Fluctuations in Physical Systems by Hans L. Pécseli

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66) is just the sum of the spectral intensity contributions. The second term accounts for the interference (or `beating') in the signal due to the time delay caused by the two paths of propagation. e. as  1 „ 1 ‰E…t† ‡ E…t ‡ †Š2 dt J„ ˆ 2„ À„ 2   1 „ 2 1 „ E …t† dt ‡ E…t†E…t ‡ † d; …2:67† % 2„ À„ 2„ À„ the latter approximation being valid for large „ . Since the semitransparent mirror was assumed to be ideal, the two electric-®eld amplitudes are the same. 65) at zero time delay,  ˆ 0. 67) is the correlation function for time-stationary, ergodic processes.

1. Times at which the electron collides with neutral atoms are marked by vertical dashed lines. 32 Fluctuations in electric circuits p  „ 2 I` ˆ i…t†eÀi2`t=„ dt; „ 0  1 „ i…t† dt: …3:3† I0 ˆ „ 0 p The coef®cient 2 is introduced to make I` the complex effective value of the current corresponding to the frequency 2`=„ . This a standard convention. Assume that there are N collisions in the record. ) Then N 1ˆ i „ sˆ1 s p  t   t2 „ 1 2 Ài2`t=„ Ài2`t=„ Ài2`t=„ I` ˆ i1 e dt ‡ i2 e dt ‡ Á Á Á ‡ iN e dt „ tNÀ1 0 t1 p N 2ˆ i f eÀi2`ts =„ ; ˆ „ sˆ1 s s I0 ˆ …3:4† where fs ˆ 1 À eÀi2`…tsÀ1 Àts †=„ : i2`=„ …3:5† Assume now that an ensemble of records like the one shown in Fig.

For this purpose we take a simple illustration based on the Michelson interferometer shown in Fig. 3. , to re¯ect/transmit exactly 50% of the incoming light. The mirror splits the light beam (full and dashed lines) into two branches. The lengths of the two branches are the same when the movable (top) mirror is at its reference position. The displacement of the mirror from this position is d. 2 . 3 A schematic representation of a standard Michelson interferometer. A semitransparent, partially re¯ecting mirror splits the light beam (full and dashed lines) into two branches.