Generalized pt symmetry and real spectra
WebJan 5, 2024 · Here, because of PT symmetry, the band gaps can entirely close and the two first bands can merge, forming a closed surface exhibiting complex conjugate pairs in the overlapping regions and real ... WebApr 28, 2013 · If the characteristic polynomial has real coefficients, then H has a generalized -symmetry. Interesting models arise in statistical mechanics with hidden -symmetry when the transfer matrix T is real but not symmetric, as will be discussed in §4. The striking feature of the ix 3 model is that all of its energy eigenvalues are real.
Generalized pt symmetry and real spectra
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WebHamiltonian commutes with a generalized PT symmetry. Here, “adiabatically” refers to keeping the gap to all other states finite and “generalized PT” indicates that P does not have to be spatial inversion, but might be any unitary operator. We first discuss a general mathematical condition for the eigenvalues to stay real and, hence ... WebFeb 1, 2024 · We study a class of physically intriguing PT-symmetric generalized Scarf-II (GS-II) potentials, which can support exact solitons in one- and multi-dimensional nonlinear Schrödinger equation.In the 1D and multi-D settings, we find that a properly adjusted localization parameter may support fully real energy spectra.Also, continuous families of …
WebJul 26, 2002 · Generalized PT symmetry and real spectra. Carl M Bender 1, M V Berry 2 and Aikaterini Mandilara 1. Published 26 July 2002 • Published under licence by IOP Publishing Ltd Journal of Physics A: Mathematical and General, Volume 35, Number 31 … INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF PHYSICS A: … iopscience.iop.org WebApr 16, 2024 · The PTX -symmetric metasurfaces can exhibit similar scattering properties as their PT -symmetric counterparts at singular points, while achieving a higher sensitivity …
WebJan 18, 2024 · Abstract. The establishment of non-Hermitian quantum mechanics (such as parity–time (PT) symmetry) stimulates a paradigmatic shift for studying symmetries of complex potentials. Owing to the convenient manipulation of optical gain and loss in analogy to complex quantum potentials, photonics provides an ideal platform for the visualization … WebA generalized antiunitary operator of the class (11), whose symmetry is not reducible to PT, describes a particle in the plane with a complex two …
Webunder certain circumstances. The condition is called PT symmetry and means just the commutativity [H(toy)(ω),PT ] = 0 (1) where T performs complex conjugation. The …
WebGeneralized PT symmetry and real spectra. The fact that eigenvalues of PT-symmetric Hamiltonians H can be real for some values of a parameter and complex for others is explained by showing that the matrix elements of H, and hence the secular equation, are real, not only for PT but also for any antiunitary operator A satisfying A 2k = 1 with k odd. golf in des moines iowahealth and safety emergency plan pdfWebSep 30, 2024 · Our electrostatics analogy exploits the hitherto unexploited parallel between the conformal structure of electric field lines in real space, and the complex spectral flow as non-Hermitian states accumulate along boundaries (Fig. 1 and Table 1).It identifies non-Hermitian periodic/open boundary condition (PBC/OBC) spectra respectively with the … golf in dayton ohWebJun 18, 2024 · In this case, H is of the exact PT symmetry. Or, PT symmetry is spontaneously broken. In summary, H in eq. is a generalized APT-symmetric Hamiltonian, having various phases, such as real- and non-real-spectra phases, PT-exact symmetry or PT-spontaneously-broken phases, APT and Hermitian symmetry phases, etc., as the … health and safety employee dutiesWebNov 28, 2024 · To derive non-\(\mathbb {PT}\)-symmetric complex potentials with all-real spectra, one strategy is to impose an operator symmetry in order to guarantee conjugate-pair eigenvalue symmetry [].Like the case of \(\mathbb {PT}\)-symmetric potentials, this conjugate-pair eigenvalue symmetry guarantees that either the spectrum of L is all-real, … golf in dallas areaWebJul 26, 2002 · Generalized PT symmetry and real spectra. Carl M Bender 1, M V Berry 2 and Aikaterini Mandilara 1. Published 26 July 2002 • Published under licence by IOP … golf in death valleyWebApr 8, 2024 · Since 1998 when Bender and Boettcher showed that a wide class of non-Hermitian Hamiltonians can exhibit real spectra if they commute with the PT operator 9, PT symmetry has become an active ... golf in dayton ohio