Jani Lukkarinen 1999 J. Phys. A: Math. Gen. 32 287 doi:10.1088/0305-4470/32/2/005
Jani Lukkarinen
Show affiliationsWe develop a regularization of the quantum microcanonical ensemble, called a Gaussian ensemble, which can be used for derivation of the canonical ensemble from microcanonical principles. The derivation differs from the usual methods by giving an explanation for the, at the first sight unreasonable, effectiveness of the canonical ensemble when applied to certain small, isolated, systems. This method also allows a direct identification between the parameters of the microcanonical and the canonical ensemble and it yields simple indicators and rigorous bounds for the effectiveness of the approximation. Finally, we derive an asymptotic expansion of the microcanonical corrections to the canonical ensemble for those systems, which are near, but not quite, at the thermodynamical limit and show how and why the canonical ensemble can be applied also for systems with an exponentially increasing density of states. The aim throughout the paper is to keep mathematical rigour intact while attempting to produce results which are both physically and practically interesting.
81Qxx General mathematical topics and methods in quantum theory
41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (See also 30E15)
Issue 2 (15 January 1999)
Received 4 September 1998
Jani Lukkarinen 1999 J. Phys. A: Math. Gen. 32 287
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