*6.2. Mixed Noise*

Density plots in Figure 3 show the behavior of the charge-heat mixed noise as a function of the AC voltage amplitude *α* and of the DC voltage amplitude *q*. In particular, the first row represents the case of a sinusoidal drive both in the free fermion case *ν* = 1 (top left panel) and at *ν* = 1/3 (top right panel). In this case, all curves show the properties S*X*(*<sup>α</sup>*, *q*) = S*X*(−*α*, *q*), S*X*(*<sup>α</sup>*, *q*) = −S*X*(*<sup>α</sup>*, −*q*) and consequently

$$\mathcal{S}\_X(\mathfrak{a}, q) = -\mathcal{S}\_X(-\mathfrak{a}, -q). \tag{85}$$

The curves at *ν* = 1 are increasing (decreasing) for increasing |*α*| at positive (negative) *q*, while the opposite is true for *ν* = 1/3. This overall profile is dictated by the power-law behavior (exponent 2*ν* in Equation (71)) which is parabolic for *ν* = 1 and sub-linear (2*ν* = 2/3, further suppressed by the fast decreasing photo-assisted tunneling amplitude) for *ν* = 1/3.

While these general considerations about the asymptotic behavior of the curves at increasing |*α*| still hold in the case of the Lorentzian case (second row of Figure 3), here both plots are manifestly asymmetric. Again, this fact can be directly attributed to the (lack of) symmetries of the photo-assisted tunneling amplitudes *p*(Lor) *l*(*α*). This asymmetry in *α* is very evident at small values of |*q*| and becomes

progressively less important by increasing |*q*|. Despite this, it is possible to note that Equation (85) is still satisfied.

**Figure 3.** Density plot of the mixed noise S*X* (in units of S(0) *X* = *e*|*λ*|2) as a function of the DC voltage amplitude *q* (*x*ˆ-axis) and the AC voltage amplitude *α* (*y*ˆ-axis). Other parameters are: *η* = 0.1, *θ* = 0 and *ω*c = 10*<sup>ω</sup>*.

*6.3. Heat Noise*

The density plots of the heat current fluctuations as a function of the AC voltage amplitude *α* and of the DC voltage amplitude *q* are reported in Figure 4. As before, the two upper panels show the sinusoidal drive case both in the free fermion case *ν* = 1 (top left panel) and at *ν* = 1/3 (top right panel). Here, according to the conditions in Equations (76) and (77), all curves satisfy <sup>S</sup>*Q*(*<sup>α</sup>*, *q*) = <sup>S</sup>*Q*(−*α*, *q*). In addition, differently from what happens in the mixed noise case, one has that this quantity is positively defined and that <sup>S</sup>*Q*(*<sup>α</sup>*, *q*) = <sup>S</sup>*Q*(*<sup>α</sup>*, <sup>−</sup>*q*).

Because of the greater power-law in Equation (72) with respect to the one in Equation (71), the curves are always increasing by increasing |*α*| for both the free and the strongly interacting case. The same is true also for the Lorentzian drive (bottom panels of Figure 4) although, in this case, the asymmetry of the *p*(Lor) *l* (*α*) directly reflects in the asymmetry of the curves for *α* → −*α* (S*Q*(*<sup>α</sup>*, *q*) = <sup>S</sup>*Q*(−*α*, *q*)) and *q* → −*q* (S*Q*(*<sup>α</sup>*, *q*) = <sup>S</sup>*Q*(*<sup>α</sup>*, −*q*)). However, the curves are characterized by the condition

$$\mathcal{S}\_{\mathbb{Q}}(\mathfrak{a},q) = \mathcal{S}\_{\mathbb{Q}}(-\mathfrak{a},-q) \tag{86}$$

due to the property in Equation (83).

**Figure 4.** Density plot of the heat noise <sup>S</sup>*Q* (in units of S(0) *Q* = *ω*|*λ*|2) as a function of DC voltage amplitude *q* (*x*ˆ-axis) and the AC voltage amplitude *α* (*y*ˆ-axis). Other parameters are: *η* = 0.1, *θ* = 0 and *ω*c = 10*<sup>ω</sup>*.
