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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).
In physics, this property is referred to as PT symmetry. This definition extends also to functions of two or more variables, e.g., in the case that f {\displaystyle f} is a function of two variables it is Hermitian if
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.
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 ...
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 mechanics, the Hamiltonian of a system is an operator corresponding to the total energy of that system, including both kinetic energy and potential energy.Its spectrum, the system's energy spectrum or its set of energy eigenvalues, is the set of possible outcomes obtainable from a measurement of the system's total energy.