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- W3102871608 abstract "A bstract We propose how to compute the complexity of operators generated by Hamiltonians in quantum field theory (QFT) and quantum mechanics (QM). The Hamiltonians in QFT/QM and quantum circuit have a few essential differences, for which we introduce new principles and methods for complexity. We show that the complexity geometry corresponding to one-dimensional quadratic Hamiltonians is equivalent to AdS 3 spacetime. Here, the requirement that the complexity is nonnegative corresponds to the fact that the Hamiltonian is lower bounded and the speed of a particle is not superluminal. Our proposal proves the complexity of the operator generated by a free Hamiltonian is zero, as expected. By studying a non-relativistic particle in compact Riemannian manifolds we find the complexity is given by the global geometric property of the space. In particular, we show that in low energy limit the critical spacetime dimension to ensure the ‘nonnegative’ complexity is the 3+1 dimension." @default.
- W3102871608 created "2020-11-23" @default.
- W3102871608 creator A5003981995 @default.
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- W3102871608 date "2019-03-01" @default.
- W3102871608 modified "2023-10-17" @default.
- W3102871608 title "Complexity of operators generated by quantum mechanical Hamiltonians" @default.
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- W3102871608 doi "https://doi.org/10.1007/jhep03(2019)010" @default.
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