Solving dispersion relations of one-dimensional diatomic chain with on-site potential by invariant eigen-operator method

The Thermal Field Theory methods are applied to calculate the dispersion relation of the photon propagating modes in a strictly one-dimensional (1D) ideal plasma. The electrons are treated as a gas of particles that are confined to a 1D tube or wire, but are otherwise free to move, without reference to the electronic wave functions in the coordinates that are transverse to the idealized wire, or relying on any features of the electronic structure. The relevant photon dynamical variable is an effective field in which the two space coordinates that are transverse to the wire are collapsed. The appropriate expression for the photon free-field propagator in such a medium is obtained, the one-loop photon self-energy is calculated and the (longitudinal) dispersion relations are determined and studied in some detail. Analytic formulas for the dispersion relations are given for the case of a degenerate electron gas, and the results differ from the long-wavelength formula that is quoted in the literature for the strictly 1D plasma. The dispersion relations obtained resemble the linear form that is expected in realistic quasi-1D plasma systems for the entire range of the momentum, and which have been observed in this kind of system in recent experiments.

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Predicting the Dispersion Relations of One-Dimensional Phononic Crystals by Neural Networks

Scientific Reports ◽

10.1038/s41598-019-51662-3 ◽

2019 ◽

Vol 9 (1) ◽

Author(s):

Chen-Xu Liu ◽

Gui-Lan Yu

Keyword(s):

Neural Networks ◽

Prediction Accuracy ◽

Mass Density ◽

Back Propagation ◽

Dispersion Relations ◽

Phononic Crystals ◽

Training Time ◽

One Dimensional ◽

Density Ratios ◽

Parameter Prediction

Abstract In this paper, deep back propagation neural networks (DBP-NNs) and radial basis function neural networks (RBF-NNs) are employed to predict the dispersion relations (DRs) of one-dimensional (1D) phononic crystals (PCs). The data sets generated by transfer matrix method (TMM) are used to train the NNs and detect their prediction accuracy. In our work, filling fractions, mass density ratios and shear modulus ratios of PCs are considered as the input values of NNs. The results show that both the DBP-NNs and the RBF-NNs exhibit good performances in predicting the DRs of PCs. For one-parameter prediction, the RBF-NNs have shorter training time and remarkable prediction accuracy, for two- and three-parameter prediction, the DBP-NNs have more stable performance. The present work confirms the feasibility of predicting the DRs of PCs by NNs, and provides a useful reference for the application of NNs in the design of PCs and metamaterials.

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Dispersion relations of elastic waves in one-dimensional piezoelectric phononic crystal with initial stresses

International Journal of Mechanical Sciences ◽

10.1016/j.ijmecsci.2015.12.020 ◽

2016 ◽

Vol 106 ◽

pp. 231-244 ◽

Cited By ~ 10

Author(s):

Xiao Guo ◽

Peijun Wei

Keyword(s):

Elastic Waves ◽

Phononic Crystal ◽

Dispersion Relations ◽

Initial Stresses ◽

One Dimensional

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Tutorial Notes on One-Party and Two-Party Gaussian States

International Journal of Quantum Information ◽

10.1142/s0219749903000206 ◽

2003 ◽

Vol 01 (02) ◽

pp. 153-188 ◽

Cited By ~ 32

Author(s):

Berthold-Georg Englert ◽

Krzysztof Wódkiewicz

Keyword(s):

Quantum Information ◽

Phase Space ◽

Characteristic Function ◽

Information Science ◽

Operator Method ◽

Two Dimensional ◽

Quantum Information Science ◽

Gaussian States ◽

One Dimensional ◽

Practical Applications

Gaussian states — or, more generally, Gaussian operators — play an important role in Quantum Optics and Quantum Information Science, both in discussions about conceptual issues and in practical applications. We describe, in a tutorial manner, a systematic operator method for first characterizing such states and then investigating their properties. The central numerical quantities are the covariance matrix that specifies the characteristic function of the state, and the closely related matrices associated with Wigner's and Glauber's phase space functions. For pedagogical reasons, we restrict the discussion to one-dimensional and two-dimensional Gaussian states, for which we provide illustrating and instructive examples.

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