basic branch cut visualization

kondo.py

@@ -2036,7 +2036,7 @@ class Kondo:
                 self.odeFunctionIm,
                 (eiminit, eimfinal),
                 init_values,
-                t_eval = ((eimfinal,) if only_final else None),
+                t_eval = solveopts.pop("t_eval", ((eimfinal,) if only_final else None)),
                 **solveopts
             )
         return output
@@ -2067,7 +2067,7 @@ class Kondo:
                 self.odeFunctionRe,
                 (reEinit, reEfinal),
                 init_values,
-                t_eval = ((eimfinal,) if only_final else None),
+                t_eval = solveopts.pop("t_eval", ((eimfinal,) if only_final else None)),
                 **solveopts
             )
         return output

poles.py

+#!/usr/bin/env python3
+
+# Copyright 2022 Valentin Bruch <valentin.bruch@rwth-aachen.de>
+# License: MIT
+"""
+Kondo FRTRG, analyze poles and branch cuts
+"""
+from kondo import Kondo
+import numpy as np
+import matplotlib.pyplot as plt
+from settings import logger
+from matplotlib.colors import LogNorm
+
+def plot_bc(
+        epsilon=1e-4,
+        ir_cutoff=0.1,
+        depth=20,
+        solver_parameters={},
+        nmax=10,
+        voltage_branches=4,
+        omega=16.5372,
+        vdc=1,
+        resolution=100,
+        **parameters):
+    """
+    Plot branch cuts for directly calculated data.
+    """
+    t = np.linspace(ir_cutoff, -depth, resolution)
+    logger.info("Starting initial RG flow")
+    kondo = Kondo(
+            nmax=nmax,
+            voltage_branches=voltage_branches,
+            omega=omega,
+            vdc=vdc,
+            **parameters,
+            compact=0)
+    solver = kondo.run(**solver_parameters, ir_cutoff=ir_cutoff)
+
+    # left of center
+    logger.info("Moving to left branch")
+    solver_left = kondo.solveOdeRe(
+            0., -epsilon,
+            **solver_parameters,
+            init_values=solver.y[:,-1])
+    assert np.allclose(kondo.energy, 1j*ir_cutoff - epsilon)
+    logger.info("Solving along left branch")
+    solver_left_down = kondo.solveOdeIm(
+            ir_cutoff, -depth,
+            **solver_parameters,
+            init_values=solver_left.y[:,-1],
+            t_eval=t)
+
+    # right of center
+    kondo.global_properties.energy = 1j*ir_cutoff
+    logger.info("Moving to right branch")
+    solver_right = kondo.solveOdeRe(
+            0., epsilon,
+            **solver_parameters,
+            init_values=solver.y[:,-1])
+    assert np.allclose(kondo.energy, 1j*ir_cutoff + epsilon)
+    logger.info("Solving along right branch")
+    solver_right_down = kondo.solveOdeIm(
+            ir_cutoff, -depth,
+            **solver_parameters,
+            init_values=solver_right.y[:,-1],
+            t_eval=t)
+
+    gamma_size = kondo.gamma.values.size
+    y_diff_abs = np.abs(solver_right_down.y - solver_left_down.y)
+    gamma_diff_abs = y_diff_abs[:gamma_size].reshape((*kondo.gamma.values.shape, resolution))
+
+    logger.info("Preparing plot")
+    fig, ax = plt.subplots()
+    x_data = []
+    y_data = []
+    z_data = []
+    for vb in range(-voltage_branches, voltage_branches+1):
+        for n in range(-nmax, nmax+1):
+            x_data.append((vb*vdc + omega*n)*np.ones_like(t))
+            y_data.append(t)
+            z_data.append(gamma_diff_abs[vb+voltage_branches, n+nmax, n+nmax])
+    x_data = np.concatenate(x_data, axis=None)
+    y_data = np.concatenate(y_data, axis=None)
+    z_data = np.concatenate(z_data, axis=None)
+    plot = ax.scatter(
+            x_data,
+            y_data,
+            c=z_data,
+            norm=LogNorm(epsilon, 3),
+            cmap=plt.cm.viridis)
+    fig.colorbar(plot, ax=ax)
+    plt.show()
+
+
+if __name__ == "__main__":
+    plot_bc(
+            epsilon=1e-6,
+            solver_parameters=dict(rtol=1e-10, atol=1e-12),
+            d=1e9,
+            omega=16.5372,
+            vdc=5,
+            vac=7,
+            nmax=12,
+            voltage_branches=5,
+            method="mu")