Open AccessA new method of calculating the unitary evolution matrix ds(t) of the spin-s operators and its applications
Author(s) -
MingLiang Hu,
Xiao-Qiang Xi
Publication year - 2008
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.57.3319
Subject(s) - hamiltonian (control theory) , unitary state , physics , hamiltonian matrix , time evolution , operator (biology) , quantum mechanics , unitary operator , unitary matrix , matrix (chemical analysis) , mathematical physics , state (computer science) , eigenvalues and eigenvectors , mathematics , symmetric matrix , hilbert space , algorithm , composite material , materials science , political science , law , mathematical optimization , biochemistry , chemistry , repressor , transcription factor , gene
We propose a method for calculating the unitary evolution matrix of the arbitrary spin-s operators rigorously. This is an indirect method, which differs from the method of group theory or the method of direct calculation. The kernel of our method is to use the identity of two systems in their expressions, namely the Hamiltonian Hs=Sx of spin-s particle and the Hamiltonian of the Heisenberg XX open chain with interaction J=n(N-n). Because of this identity, the calculation of the unitary evolution matrix of the spin-s operators is substituted by the calculation of the state evolution matrix in Heisenberg XX open chain. As examples, the unitary evolution matrix of s=3/2, s=2 and s=5/2 are calculated by using our method. Since the evolution of the state |sm〉 under the operator e-itSx corresponds to the rotation of the initial state |sm〉 around the x-axis by an angle βt, and the evolution matrix element dsm′m(t)=〈sm′|e-itSx|sm〉 is just the projection of the finial state e-itSx|sm〉 on the initial state |sm′〉, the evolution matrix at t=π corresponds the perfect transmission of quantum state in the Heisenberg XX open chain.