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The first paper that has "non-Hermitian quantum mechanics" in the title was published in 1996 [1] by Naomichi Hatano and David R. Nelson. The authors mapped a classical statistical model of flux-line pinning by columnar defects in high-T c superconductors to a quantum model by means of an inverse path-integral mapping and ended up with a non-Hermitian Hamiltonian with an imaginary vector ...
For non-Hermitian quantum systems with PT symmetry, fidelity can be used to analyze whether exceptional points are of higher-order. Many numerical methods such as the Lanczos algorithm , Density Matrix Renormalization Group (DMRG), and other tensor network algorithms are relatively easy to calculate only for the ground state, but have many ...
Carl M Bender and Stefan Boettcher, "Real Spectra in non-Hermitian Hamiltonians Having PT Symmetry," Physical Review Letters 80, 5243 (1998). Carl M Bender, "Making Sense of Non-Hermitian Hamiltonians," Reports on Progress in Physics 70, 947 (2007).
The non-chiral Su–Schrieffer–Heeger model (=), can be associated with symmetry class BDI with an integer topological invariant due to gauge invariance. [6] [7] The problem is similar to the integer quantum Hall effect and the quantum anomalous Hall effect (both in =) which are A class, with integer Chern number.
In physics and mathematics, the Lorentz group is the group of all Lorentz transformations of Minkowski spacetime, the classical and quantum setting for all (non-gravitational) physical phenomena. The Lorentz group is named for the Dutch physicist Hendrik Lorentz. For example, the following laws, equations, and theories respect Lorentz symmetry:
In quantum electrodynamics, the local symmetry group is U(1) and is abelian. In quantum chromodynamics, the local symmetry group is SU(3) and is non-abelian. The electromagnetic interaction is mediated by photons, which have no electric charge. The electromagnetic tensor has an electromagnetic four-potential field possessing gauge symmetry.
The form φ 1 is Hermitian (while the first form on the left hand side is skew-Hermitian) of signature (n, n). The signature is made evident by a change of basis from (e, f) to ((e + if)/ √ 2, (e − if)/ √ 2) where e, f are the first and last n basis vectors respectively. The second form, φ 2 is symmetric positive definite.
At the quantum level, translations in s would be generated by a "Hamiltonian" H − E, where E is the energy operator and H is the "ordinary" Hamiltonian. However, since s is an unphysical parameter, physical states must be left invariant by " s -evolution", and so the physical state space is the kernel of H − E (this requires the use of a ...