Light amplification in organic thin films using cascade energy transfer

Abstract

Nature © Macmillan Publishers Ltd 1997fluctuational paths. The relaxational tail leading back to the stable state S is common to the two fluctuational paths that form the resultant corral 12 . From Fig. 2c we see that the ridges of the distribution are strongly asymmetric in time, but agree well with the fluctuational and relaxational paths predicted from equations (3). The observed asymmetry of the distribution implies 4 a lack of detailed balance; and it leads directly 15,26 to macroscopic irreversibility in the D → 0 limit where the width of the distribution tends to zero. In verifying the existence of the switching line, the results demonstrate the non-differentiability of the generalized nonequilibrium potential.One third example (Fig. 3) is the system suggested by Maier and Stein 19,26 for analysis of the escape problem in nonequilibrium systems. It consists of a bistable system driven from equilibrium by a stationary field of (in general) the nongradient type. In measurements near one of the stable states, the lack of detailed balance and the irreversibility of the fluctuations become strikingly apparent. Figure 3a shows the measured P f (x,y) distribution for fluctuations to the two different remote states x f placed symmetrically on either side of the y axis; P f (x,y) is the projection ofWhen the paths traced out by the ridges are plotted (Fig. 3b), it can be seen: (1) that the fluctuational trajectories are completely different from the relaxational ones; and (2) that they are in good agreement with the fluctuational and relaxational trajectories predicted from equations (3). Figure 3c shows the corresponding picture measured for fluctuations to a single remote state x f on the switching line (lying on the x axis). The two fluctuational paths to the remote state are, again, markedly different from the common relaxational path leading back to S. Both parts of the trajectory are well described by the corresponding optimal paths calculated from equations (3). In this case too, therefore, the observations link a lack of detailed balance to macroscopic irreversibility, and demonstrate the nondifferentiability of the generalized nonequilibrium potential; the closed loops traversed during fluctuations verify the expected 2,26,27 occurrence of rotational flow in nonequilibrium systems.Thus, after more than 60 years of ''thought experiments'' on large fluctuations 2,3,30 , it has now become possible to do real experiments yielding quantitative results. Our work has already verified several long-standing theoretical predictions, including those of symmetry between the growth and decay of classical fluctuations in equilibrium 2,30 , the breaking of this symmetry under nonequilibrium conditions 7,15,26 , the relationship of symmetry-breaking to a lack of detailed balance [15][16][17]26 , and the existence of an optimal force derived from the fluctuating field and related to the momentum of an auxiliary hamiltonian system [8][9][10]20,21 . The technique has also enabled us to reveal new dynamical features of larg...

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