functions, magnetic, or charge susceptibilities, describe the response of a system to an external perturbation. They are the central objects of interest in field theories and quantum computing and measured directly in experiment. Response functions are intrinsically causal. In equilibrium and steadystate systems, they correspond to a positive spectral function in the frequency domain. This talk shows that response functions define an inner product on a Hilbert space and thereby induce a positive definite function. The properties of this function can be used to reduce noise in measured data and, in equilibrium and steady state, to construct positive definite extensions for data known on finite time intervals, which are then guaranteed to correspond to positive spectra.
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