$\mathcal{PT}$ symmetry-protected exceptional cones and analogue Hawking radiation

Artificial Hawking radiation, weak pseudo-Hermiticity and Weyl semimetal blackhole analogy

“…Examples of Hamiltonians endowed with the property of weak pseudo-Hermiticity but not being PT -symmetric have been explicitly constructed before [17]. In contrast to the weak pseudo-Hermiticity as just now defined, it needs to be emphasized that in the scheme of [32], the idea of PT -symmetry preservation was pursued. The latter was defined in terms of an operator P and a non-conventional K-matrix such that KK * = 1, P 2 = 1, and KP * = PK.…”

“…Employing the same arguments leading to (2.5), here too with the Hamiltonian H h results in a similar metric containing the coupling parameter λ and with an additional presence of a term dy 2 . If we consider a slice of y = constant, then the latter contribution drops out and the metric transforms to the Schwarzschild black hole in Painlevé-Gullstrand coordinates [32,44,45]…”

“…The electronic analogs of stimulated Hawking emission was studied and physical observables were addressed in the context of Weyl semimetal black hole analogs. A related work [32] looked at the PT symmetry-protected cones and analogue Hawking radiation was explored.…”

An effective curved space-time geometric theory of generic twist angle graphene with application to a rotating bilayer configuration

“…Very recently, Refs. [60][61][62] have argued the duality between non-Hermitian model in flat space and Hermitian system in curved space. So treating a non-Hermitian Dirac action is justified.…”

Real non-Hermitian energy spectra without any symmetry

“…Non-Hermitian systems have recently inspired intense research efforts for their unconventional mathematical properties and physical robustness, such as enlarged topological symmetries, [1][2][3][4][5][6][7][8] exceptional point sensing, [9][10][11][12][13][14][15] quantized classical responses, [16] modified bulk-boundary correspondences, [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32] unconventional entanglement entropy scaling, [4,[33][34][35][36][37][38][39] enhanced Rabi oscillations, [26,40,41] and effective non-Hermitian curved space. [42,43] Yet, many of these exciting phenomena are often difficult to probe experimentally due to their intrinsically unstable nature from complex eigenenergies. While real eigenenergies can be symmetryenforced, i.e., through PT-symmetry, …”