Table 1 The critical values of the LGI in the energy constraint (i.e., \(\theta =\frac{\pi }{2}\), \(\tau =\frac{\pi }{4\omega }\) and \(\phi =\frac{\pi }{4}\)) for the dynamics under driven (with the coarsening measurement reference, the coarsening final measurement resolution and the coarsening time reference), the dynamics under dissipation and dephasing (with the coarsening measurement reference and the coarsening final measurement resolution), for \(g/\gamma =0, 0.05\omega , 0.1\omega , 0.2\omega , 0.3\omega , 0.4\omega , 0.5\omega , 0.6\omega , 0.7\omega , 0.8\omega ,\) \( 0.9\omega , \omega \), respectively.
From: Quantum violation of LGI under an energy constraint for different scenarios systems
\(g/\gamma \) | Dynamics with driven | Dynamics under dissipation | Dynamics under dephasing | ||||
|---|---|---|---|---|---|---|---|
\(\Delta _{critical}\) | Â Â Â \(\delta _{critical}\) | \(\Delta '_{critical}\) | \(\Delta _{critical}\) | Â Â Â \(\delta _{critical}\) | \(\Delta _{critical}\) | Â Â Â \(\delta _{critical}\) | |
0 | 0.4162 | 0.0795 | 0.8325 | 0.4162 | 0.0795 | 0.4162 | 0.0795 |
\(0.05\omega \) | 0.4156 | 0.0793 | 0.8321 | 0.3919 | 0.0712 | 0.3078 | 0.0451 |
\(0.1\omega \) | 0.4136 | 0.0786 | 0.8308 | 0.366 | 0.0627 | 0.1272 | 0.008 |
\(0.2\omega \) | 0.4056 | 0.0758 | 0.824 | 0.3078 | 0.0451 | No | No |
\(0.3\omega \) | 0.3919 | 0.0712 | 0.8069 | 0.2355 | 0.0269 | No | No |
\(0.4\omega \) | 0.3719 | 0.0645 | 0.7647 | 0.1272 | 0.008 | No | No |
\(0.5\omega \) | 0.3444 | 0.0559 | 0.6605 | No | No | No | No |
\(0.6\omega \) | 0.3074 | 0.045 | 0.4809 | No | No | No | No |
\(0.7\omega \) | 0.2569 | 0.0319 | 0.3278 | No | No | No | No |
\(0.8\omega \) | 0.1822 | 0.0163 | 0.1988 | No | No | No | No |
\(0.9\omega \) | No | No | No | No | No | No | No |
\(\omega \) | No | No | No | No | No | No | No |
