LORENTZ TRANSFORMATIONS IN BIFURCATING SYSTEMS

The linear response of a driven dissipative system near a bifurcation instability is studied. Using a previously established scaling relation, it is shown that the response to a small coherent signal can be characterized by a Lorentz transformation of a spinor whose components are the two orthogonal phases (quadratures) of the signal. The analysis shows that by forming an array of such systems it should be possible to demonstrate features of the Lorentz group experimentally, e.g., Wigner rotations and Berry's phase of the Lorentz group, in simple bifurcating systems.