We discuss how the crossovers in models like spin-boson model are changed byadding the coupling of the central spin to localised modes- the latter modelledas a 'spin bath'. These modes contain most of the environmental entropy andenergy at low T in solid-state systems. We find that the low T crossoverbetween oscillator bath and spin bath dominated decoherence, occurring as onereduces the energy scale of the central spin, is characterised by very lowdecoherence- we show how this works out in practise in magnetic insulators. Wethen reconsider the standard quantum-classical crossover in the dynamics of atunneling system, including both spin and oscillator baths. It is found thatthe general effect of the spin bath is to broaden the crossover in temperaturebetween the quantum and classical activated regimes. The example of tunnelingnanomagnets is used to illustrate this.
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