Breaking the Fluctuation-Dissipation Relation by Universal Transport Processes

Universal phenomena far from equilibrium exhibit additional independent scaling exponents and functions as compared to thermal universal behavior. For the example of an ultracold Bose gas we simulate nonequilibrium transport processes in a universal scaling regime and show how they lead to the breaking of the fluctuation-dissipation relation. As a consequence, the scaling of spectral functions (commutators) and statistical correlations (anticommutators) between different points in time and space become linearly independent with distinct dynamic scaling exponents. As a macroscopic signature of this phenomenon, we identify a transport peak in the statistical two-point correlator, which is absent in the spectral function showing the quasiparticle peaks of the Bose gas.

Figure 1

Quasiparticle peaks of the spectral function $\rho$ and (rescaled) statistical function $F$ at different times $\tau$ and momenta $p$. The statistical function exhibits an additional transport peak, which is not present in $\rho$, thus breaking the FDR.

Figure 2

Distribution function $f_c(\tau ,p)$, dispersion ${\omega }_c(\tau ,p)$ and decay function ${\gamma }_c(p)$ for the transport peak. The insets in the left two panels show the rescaled functions to demonstrate their self-similar behavior with universal exponents $\alpha$, $\beta$, and $z_c$.

Figure 3

Quasiparticle dispersion relation $\omega (p)$ and time-dependent decay rate ${\gamma }_{\pm }(\tau ,p)$.

Figure 4

Nonequilibrium zero-mode $n_0(\tau )$ and sum over the dominant transport modes $n_{<}(\tau )$ defined in Eq. (14), compared to the thermal value of the zero-mode condensate density $n_0^T$.

Figure 5

Left panels: $F$ and $\rho$ as a function of $\omega -\mu$ at different $\tau$ keeping ${\tau }^{\beta }p$ fixed. Right: Same functions rescaled in time.