By Heinz-Peter Breuer, Francesco Petruccione
ISBN-10: 3540410619
ISBN-13: 9783540410614
The improvement of a constant photo for the techniques of decoherence and quantum dimension calls for a therapy that's appropriate with the idea of relativity. This quantity studies a number of the techniques prompt to unravel or avoid the bobbing up problems. ranging from an research of the extent of compatibility of the dimension challenge with the exact thought of relativity, the position of non-locality and entanglement are mentioned. the topic can also be addressed from the viewpoint of quantum optics and quantum info thought, in addition to at the foundation of crew theoretic and algebraic equipment. The emergence of decoherence in quantum electrodynamics is mentioned from an open structures viewpoint.
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Additional resources for Relativistic Quantum Measurement and Decoherence: Lectures of a Workshop Held at the Istituto Italiono per gli Studi Filosofici, Naples, April 9-10, 1999
Sample text
141), is similar to the spreading σ(tf )2free which is obtained from the free Schr¨ odinger equation, σ(tf )2free = σ02 + If we write σ(tf )2 = σ02 + t2f 4m2R σ02 t2f . 4m2R σ02 1+ 4σ02 L(tf )2 (142) (143) we observe that the decoherence function affects the probability density only though the width σ(tf ) and leads to an increase of the spreading. In view of the estimate (136) the correction term in Eq. (143) is, however, small for times satisfying L(tf ) ∼ c · tf σ0 . (144) This means that the influence of the radiation field can safely be neglected for times which are large compared to the time it takes a light signal to travel the width of the wave packet.
57) This is a double path integral which is to be extended over all paths x(t) and x (t) with the boundary conditions x (ti ) = xi , x (tf ) = xf , x(ti ) = xi , x(tf ) = xf . (58) Sm [x] denotes the action functional for the electron, Sm [x] = tf ti dt 1 mx˙ 2 − V (x) , 2 (59) while the influence phase functional becomes, iΦ[x, x ] = tf ti dt t ti dt i ˙ D(t − t ) x(t) − x˙ (t) 2 1 ˙ − D1 (t − t ) x(t) − x˙ (t) 2 ˙ ) + x˙ (t ) x(t ˙ ) − x˙ (t ) x(t . (60) We define the new variables q =x−x, r= 1 (x + x ), 2 (61) 44 Heinz–Peter Breuer and Francesco Petruccione and set, for simplicity, the initial time equal to zero, ti = 0.
1 which clearly shows the crossover between the two regions of time. Eq. (132) implies that the vacuum coherence length is roughly of the order L(tf )vac ∼ c · tf . (136) To see this let us assume a typical preparation time scale of the order τp ∼ 10−21 s. If we take tf to be of the order of 1s we find that ln(tf /τp ) ∼ 48. In the rather extreme case tf ∼ 1017 , which is of the order of the age of the universe, we get ln(tf /τp ) ∼ 87. On using 3π/4α ≈ 322 and Eq. (132) for T = 0 one is led to the estimate (136).
Relativistic Quantum Measurement and Decoherence: Lectures of a Workshop Held at the Istituto Italiono per gli Studi Filosofici, Naples, April 9-10, 1999 by Heinz-Peter Breuer, Francesco Petruccione
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