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Raikh, Glazman, and Zhukov Reply:

M. E. Raikh, L. I. Glazman, L. E. Zhukov

1997
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Physical Review Letters
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Raikh, Glazman, and Zhukov Reply: In their Comment Wan, Ortiz, and Phillips [1] make three points about our Letter [2]: (i) proposed mechanism of the pair formation requires a single prior occupancy of the cluster of four localized states, that we have considered; (ii) our mechanism relies on geometric accidents and lacks robustness with respect to the change of the interaction law; (iii) calculating the energy balance, we assumed the localized states to be pointlike and neglected the finite
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... e of the corresponding wave functions. The first objection is quite relevant. Indeed, in the experiment [3], in some runs the very first peak observed was double [4] . However, one cannot say for sure that all the localized states in the dot reveal themselves in the spectroscopy. The experiment was performed using the ac excitation; if the tunneling time into a localized state exceeds the period of excitation, it would get eventually populated, but would not be detected [4] . The widths of the peaks in experiment [3] cannot be used as a measure of tunneling times for the following reason. The data were taken at temperature T 6 mK, which is much larger than the inverse tunneling time. So it was T that determined the widths of the peaks, and that is why they were similar. The second objection can be addressed to any event which occurs with some finite probability; formation of any cluster in a random system can be regarded as accidental. The possibility of moving a localized state, located at the apex of the triangle (as well as all the other localized states) was explicitly taken into account in the calculation of the probability, P , of the occurrence of a double peak, presented in the Letter. We do not see why the difference in numerical coefficients in P , calculated for a model and for realistic interaction laws, should be considered as a drawback of our mechanism. In fact, the model "hard core" interaction, which we used only for illustration, contains two adjustable parameters: magnitude and radius. Bringing them in correspondence with e 2 ͞kd and d is possible only within some numerical factors.

doi:10.1103/physrevlett.78.3980
fatcat:s5ud2gmvkfg3pfb25dcgctrfoa