PT-symmetric brachistochrone problem, Lorentz boosts, and nonunitary operator equivalence classes
نویسندگان
چکیده
منابع مشابه
Naimark-dilated PT-symmetric brachistochrone.
The quantum mechanical brachistochrone system with a PT-symmetric Hamiltonian is Naimark-dilated and reinterpreted as a subsystem of a Hermitian system in a higher-dimensional Hilbert space. This opens a way to a direct experimental implementation of the recently hypothesized PT-symmetric ultrafast brachistochrone regime of Bender et al. [Phys. Rev. Lett. 98, 040403 (2007)] in an entangled two-...
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1550-7998=20 A non-Hermitian Hamiltonian has a real positive spectrum and exhibits unitary time evolution if the Hamiltonian possesses an unbroken PT (space-time reflection) symmetry. The proof of unitarity requires the construction of a linear operator called C. It is shown here that C is the complex extension of the intrinsic parity operator and that the C operator transforms under the Lorent...
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It is possible to associate two angles with two successive non-collinear Lorentz boosts. If one boost is applied after the initial boost, the result is the final boost preceded by a rotation called the Wigner rotation. The other rotation is associated with Wigner’s O(3)-like little group. These two angles are shown to be different. However, it is shown that the sum of these two rotation angles ...
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If a HamiltonianH has an unbroken PT symmetry, then it also possesses a hidden symmetry represented by the linear operator C. The operator C commutes with both H and PT . The inner product with respect to CPT is associated with a positive norm and the quantum theory built on the associated Hilbert space is unitary. In this paper it is shown how to construct the operator C for the non-Hermitian ...
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Let $G$ be a non-abelian group and let $Gamma(G)$ be the non-commuting graph of $G$. In this paper we define an equivalence relation $sim$ on the set of $V(Gamma(G))=Gsetminus Z(G)$ by taking $xsim y$ if and only if $N(x)=N(y)$, where $ N(x)={uin G | x textrm{ and } u textrm{ are adjacent in }Gamma(G)}$ is the open neighborhood of $x$ in $Gamma(G)$. We introduce a new graph determined ...
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ژورنال
عنوان ژورنال: Physical Review A
سال: 2008
ISSN: 1050-2947,1094-1622
DOI: 10.1103/physreva.78.042115