## 3 Results
From Equation (2), it follows that the increase in losses Re\(Y_{e}(f)\) at some frequencies results in a local decrease of the current \(\Delta I(V)\) through the JJ. If the loss function Re\(Y_{e}(f)\) has a Gaussian or Lorentzian form, then its mapping on the dependence of dI/d\(V\) on the voltage \(V\) should have an odd-symmetric form (see a green curve on the top panel of Figure 2). At low voltages, it deviates towards a smaller dI/d\(V\), referring to the dependence dI\({}_{0}\)/d\(V\) vs. \(V\) (a dashed grey curve on the top panel in Figure 2), and then, with increasing voltage--towards higher dI/d\(V\). In this work, localized resonant features in \(dI\)/d\(V\) vs. \(V\) of odd symmetry, high reproducibility, and various intensities are of interest due to collective modes in high-\(T\) material of JJ. The extended features of low reproducibility and low intensity can be considered later. Indeed, the upper curve in Figure 4a for the JJ with \(R_{n}\) = 0.8 \(\Omega\) at voltages of about 9.4 mV has a well-defined feature that deviates at V \(<\) 9.4 mV towards lower conductances and at V \(>\) 9.4 mV--towards higher ones. In addition, the upper curve in Figure 4a has similar, but of low intensity, odd-symmetric features with centers at voltages V = 4.66 mV, 7.403 mV, 11.79 mV, and 11.98 mV (see also the enlarged features on the insets). The same features manifest in other JJs. Figure 4a also shows the dependence of dI/d\(V\) on voltage \(V\) for the JJ with \(R_{n}\) = 1.9 \(\Omega\) (lower curve). The centers of the features on the upper curve in Figure 4a fit the centers of similar features on the lower curve. Moreover, the position of the singularities also remains unchanged with an increase in the JJ temperature. Figure 4b shows two dependences of dI/d\(V\) on voltage \(V\) for a JJ with \(R_{n}\) = 1.8 \(\Omega\) at two temperatures of 5 K (lower curve) and 42 K (upper curve). It can be seen that all the main features retain their positions as the temperature rises by almost an order of magnitude. Figure 3: \(I\)–\(V\) curves and differential conductances dI/d\(V\) of typical bicrystal YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{7-x}\) junctions formed from two \(c\)-axis thin films (**a**) and two films with mutually tilted \(c\)-axes (**b**) as a function of voltage \(V\) (bottom scale) and Josephson frequency \(f_{j}\) = 2 eV/h (top scale). Dashed grey lines are fits to the \(I\)–\(V\) curves according to the RS] model (Equation (1)). The features found on the \(I\)-\(V\) curves of YBa\({}_{2}\)Cu\({}_{3}\)O\({}_{7-x}\) bicrystal junctions with mutually tilted \(c\)-axes can be associated with both inelastic quasiparticle tunneling and Josephson tunneling. In the first case, the transformation of the voltages \(V_{\rm k}\) of the features on the \(I\)-\(V\) curves of JJs into the position of the features on the frequency axis should occur according to the relation \(V_{\rm k}=\rm hf_{\rm k}/e\), while in the second case, \(V_{\rm k}=\rm hf_{\rm k}/2e\). To remove this uncertainty, we measured the \(I\)-\(V\) curves of JJs under irradiation with a frequency of 94 GHz and showed how the main feature on the \(I\)-\(V\) curves changed with the increasing power of this radiation. The results are presented in Figure 5 for the dependence of the differential conductance \(\rm dI/d\)\(V\) on the voltage \(V\) for one of the JJs. The unperturbed differential conductance \(\rm dI/d\)\(V\) vs. \(V\) (red curve) has a peak at \(V\) = 9.6 mV. With a monotonous increase in radiation power, which corresponds to a decreasing the attenuation of a precision rotary-wave W10 attenuator from 60 dB to 4 dB, the dependence of \(\rm dI/d\)\(V\) on the voltage \(V\) changes (see a corresponding set of curves with colors from red to purple). The main peak at 9.6 mV gradually fades to zero (blue curve) and reappears (navy and purple curve). In this case, additional local maxima show up, which are symmetrically situated from the main peak at \(V\)= 9.6 mV by \(\pm\)194 \(\mu\)V (yellow curve).