Effective dimension of Wasserstein space for quantum energy eigenstates reduces with increasing chaos, capturing Lyapunov exponents and indicating scar states via optimal transport geometry.
Out-of-time-order correlators in quantum mechanics
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abstract
The out-of-time-order correlator (OTOC) is considered as a measure of quantum chaos. We formulate how to calculate the OTOC for quantum mechanics with a general Hamiltonian. We demonstrate explicit calculations of OTOCs for a harmonic oscillator, a particle in a one-dimensional box, a circle billiard and stadium billiards. For the first two cases, OTOCs are periodic in time because of their commensurable energy spectra. For the circle and stadium billiards, they are not recursive but saturate to constant values which are linear in temperature. Although the stadium billiard is a typical example of the classical chaos, an expected exponential growth of the OTOC is not found. We also discuss the classical limit of the OTOC. Analysis of a time evolution of a wavepacket in a box shows that the OTOC can deviate from its classical value at a time much earlier than the Ehrenfest time.
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UNVERDICTED 2representative citing papers
Discretized λφ⁴ theory yields thermal OTOC with exponential growth and Lyapunov exponent scaling as T^{1/4}, showing quantum chaos signatures at low perturbative orders in the oscillator chain.
citing papers explorer
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Wasserstein Space of Quantum Chaos
Effective dimension of Wasserstein space for quantum energy eigenstates reduces with increasing chaos, capturing Lyapunov exponents and indicating scar states via optimal transport geometry.
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OTOC and Quamtum Chaos of Interacting Scalar Fields
Discretized λφ⁴ theory yields thermal OTOC with exponential growth and Lyapunov exponent scaling as T^{1/4}, showing quantum chaos signatures at low perturbative orders in the oscillator chain.