Scalar Domination and Normal Fluctuations in N-Vector Quantum Anharmonic Crystals |
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Authors: | Yuri Kozitsky |
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Institution: | (1) Institute of Mathematics, Marie Curie-Sklodowska University, Lublin, PL 20-031, Poland |
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Abstract: | A lattice model of N-dimensional quantum anharmonic oscillators with a polynomial anharmonicity and a ferroelectric pair interaction is considered. For arbitrary N
, correlation inequalities, showing that the temperature Green functions of this model are dominated by the corresponding Green functions of the scalar (N=1) model, are proven. These inequalities are then used to prove that the fluctuations of displacements of particles remain normal at all temperatures provided the model parameters obey a certain condition. In particular this means that the smallest distance between the energy levels of the corresponding one-dimensional isolated oscillator should be large enough or its mass should be small enough. |
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Keywords: | Euclidean Gibbs states correlation inequalities normal fluctuations |
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