Quantum phase transitions without thermodynamic limits

Details Quantum phase transitions without thermodynamic limits Quantum phase transitions without thermodynamic limits

2005-11-16

arxiv.org/abs/quant-ph/0511162v3

Proc. R. Soc. A (2007) 463, 2021--2030

Physics

Quantum Physics

4 Pages, further references added

Scientific paper

10.1098/rspa.2007.1865

A new microcanonical equilibrium state is introduced for quantum systems with finite-dimensional state spaces. Equilibrium is characterised by a uniform distribution on a level surface of the expectation value of the Hamiltonian. The distinguishing feature of the proposed equilibrium state is that the corresponding density of states is a continuous function of the energy, and hence thermodynamic functions are well defined for finite quantum systems. The density of states, however, is not in general an analytic function. It is demonstrated that generic quantum systems therefore exhibit second-order (continuous) phase transitions at finite temperatures.

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