# Technical Document Extraction: Conductance Oscillations in Quantum Systems ## Main Plot (Panel c) ### Axes and Labels - **X-axis**: $\lambda_I/t$ (dimensionless interaction strength) - **Y-axis**: $G (e^2/h)$ (conductance normalized by quantum of conductance) - **Subplots**: - Top: $K_1$ (upper conductance regime) - Bottom: $K_2$ (lower conductance regime) ### Legend - **$n=1$**: Black curve (lowest conductance) - **$n=2$**: Blue curve - **$n=3$**: Red curve - **$n=4$**: Green curve (highest conductance) ### Parameters - $\lambda_R = 0.015t$ - $\Delta = 0.005t$ - $E_F = +0.035t$ ### Key Trends 1. **Oscillatory Behavior**: All $n$ curves exhibit periodic oscillations in $G$ as $\lambda_I/t$ increases. 2. **Amplitude Modulation**: - $n=1$ (black) shows the most pronounced oscillations. - Higher $n$ values (blue, red, green) exhibit damped oscillations with reduced amplitude. 3. **Resonance Peaks**: - Peaks in $G$ occur at regular intervals of $\lambda_I/t$. - $K_1$ (top) displays sharper peaks compared to $K_2$ (bottom). ## Inset: Zoom in $K_2$ (Panel a) ### Axes and Labels - **X-axis**: $\lambda_I/t$ (range: 0.055–0.065) - **Y-axis**: $G (e^2/h)$ (range: 0–1.2) - **Focus**: Highlights fine structure of oscillations near resonance. ### Key Observations - **Damping Effect**: Higher $n$ curves (blue, red, green) show rapid decay in $G$ compared to $n=1$ (black). - **Phase Shifts**: - $n=2$ (blue) and $n=3$ (red) exhibit phase differences relative to $n=1$. - $n=4$ (green) shows a distinct secondary peak near $\lambda_I/t \approx 0.06$. ## Inset: Zoom in $K_1$ (Panel b) ### Axes and Labels - **X-axis**: $\lambda_I/t$ (range: 0.055–0.065) - **Y-axis**: $G (e^2/h)$ (range: 2.0–3.2) - **Focus**: Details oscillations in the higher conductance regime. ### Key Observations - **Peak Sharpness**: $n=1$ (black) maintains the sharpest resonance peak. - **Interference Patterns**: - $n=2$ (blue) and $n=3$ (red) display destructive interference near $\lambda_I/t \approx 0.06$. - $n=4$ (green) exhibits a secondary peak at $\lambda_I/t \approx 0.062$. ## Cross-Referenced Legend Consistency - **Color-Line Matching**: - All panels confirm $n=1$ (black), $n=2$ (blue), $n=3$ (red), $n=4$ (green). - No discrepancies observed between legend labels and curve colors. ## Summary The plots demonstrate quantized conductance oscillations in a system with parameters $\lambda_R = 0.015t$, $\Delta = 0.005t$, and $E_F = +0.035t$. The oscillations exhibit $n$-dependent damping and phase shifts, with sharper features in $K_1$ compared to $K_2$. Zoomed insets reveal fine interference patterns critical for understanding many-body effects.