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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 ...
For a field F, the generalized special unitary group over F, SU(p, q; F), is the group of all linear transformations of determinant 1 of a vector space of rank n = p + q over F which leave invariant a nondegenerate, Hermitian form of signature (p, q). This group is often referred to as the special unitary group of signature p q over F.
Rotational symmetry with reflection [p +,2] = [p] + ×[ ] = SO(2)⋊C 2: C ∞ ⋊C 2: Rotational symmetry with half turn [p,2] + = O(2)×SO(1) Dih ∞ Circular symmetry: Full symmetry of a hemisphere, cone, paraboloid or any surface of revolution [p,1] = [p] = SO(2)×SO(1) C ∞ Circle group: Rotational symmetry [p,1] + = [p] + =
The term "classical group" was coined by Hermann Weyl, it being the title of his 1939 monograph The Classical Groups. [3] The classical groups form the deepest and most useful part of the subject of linear Lie groups. [4] Most types of classical groups find application in classical and modern physics. A few examples are the following.
The Higgs part of the Lagrangian is = [(′)] + † (†), where λ > 0 and μ 2 > 0, so that the mechanism of spontaneous symmetry breaking can be used. There is a parameter here, at first hidden within the shape of the potential, that is very important.
CP-symmetry states that the laws of physics should be the same if a particle is interchanged with its antiparticle (C-symmetry) while its spatial coordinates are inverted ("mirror" or P-symmetry). The discovery of CP violation in 1964 in the decays of neutral kaons resulted in the Nobel Prize in Physics in 1980 for its discoverers James Cronin ...
The Lorentz group is a six-dimensional noncompact non-abelian real Lie group that is not connected. The four connected components are not simply connected. [1] The identity component (i.e., the component containing the identity element) of the Lorentz group is itself a group, and is often called the restricted Lorentz group, and is denoted SO ...
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