For r 1=r 2=0, the wave function in the DSN exactly reduces to th

For r 1=r 2=0, the wave function in the DSN exactly reduces to that of the DN. We analyzed the probability densities in the DN and in the DSN from Figures 2 and 3, respectively, with the choice of sinusoidal signal source. The probability densities in the DN given in Figure 2b,c,d oscillate with time. Moreover, their time behaviors are more

Cyclosporin A manufacturer or less distorted. The probability density, however, does not oscillate when there are no displacement and no signal of power source (see Figure 2a). The probability densities in the DSN are distorted much more significantly than those of the DN. The time behavior of probability densities of quantum states, CP-868596 mouse both the DN and the DSN, is highly affected by external driving power source. When there is no external power source( =0), the displacement of charges, specified with a certain initial condition, gradually disappears as time goes by like a classical state. The fluctuations and uncertainty products of charges and currents are derived in the DSN, and it is shown that their value is independent of the size of the particular solutions q j p (t) and p j p (t). From this, together with the fact that q j

p (t) and p j p (t) are determined by the characteristics of , it is clear that the electric power source does not affect on the fluctuation of canonical variables. If we ignore the time dependence of Megestrol Acetate F j (t) and , decrease exponentially with time, whereas increase exponentially. From Equations 64 and 65, we can see that the time behavior of q j is determined

by two factors: One is displacement and the other is the signal of power source. For better understanding of this, recall that the amplitude of complementary functions gives displacement of the system, and the particular solutions are closely related to external driving force (i.e., in this case, the power source). In this paper, we did not consider thermal effects for the system. The thermal effects, as well as dissipation, may be worth to be considered in the studies of quantum fluctuations of Fludarabine supplier electronic circuits with nanosize elements because the practical circuits are always working in thermal states with the presence of damping. It may therefore be a good theme to investigate DSNs with thermalization as a next task, and we plan to investigate it in the near future. Appendix 1 The eighth formula of 7.

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