  We propose a simple non-equilibrium model of a financial market as an open
system with a possible exchange of money with an outside world and market
frictions (trade impacts) incorporated into asset price dynamics via a feedback
mechanism. Using a linear market impact model, this produces a non-linear
two-parametric extension of the classical Geometric Brownian Motion (GBM)
model, that we call the "Quantum Equilibrium-Disequilibrium" (QED) model. The
QED model gives rise to non-linear mean-reverting dynamics, broken scale
invariance, and corporate defaults. In the simplest one-stock (1D) formulation,
our parsimonious model has only one degree of freedom, yet calibrates to both
equity returns and credit default swap spreads. Defaults and market crashes are
associated with dissipative tunneling events, and correspond to instanton
(saddle-point) solutions of the model. When market frictions and
inflows/outflows of money are neglected altogether, "classical" GBM
scale-invariant dynamics with an exponential asset growth and without defaults
are formally recovered from the QED dynamics. However, we argue that this is
only a formal mathematical limit, and in reality the GBM limit is non-analytic
due to non-linear effects that produce both defaults and divergence of
perturbation theory in a small market friction parameter.
