Zeeman effects on the entanglement of non-equilibrium finite-spin systems

We study the Zeeman effect on entanglement of non-equilibrium finite-spin systems with external fields using a method based on thermofield dynamics (TFD). For this purpose, the extended density matrices and extended entanglement entropies of two systems with either non-competing or competing external fields are calculated according to the dissipative von Neumann equation, and the numerical results are compared. Consequently, through the "twin-peaks" oscillations of the quantum entanglement, we have illustrated the Zeeman effect on the entanglement of non-equilibrium finite-spin systems with competing external fields in the TFD algorithm.Comment: Title and abstract were correcte

Application of Tauberian Theorem to the Exponential Decay of the Tail Probability of a Random Variable

We give a sufficient condition for the exponential decay of the tail probability of a non-negative random variable. We consider the Laplace-Stieltjes transform of the probability distribution function of the random variable. We present a theorem, according to which if the abscissa of convergence of the LS transform is negative finite and the real point on the axis of convergence is a pole of the LS transform, then the tail probability decays exponentially. For the proof of the theorem, we extend and apply so-called a finite form of Ikehara's complex Tauberian theorem by Graham-Vaaler.Comment: 22pages, 1 figure, submitted to IEEE Transactions on Information Theor

A description based on Schubert classes of cohomology of flag manifolds

We describe the integral cohomology rings of the flag manifolds of types B_n, D_n, G_2 and F_4 in terms of their Schubert classes. The main tool is the divided difference operators of Bernstein-Gelfand-Gelfand and Demazure. As an application, we compute the Chow rings of the corresponding complex algebraic groups, recovering thereby the results of R. Marlin.Comment: 25 pages, AMS-LaTeX; typos corrected, an error concerning the Schubert classes corrected, Remarks 4.4 and 4.8 adde

The integral cohomology ring of E_8/T

We give a complete description of the integral cohomology ring of the flag manifold E_8/T, where E_8 denotes the compact exceptional Lie group of rank 8 and T its maximal torus, by the method due to Borel and Toda. This completes the computation of the integral cohomology rings of the flag manifolds for all compact connected simple Lie groups.Comment: 5 pages, AMS-LaTeX, Minor errors corrected