Kms States and Complex Multiplication

@inproceedings{Connes2005KmsSA,
  title={Kms States and Complex Multiplication},
  author={Alain Connes and Matilde Marcolli and Niranjan Ramachandran},
  year={2005}
}
Problem 1.1. For some number field K (other than Q) exhibit an explicit quantum statistical mechanical system (A, σt) with the following properties: (1) The partition function Z(β) is the Dedekind zeta function of K. (2) The system has a phase transition with spontaneous symmetry breaking at the pole β = 1 of the zeta function. (3) There is a unique equilibrium state above critical temperature β = 1. (4) The quotient CK/DK of the idèle class group CK of K by the connected component DK of the… CONTINUE READING

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