Fragility to quantum fluctuations of classical Hamiltonian period doubling

• URL: http://arxiv.org/abs/2108.11408v2
• Date: Fri, 5 Nov 2021 12:31:59 GMT
• Title: Fragility to quantum fluctuations of classical Hamiltonian period doubling
• Authors: Reyhaneh Khasseh, Angelo Russomanno, Rosario Fazio
• Abstract summary: We add quantum fluctuations to a classical period-doubling Hamiltonian time crystal, replacing the $N$ classical interacting angular momenta with quantum spins of size $l$. The full permutation symmetry of the Hamiltonian allows a mapping to a bosonic model and the application of exact diagonalization for quite large system size.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We add quantum fluctuations to a classical period-doubling Hamiltonian time crystal, replacing the $N$ classical interacting angular momenta with quantum spins of size $l$. The full permutation symmetry of the Hamiltonian allows a mapping to a bosonic model and the application of exact diagonalization for quite large system size. In the thermodynamic limit $N\to\infty$ the model is described by a system of Gross-Pitaevskii equations whose classical-chaos properties closely mirror the finite-$N$ quantum chaos. For $N\to\infty$, and $l$ finite, Rabi oscillations mark the absence of persistent period doubling, which is recovered for $l\to\infty$ with Rabi-oscillation frequency tending exponentially to 0. For the chosen initial conditions, we can represent this model in terms of Pauli matrices and apply the discrete truncated Wigner approximation. For finite $l$ this approximation reproduces no Rabi oscillations but correctly predicts the absence of period doubling. Our results show the instability of time-translation symmetry breaking in this classical system even to the smallest quantum fluctuations, because of tunneling effects.

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