Quantum Fluctuations and Chaotic States of Two-Level Atomic Systems
Many coupled sets of non-linear ordinary differential equations have shown strange attractorsl, eg the Maxwell-Bloch equations2 in mean field theory. We will first investigate whether dissipative two level atomic systems interacting with a single mode of the electromagnetic field will always have such strange attracting sets. Secondly the role of noise on the strange attractors will be discussed. In numerical calculations inevitably random errors are introduced. Consequently the effect on the structure of the attractors when additional random Gaussian forces are present in the equations of motion has been studied recently3,4. Details of the attractor structure are lost below a certain length scale determined by the variance of the stochastic force and the fractal dimension approaches the noise variance value of 2 for finer and finer resolution rather than the value expected from the appropriate attractor. We wish to discuss the case when a different type of noise term is considered, viz quantum fluctuations. Unlike the addition of noise terms discussed above, quantum fluctuations alter the form and number of equations.
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