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Quantum fluctuations in a quantum dot array in the regime of ferroelectric phase transitions

Quantum fluctuations in a molecular-like array of quantum dots undergoing ferroelectric (antiferroelectric) phase transitions are considered. We calculate the spectrum of collective excitations and investigate the behaviour of soft modes in the vicinity of the phase transitions. The amplitude of quantum fluctuations as a function of parameters of the system is found. We show that an external magnetic field can induce phase transitions and suppresses quantum fluctuations.