Pavel Stránský
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Last updated: 14.5.2024

Peres lattice and classical Peres invariant

B = 0.41
FIRST -10 -5 -2 -1   +1 +2 +5 +10 LAST
freg(B,E=0) Section of regularity (B=0.41,E=0)
Figure 1: freg (B, E=0) Figure 2: Section of regularity
Calculated using the sections of regularity (see Figure 2). Poincaré section y = 0 calculated on the 100 x 100 grid. A trajectory is started at each point of the grid and the SALI method is used to distinguish regular (blue colour) from chaotic (red colour) trajectories.
Peres lattice B=0.41 Peres invariant B=0.41
Figure 3: Peres lattice of the operator L^2 Figure 4: Classical Peres invariant
3000 lowest lying well-converging states are displayed. The grey line corresponds with the energy E=0, on which the section of regularity (Figure 2) and the Peres invariant (Figure 4) are calculated. Time averaged value of the variable L^2, calculated on the 400 x 400 grid.