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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 ...
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 ...
CPT is the only combination of C, P, and T that is observed to be an exact symmetry of nature at the fundamental level. [1] [2] The CPT theorem says that CPT symmetry holds for all physical phenomena, or more precisely, that any Lorentz invariant local quantum field theory with a Hermitian Hamiltonian must have CPT symmetry.
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 mathematical analysis, a Hermitian function is a complex function with the property that its complex conjugate is equal to the original function with the variable changed in sign: f ∗ ( x ) = f ( − x ) {\displaystyle f^{*}(x)=f(-x)}
Since translation operators all commute with each other (see above), and since each component of the momentum operator is a sum of two scaled translation operators (e.g. ^ = (^ ((,,)) ^ ((,,)))), it follows that translation operators all commute with the momentum operator, i.e. ^ ^ = ^ ^ This commutation with the momentum operator holds true ...
In 2 dimensions, the adiabatic exchange of particles is not necessarily possible. Instead, the eigenvalues of the exchange operator may be complex phase factors (in which case ^ is not Hermitian), see anyon for this case. The exchange operator is not well defined in a strictly 1-dimensional system, though there are constructions of 1 ...
The Standard Model exhibits a (−1) F symmetry, where F is the fermion number operator counting how many fermions are in a state. Since all particles in the Standard Model satisfy F = B + L, the discrete symmetry is also part of the e iα(B + L) continuous symmetry group.