Sanyal, G. ; Mandal, Sk. H. ; Mukherjee, D. (1994) On optimal meanfield descriptions in finitetemperature manybody theories: use of thermal Brillouin and Bruckner conditions Proceedings of the Indian Academy of Sciences  Chemical Sciences, 106 (2). pp. 407432. ISSN 02534134

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Official URL: http://www.ias.ac.in/j_archive/chemsci/106/5/4074...
Related URL: http://dx.doi.org/10.1007/BF02840760
Abstract
Although the structural similarity between the properties of a thermal trace and the zerotemperature expectation values for quantum systems has been known for quite some time, not all the practical computational methods in the thermal field theories exploit this correspondence explicitly. Using a thermal field theory derived by us, which introduces the thermal analogues of normal ordering and Wick's expansion, a very close resemblance between zerotemperature and finitetemperature field theories can be established. We use this apparatus in this paper to derive optimal conditions of meanfield and correlated descriptions of thermally averaged quantities. It is shown that the optimal meanfield conditions for the free energy is equivalent to the minimum value for the average energy. The optimality conditions turn out to be exact thermal analogues of the Brillouin conditions. The optimal meanfield condition to generate the minimum value of the ratio Z/Z_{o}, where Z and Z_{o} are the exact and the meanfield partition functions, yields the exact thermal analogue of the Bruckner condition. In a similar vein, we generalize the thermal Brillouin condition to include correlated functions used in the evaluation of the thermal trace. The optimal choice of the correlated ground states leads to manyparticle generalizations of the thermal Brillouin conditions. In the context of the pathintegral methods for determining Z, we envisage use of a local optimal mean field that depends on each point on the pathleading to local thermal analogues of Brillouin and Bruckner conditions. To derive these conditions, we have used another apparatus of field theory derived recently by us that uses concepts of normal ordering and Wick expansion with respect to a pathintegral measure (rather than the measure implied by thermal trace). We hope to demonstrate in our discussions that this way of formulating thermal manybody problems enables us to exploit deep similarities between thermal and zerotemperature situations which are difficult to discern in the traditional methods. Illustrative examples by way of deriving thermal Brillouin and Bruckner conditions for typical Fermionic and Bosonic problems are presented.
Item Type:  Article 

Source:  Copyright of this article belongs to Indian Academy of Sciences. 
Keywords:  Optimal Meanfield Description; Finitetemperature Manybody Theory; Thermal Brillouin Condition; Bruckner Conditions 
ID Code:  21847 
Deposited On:  23 Nov 2010 13:06 
Last Modified:  17 May 2016 06:00 
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