Noise and decoherence induced by gravitons

State-dependent graviton noise in the equation of geodesic deviation

“…The modification of the deviation equation coincides with the one of Ref. [29] (up to an infinite renormalization term). It is discussed already in [37] (sec.…”

“…There are minor changes from the setting of Parikh, Wilczek and Zahariade [2]where the effect of gravitons on geodesic deviation is considered. The Lagrangian (72) with an infinite number of modes in the coordinate space is [29]…”

“…The spectrum of the noise (of the quadrupole q rl ) as seen from Eqs. (89), ( 90) is 8π Gkh coth(h βk 2 ) which at low temperature is 8π Gk and at high temperature 8π Gβ −1 (the spectrum of the coordinates ξ , as considered by [29] in Eqs. (3.13)- (3.14), is multiplied by k 4 as a result of the fourth order derivative in Eq.…”

“…(102) only the term (103) contributes, where u s σ cos(ks). Hence Equation ( 109) gives the spectrum of the noise of the quadrupole q rl as 8π Gak (defined in [39]) or the spectrum of the noise of the measured coordinate ξ (if we perform the differentiation by parts over s contained in q rl ) as 8π Gak 5 in agreement with [29] (Eqs. (3.13)- (3.14)).…”

“…(71) 6 Particle interacting with gravitons: PWZ model in one mode approximation Parikh,Wilczek and Zahariade [2] consider two masses M and m 0 interacting with gravitational field q ω . In a one mode approximation the Lagrangian describing the geodesic deviation of the m 0 mass (in the free falling frame and M >> m 0 )is[2,29]…”