We have found spatial decoherence (loss of phase coherence between dis
tant points in space) of quantum states and chaotic behavior (''turbul
ence'') of quantum-mechanical currents for a nonlinear oscillator in a
magnetic field. Use of quantum currents is dictated by the fact that
they are simultaneously phase-sensitive and gauge-invariant measures.
The theory is applicable to an electron in a quantum dot with soft con
fining potential in a magnetic field. [S0031-9007(98)07722-9].