Numerical verification of the open-system mechanism
In this section, I use experimentally measured values to show how they directly align with the mechanism described above.
Excitation energy
The system is excited with light of energy:
E_in = 2.25 eV
This photon acts as a trigger impulse that initiates the internal process in the structure.
Observed emission states
The experiment reveals two distinct emission energies:
E_free = 1.88 eV — free exciton
E_loc = 1.83 eV — localized state
The energy difference is:
ΔE = 0.05 eV (50 meV)
This value defines the emergence of a new structural state.
Structural interpretation
Within the mechanism, this shift corresponds to a change in structural resistance:
I_γ = (P · Π) / R_s
The localized state is characterized by higher resistance:
R_s^loc > R_s^free
From the measured energies:
R_s^loc / R_s^free ≈ 1.027
This corresponds to an increase of approximately 2.7% in structural resistance, consistent with the observed energy shift.
Excitation level
The energy splitting can be expressed as an effective excitation level:
T_eff ≈ 580 K
This value characterizes the degree of structural excitation associated with localization.
Spectral broadening
The measured linewidths are:
Γ_free = 49 meV
Γ_loc = 68 meV
Their ratio:
Γ_loc / Γ_free ≈ 1.39
This reflects an increase in structural variation within the localized state and is consistent with the measured spectral broadening.
Spatial control
The structure is defined by a periodic pattern with spacing:
L = 170 nm
This sets the emitter density:
ρ_sites ≈ 3.5×10¹⁰ cm⁻²
The emission is therefore spatially controlled by the geometry of the system.
Conclusion
The experimentally measured values:
ΔE = 50 meV
ΔR_s ≈ 2.7%
Γ increase ≈ 1.39×
follow directly from the relations:
E = hν
I_γ = (P · Π) / R_s
I_γ ∝ N_cycles
These results demonstrate that the observed emission behavior arises as a direct consequence of the described mechanism and are consistent with the experimental measurements.
Report: doi.org/10.5281/zenodo…
Supplement: doi.org/10.5281/zenodo…
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