Quasi-Bound States of Two Magnons in the Spin-1/2XXZ Chain

We study two-magnon Bethe states in the spin-1/2 XXZ chain. The string hypothesis assumes that complex rapidities of the bound states take special forms. It is known, however, that there exist “non-string states,” which substantially disagrees with the string hypothesis. In order to clarify their nature, we study the large-N behavior of solutions of the Bethe-Ansatz equations to obtain explicit forms of typical Bethe states, where N is the length of the chain, and apply the scaling analysis (the multifractal analysis) to the Bethe states. It turns out that the non-string states contain “quasi-bound” states, which in some sense continuously interpolate between extended states and localized states. The “quasi-bound” states can be distinguished from known three types of states, i.e., extended, localized, and critical states. Our results indicate that there might be a need to reconsider the standard classification scheme of wavefunctions.     

Cluster approximation for an infinite-dimensional determinant

A systematic approximation scheme is proposed for the evaluation of the determinant of an infinite-dimensional matrix which is encountered with, for example, in the theoretical study of Fermion aggregate. This scheme is compatible with the cluster variation method for Ising problems since the combination of the two methods ensures that the total probability is unity. It is useful for the extension of the Gutzwiller variation method in the electron correlation problem.     

Comment on "Determination of the critical micelle concentration of dodecylguanidine monoacetate (dodine)"

In a work published in this journal by J.P.S. Cabral and A.R.W. Smith [J. Colloid Interface Sci. 149 (1992) 27], it is reported that the 1-dodecylguanidinium acetate (dodine) exhibits first CMC at 20-30 microM and second CMC at 110-120 microM in aqueous solution at 22.5 degrees C. Such low CMCs are unusual for ionic surfactants with dodecyl chain, and is quite interesting if this is the case. Thus, we investigated the micelle formation of dodine by electrical conductivity measurements. The specific conductivity, kappa, vs concentration plot showed no evidence for micelle formation up to a few hundreds microM at 25 degrees C. The Krafft temperature of dodine was found to be approx. 52 degrees C. When conductivity measurements were made at 54 degrees C, a clear break point was observed in the kappa vs concentration plot at 9.5 mM, which must correspond to the CMC of dodine. This CMC value is quite normal for cationic surfactant with dodecyl chain.     

Reaction of 3,3-di-tert-butylthiirane-2-thione S-oxide (α-dithiolactone S-oxide): synthesis of thiolato sulfinato-platinum and palladium complexes

Thermolysis of 3,3-di-tert-butylthiirane-2-thione S-oxide 4 gave di-tert-butyl ketone 5 and carbon disulfide (CS₂). Treatment of α-dithiolactone S-oxide 4 with excess m-CPBA or triphenylphosphine gave di-tert-butylthioketene S-oxide 3 almost quantitatively. Treatment of 4 with (η²-ethylene)bis(triphenylphosphine)platinum(0) 13 or tetrakis(triphenylphosphine) palladium 17 resulted in the formation of thiolato sulfinato-platinum complex 15 or palladium complex 18, respectively. The structure of complex 15 was determined by X-ray crystallographic analysis.