Figure 1

Effective bath occupation (solid black line) in Eq. (28) generated by two fermionic baths [dotted red and dashed green curves, chemical potentials $\mu {}^{(k)}$, and temperatures $[\beta {}^{(k)}]{}^{-1}$ are given by the center and width of the shaded boxes, respectively] with Lorentzian tunneling rates of the form of Eq. (29). The detuning of the tunneling rates is adjusted such that the average hypothetical occupation function $\overline{\mathrm{f}}(\omega )$ is not monotonically decaying. Then the threshold $1/2$ is passed several times (vertical solid blue lines) within the transition frequency window probed by the system. This will lead to an increasing population ${\rho }_{m+1}>{\rho }_m$ when $\overline{\mathrm{f}}({\omega }_{m+1,m})>1/2$ and to a decreasing population ${\rho }_{m+1}<{\rho }_m$ when $\overline{\mathrm{f}}({\omega }_{m+1,m})<1/2$ (compare the inset). Such multimodal distributions are clearly nonthermal, i.e., they cannot be generated by a single thermal bath by adjusting temperature and chemical potential. Parameters have been chosen as $\Delta {\epsilon }_0\beta {}^{(1)}=\Delta {\epsilon }_0\beta {}^{(2)}=2$, $\mu {}^{(1)}=\Delta {\epsilon }_0$, $\mu {}^{(2)}=9\Delta {\epsilon }_0$, ${\Gamma }_1={\Gamma }_2$, ${\delta }_1={\delta }_2=0.1\Delta {\epsilon }_0$, and ${\mathrm{\omega ̄}}_1=\Delta {\epsilon }_0$ with ${\mathrm{\omega ̄}}_2=9\Delta {\epsilon }_0$. The shown equidistant transition frequencies (vertical solid and dashed blue lines) correspond to eigenvalues that scale quadratically with $m$ and may be realized by the example in Sec. 5a by using $N=10$, $\epsilon =\Delta {\epsilon }_0$, $U=\Delta {\epsilon }_0$, and $T=0$.Reuse & Permissions