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The aim of this paper is to study the spectrum of the $L^p$ Laplacian and thedynamics of the $L^p$ heat semigroup on non-compact locally symmetric spaces ofhigher rank. Our work here generalizes previously obtained results in thesetting of locally symmetric spaces of rank one to higher rank spaces.Similarly as in the rank one case, it turns out that the $L^p$ heat semigroupon $M$ has a certain chaotic behavior if $p\in(1,2)$ whereas for $p\geq 2$ sucha chaotic behavior never occurs.

$L^p$ spectrum and heat dynamics of locally symmetric spaces of higher rank