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Dipole Exchange Theory of Magnons in Structured Composite Nanowires and Magnonic Crystal Arrays
Published in Gianluca Gubbiotti, Three-Dimensional Magnonics, 2019
M. G. Cottam, Z. Haghshenasfard, A. O. Adeyeye, G. Gubbiotti
The final step to determine the SW frequencies involves diagonalizing the second-order Hamiltonian H(2). To achieve this, we make a canonical (generalized Bogoliubov) transformation from operators {aq,n†,aq,n} to a new set of boson operators {αq,n†,αq,n} using (
Emergence of a new symmetry class for Bogoliubov–de Gennes (BdG) Hamiltonians: expanding 10-fold symmetry classes
Published in Phase Transitions, 2020
Bogoliubov transformation of superconductor (s-wave or p-wave) gives the energy spectrum of quasiparticle excitation. These Bogoliubov quasiparticles are combinations of particles and holes. The mean-field superconductor Hamiltonian defined in terms of first quantized Hamiltonian of single particle excitations helps in realization of Bogoliubov quasiparticles [16]. The first quantized Hamiltonian or BdG Hamiltonian for 1D and 2D p-wave superconductors helps in the realization of Majorana and chiral Majorana zero modes respectively [28]. The Majorana neutrinos of particle physics can also be found as Bogoliubov quasiparticles [17]. Thus it is clear from this discussion, the importance of Bogoliubov quasiparticles as an emergent particles in different branches of theoretical physics.
Nonlinear Mach–Zehnder interferometer with ultrabroadband squeezed light
Published in Journal of Modern Optics, 2020
D. B. Horoshko, M. I. Kolobov, F. Gumpert, I. Shand, F. König, M. V. Chekhova
In each crystal, collinear type-I PDC annihilates one pump photon with the frequency and creates two photons with the same direction and polarization, and frequencies and , where . The phase mismatch for this process has the form , where is the wave vector of the pump wave, assumed to be an undepleted quasi-monochromatic plane wave, and is the wave vector of the down-converted wave at the frequency . In general there is no phase matching at degeneracy, , where . Let us direct the z axis along the propagation of the waves, placing the origin on the front edge of the first crystal and denoting its length by . For the description of the field we use the sideband photon annihilation operator corresponding to frequency and position z, so that the field operator (in the photon-flux units) is The field transformations in both crystals have the forms of the Bogoliubov transformations where d is the distance between the crystals, is the position of the second crystal output. The functions and , where n denotes the crystal number, satisfy the relations and , required by the unitarity of the field transformation. We denote the phase acquired between the crystals by the field component at the frequency as . Writing , we obtain from Equations (2) and (3) the total input–output field transformation as where are the Bogoliubov coefficients for the entire interferometer.