volume | PIER Journals

Abstract

Rigorous quantum formulation of the Parity-Time (PT) symmetry phenomenon in the RF/microwave regime for a pair of coupled coil resonators with lump elements has been presented. The coil resonator is described by the lump-element model that consists of an inductor (L), a resistor (R) and a capacitor (C). Rigorous quantum Hamiltonian for the coupled LRC coil resonators system has been derived through twice basis transforms of the original basis. The first basis transform rotates the original basis such that off-diagonal terms of the governing matrix of the equation system of the coupled coil resonators is reduced to constants. Then a second basis transform obtains the quantum Hamiltonian, including the diagonal effective complex frequencies and off-diagonal coupling terms, together with the transformed basis. With the obtained quantum Hamiltonian, the eigenvalues and eigenvectors of the coupled coil resonators can be obtained as usual as the quantum Hamiltonian. Finally, numerical simulation verifies the correctness of the theory. The quantum formulation of the coupled coil resonators can provide better guideline to design a better PT-symmetric system.

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31. Liao, S. and R. J. Vernon, "The near-field and far-field properties of the cylindrical modal expansions with application in the image theorem," 2006 Joint 31st International Conference on Infrared Millimeter Waves and 14th International Conference on Teraherz Electronics, 260-260, September 2006.

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34. Liao, S. and R. J. Vernon, "The cylindrical Taylor-interpolation FFT algorithm," 2006 Joint 31st International Conference on Infrared Millimeter Waves and 14th International Conference on Teraherz Electronics, 259-259, September 2006.

35. Liao, S., "Beam-shaping PEC mirror phase corrector design," PIERS Online, Vol. 3, No. 4, 392-396, 2007.

36. Liao, S., "Fast computation of electromagnetic wave propagation and scattering for quasicylindrical geometry," PIERS Online, Vol. 3, No. 1, 96-100, 2007.

37. Liao, S., "On the validity of physical optics for narrow-band beam scattering and diffraction from the open cylindrical surface," PIERS Online, Vol. 3, No. 2, 158-162, 2007.

38. Liao, S., R. J. Vernon, and J. Neilson, "A high-efficiency four-frequency mode converter design with small output angle variation for a step-tunable gyrotron," 2008 33rd International Conference on Infrared, Millimeter and Terahertz Waves, 1-2, September 2008.

39. Liao, S., R. J. Vernon, and J. Neilson, "A four-frequency mode converter with small output angle variation for a step-tunable gyrotron," Electron Cyclotron Emission and Electron Cyclotron Resonance Heating (EC-15), 477-482, World Scientific, April 2009.

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42. Liao, S. and R. J. Vernon, "A fast algorithm for wave propagation from a plane or a cylindrical surface," 490, Vol. 28, No. 6, 479, June 2007.

43. Liao, S.-L. and R. J. Vernon, "Sub-THz beam-shaping mirror system designs for quasi-optical mode converters in high-power gyrotrons," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 4, 425-439, Taylor & Francis, January 2007.

44. Liao, S., "Miter bend mirror design for corrugated waveguides," Progress In Electromagnetics Research, Vol. 10, 157-162, EMW Publishing, 2009.

45. Liao, S. and R. J. Vernon, "A fast algorithm for computation of electromagnetic wave propagation in half-space," IEEE Transactions on Antennas and Propagation, Vol. 57, No. 7, 2068-2075, July 2009.

46. Liao, S., N. Gopalsami, A. Venugopal, A. Heifetz, and A. C. Raptis, "An efficient iterative algorithm for computation of scattering from dielectric objects," Optics Express, Vol. 19, No. 4, 3304-3315, Optical Society of America, February 2011.

47. Liao, S., "Spectral-domain MOM for planar meta-materials of arbitrary aperture waveguide array," 2019 IEEE MTT-S International Conference on Numerical Electromagnetic and Multiphysics Modeling and Optimization (NEMO), 1-4, May 2019.

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52. Zhu, L., N. Alkhaldi, H. M. Kadry, S. Liao, and P.-Y. Chen, "A compact hybrid-fed microstrip antenna for harmonics-based radar and sensor systems," IEEE Antennas and Wireless Propagation Letters, Vol. 17, No. 12, 2444-2448, December.

Prof. Shaolin Liao

Dr. Lu Ou