Dissipative processes in quantum theory

Ilya Prigogine

I. Prigogine

A. J. van Wonderen, K. Lendi

Paola Zizzi

We suggest that, with regard to a theory of quantum mind, brain processes can be described by a classical, dissipative, non-abelian gauge theory. In fact, such a theory has a hidden quantum nature due to its non-abelian character, which is revealed through dissipation, when the theory reduces to a quantum vacuum, where temperatures are of the order of absolute zero, and coherence of quantum states is preserved. We consider in particular the case of pure SU(2) gauge theory with a special anzatz for the gauge field, which breaks Lorentz invariance. In the ansatz, a contraction mapping plays the role of dissipation. In the limit of maximal dissipation, which corresponds to the attractive fixed point of the contraction mapping, the gauge fields reduce, up to constant factors, to the Pauli quantum gates for one-qubit states. Then tubuline-qubits can be processed in the quantum vacuum of the classical field theory of the brain, where decoherence is avoided due to the extremely low temperature. Finally, we interpret the classical SU(2) dissipative gauge theory as the quantum metalanguage (relative to the quantum logic of qubits), which holds the non-algorithmic aspect of the mind.

P. Caldirola

Rajagopal, A.K, Rendell, R.W

Three inter-related topics are discussed here. (1) the Lindblad dynamics of quantum dissipative systems; (2) quantum entanglement in composite systems and its quantification based on the Tsallis entropy; and (3) robustness of entanglement under dissipation. After a brief review of the Lindblad theory of quantum dissipative systems and the idea of quantum entanglement in composite quantum systems illustrated by describing the three particle systems, the behavior of entanglement under the influence of dissipative processes is discussed. These issues are of importance in the discussion of quantum nanometric systems of current research.