Demystifying decoherence and the master equation of quantum Brownian motion
(Color online) A Stern-Gerlach apparatus sorts atoms either up or down, depending on their spin. We insert a roulette wheel between the angular control and the Stern-Gerlach apparatus to crudely model an external environment. Each time an atom passes the roulette wheel, we spin the roulette wheel and add a random value between 0 and to the atom’s original spin angle, (Ref. 15).
(Color online) The expectation value of the spin-sorter observable with varying spin angle . Equation (17), plotted as a solid line, shows the quantum behavior of the original system. The filled circles represent destructive quantum interference, and the open circles denote constructive interference. As indicated in Eq. (19) and shown as a dashed line, the randomness of the roulette wheel destroys the quantum nature of the system.
(Color online) A cartoon of a quantum mechanical system undergoing collisions at a rate with an ideal gas at temperature . For simplicity, we consider the analogous one-dimensional system.
(Color online) The matrix elements of the state operator of a decohering quantum harmonic oscillator initially in its excited state, calculated using the approximate solution to the master equation given by Eq. (74). Dark shading indicates negative values, and light shading indicates positive values.
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