An exact and analytic control protocol of two types of finite dimensional quantum systems is proposed. The system can be drive to an arbitrary target state using cosine classical fields in finite cycles. The control parameters which are time periods of interaction between systems and control fields in each cycles are connected with the probability amplitudes of target states via triangular functions and can be determined analytically.
Using the Lindemann criterion, we analyzed the quantum and thermal melting of electronic/excitonic crystals recently discovered in 2D semiconductor moiré patterns. We show that the finite 2D screening of the atomically thin material can suppress (enhance) the inter-site Coulomb (dipolar) interaction strength, thus inhibits (facilitates) the formation of the electronic (excitonic) crystal. Meanwhile, a strong enough moiré confinement is found to be essential for realizing the crystal phase with a wavelength near 10 nm or shorter. From the calculated Lindemann ratio which quantifies the fluctuation of the site displacement, we estimate that the crystal will melt into a liquid above a critical temperature ranging from several tens Kelvin to above 100 K (depending on system parameters).
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