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Highly excited many-particle states in quantum systems (nuclei, atoms,quantum dots, spin systems, quantum computers) can be ``chaotic''superpositions of mean-field basis states (Slater determinants, products ofspin or qubit states). This is a result of the very high energy level densityof many-body states which can be easily mixed by a residual interaction betweenparticles. We consider the time dynamics of wave functions and increase ofentropy in such chaotic systems. As an example we present the time evolution in a closed quantum computer. Atime scale for the entropy S(t) increase is t_c =t_0/(n log_2{n}), where t_0 isthe qubit ``lifetime'', n is the number of qubits, S(0)=0 and S(t_c)=1. At t <<t_c the entropy is small: S= n t^2 J^2 log_2(1/t^2 J^2), where J is theinter-qubit interaction strength. At t > t_c the number of ``wrong'' statesincreases exponentially as 2^{S(t)} . Therefore, t_c may be interpreted as amaximal time for operation of a quantum computer, since at t > t_c one has tostruggle against the second law of thermodynamics. At t >>t_c the systementropy approaches that for chaotic eigenstates.

Time Dynamics in Chaotic Many-body Systems: Can Chaos Destroy a Quantum Computer?