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تسجيل مستخدم جديدSensitivity to the initial conditions of the Time-Dependent Density Functional Theory
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Since the Time-Dependent Density Functional Theory is mathematically formulated through non-linear coupled time-dependent 3-dimensional partial differential equations it is natural to expect a strong sensitivity of its solutions to variations of the initial conditions, akin to the butterfly effect ubiquitous in classical dynamics. Since the Schrodinger equation for an interacting many-body system is however linear and (mathematically) the exact equations of the Density Functional Theory reproduce the corresponding one-body properties, it would follow that the Lyapunov exponents are also vanishing within a Density Functional Theory framework. Whether for realistic implementations of the Time-Dependent Density Functional Theory the question of absence of the butterfly effect and whether the dynamics provided is indeed a predictable theory was never discussed. At the same time, since the time-dependent density functional theory is a unique tool allowing us the study of non-equilibrium dynamics of strongly interacting many-fermion systems, the question of predictability of this theoretical framework is of paramount importance. Our analysis, for a number of quantum superfluid any-body systems (unitary Fermi gas, nuclear fission, and heavy-ion collisions) with a classical equivalent number of degrees of freedom ${cal O}(10^{10})$ and larger, suggests that its maximum Lyapunov are negligible for all practical purposes.
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