Turbulence and spatial correlation of currents in quantum chaos

The study of quantum chaos and the problem of identifying the quantum analog of classical chaos have been a subject of intense interest for over two decades. We have found spatial decoherence (loss of phase coherence between distant points in space) of quantum states and chaotic behavior (turbulence) of quantum mechanical currents for a nonlinear oscillator in a magnetic field. The use of quantum currents is dictated by the fact that they are simultaneously phase-sensitive and gauge-invariant measures. The connection of the topology and the correlation of currents have been established as indicators of quantum chaos. These complement such known signs of quantum chaos as scarring of eigenfunctions, spectral properties and spectral-spatial parametric correlations. The theory is applicable to an electron in a quantum dot with soft confining potential in a magnetic field.