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WORLD SCIENTIFIC eBooks

Hamiltonian time-dependent mechanics

Published Dec 1, 1998• 1 citation
Publisher
DOI
10.1142/9789812815958_0006

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We obtain the complexity geometry associated with the Hamiltonian of a quantum mechanical system, specifically in cases where the Hamiltonian is explicitly time-dependent. Using Nielsen's geometric formulation of circuit complexity, we calculate the bi-invariant cost associated with these time-dependent Hamiltonians by suitably regularizing their norms and obtain analytical expressions of the costs for several well-known time-dependent quantum mechanical systems. In particular, we show that an equivalence exists between the total costs of obtaining an operator through time evolution generated by a unit mass harmonic oscillator whose frequency depends on time, and a harmonic oscillator whose both mass and frequency are functions of time. These results are illustrated with several examples, including a specific smooth quench protocol where the comparison of time variation of the cost with other information theoretic quantities, such as the Shannon entropy, is discussed.