  Many electronic systems exhibit striking features in their dynamical response
over a prominent range of experimental parameters. While there are empirical
suggestions of particular increasing length scales that accompany such
transitions, this identification is not universal. To better understand such
behavior in quantum systems, we extend a known mapping (earlier studied in
stochastic, or supersymmetric, quantum mechanics) between finite temperature
classical Fokker-Planck systems and related quantum systems at zero temperature
to include general non-equilibrium dynamics. Unlike Feynman mappings or
stochastic quantization methods (or holographic type dualities), the classical
systems that we consider and their quantum duals reside in the same number of
space-time dimensions. The upshot of our exact result is that a Wick rotation
relates (i) dynamics in general finite temperature classical dissipative
systems to (ii) zero temperature dynamics in the corresponding dual many-body
quantum systems. Using this correspondence, we illustrate that, even in the
absence of imposed disorder, many continuum quantum fluid systems (and possible
lattice counterparts) may exhibit a zero-point "quantum dynamical
heterogeneity" wherein the dynamics, at a given instant, is spatially
non-uniform. While the static length scales accompanying this phenomenon do not
exhibit a clear divergence in standard correlation functions, the length scale
of the dynamical heterogeneities can increase dramatically. We study "quantum
jamming" and illustrate how a hard core bosonic system may undergo a zero
temperature quantum critical metal-to-insulator-type transition with an
extremely large effective dynamical exponent z>4 consistent with length scales
that increase far more slowly than the relaxation time as a putative critical
transition is approached. We suggest ways to analyze experimental data.
