Platonic quantum networks as coherence-assisted switches in perfect and imperfect situations

Energy transport and optimal design of noisy Platonic quantum networks

“…The characteristics shown in these figures (noiseless cases) would be the same as that of the noisy cases unless the fact that in the presents of dephasing and/ or dissipation noises, the oscillating patterns of populations would be evanescent and so the sink site would be fully populated at the equilibrium (t → ∞ ). In [15] we found that the target population of the noiseless Platonic networks at the steady state are independent of their size and is only related to the number of neighboring sites (N c − 1) as of ρ sink = 1/(N c − 1), i.e. ρ sink = 0.25, 0.33, 0.2, 0.33 for N = 6, 8, 12, 20, respectively.…”

“…That some group of sites having similar or inversely oscillating populations at the steady state can be understood by the fact that the noiseless Platonic networks have eigenstate of the form of equation ( 9) and the anti-symmetric eigenstates of the form m m | | ñ -ñ, where m and m ˜are the point-symmetry or mirroring sites (equations ( 2), (3) [15]). So at the steady state, according to the energy initialization pattern, the system would be trapped in the superposition of the eigenstates of the form m m | | ñ -ñ, and would oscillate within the groups of two mirroring sites.…”

“…FCNs are defined by the property that all sites are equally connected to each other and the last site is dissipatively connected to a sink site. In [15] we studied some three-dimensional Platonic configurations with distance dependent couplings, and proved that they have some similar properties as those of an N-site FCN, where in the corresponding Platonic network N − 1 would be the number of nearest neighbours of each site. For example, it was shown that the sink populationthe energy excitation accumulated in the sink site-of the 'noiseless' Platonic quantum networks and FCNs are the same at the steady state (or infinite time).…”

Energy transport and optimal design of noisy Platonic quantum networks

“…The characteristics shown in these figures (noiseless cases) would be the same as that of noisy cases unless the fact that in the presents of dephasing and/or dissipation noises, the oscillating patterns of populations would be evanescent and the sink site would be fully populated at the equilibrium (t → ∞). In [15] we found that the target population of noiseless Platonic networks at steady state are independent of their size and is only related to the number of neighboring sites (N c − 1) as of ρ sink = 1/(N c − 1), i.e. ρ sink = 0.25, 0.33, 0.2, 0.33 for N = 6, 8, 12, 20, respectively.…”

“…FCNs are defined by the property that all sites are equally connected to each other and the last site is dissipatively connected to a sink site. In [15] we studied some three dimensional Platonic configurations with distance dependent couplings, and proved that they have some similar properties as those of an N -site FCN, where in the corresponding Platonic network N − 1 would be the number of nearest neighbours of each site. For example, it was shown that the sink population -the energy excitation accumulated in the sink site -of the "noiseless" Platonic quantum networks and FCNs are the same at the steady state (or infinite time).…”