A solvable model exhibiting a glass-like transition

A nonlinear equation of motion of an overdamped oscillator exhibiting a glass-like transition at a critical coupling constant _c is presented and solved exactly. Below _c, in the fluid phase, the oscillator coordinatex(t) decays to zero, while above _c, in the amorphous phase, it decays to a nonzero infinite time limit. Near _c the motion is slowed down by a nonlinear feedback mechanism andx(t) decays exponentially to its long time limit with a relaxation time diverging as (1 – /_c)^–3/2 and (/_c –1)^–1 for < _c and > _c respectively. At _cx(t) exhibits a power law decay proportional tot^– with exponent -1/2.