  The ground state of the quasi-one-dimensional system with bond-disorder
(CH3)2CHNH3Cu(ClxBr1-x)3 with x = 0, 0.25 and 0.3 has been investigated by
muSR. The Fourier spectrum of electron spin fluctuation in x =0.25 and 0.3
obtained by LF-muSR technique shows that there exists a soft-mode toward a
possible phase transition to an exotic phase such as Bose-glass. In gapped
system with x = 0, the Fourier spectrum is totally different from the other
two, indicating the existence of the quantum critical point at a finite x
between 0 and 0.25.
