Tunneling Catastrophes of the Partition Function
نویسندگان
چکیده
منابع مشابه
Tunneling Catastrophes of the Partition Function
We use path-integrals to derive a general expression for the semiclassical approximation to the partition function of a one-dimensional quantummechanical system. Our expression depends solely on ordinary integrals which involve the potential. For high temperatures, the semiclassical expression is dominated by single closed paths. As we lower the temperature, new closed paths may appear, includi...
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We apply the Ginzburg criterion to the dimer problem and we solve the apparent contradiction of a system with mean field α = 12 , the typical value of tricritical systems, and upper critical dimension Dcr = 6. We find that the system has upper critical dimensionDcr = 6 , while for D ≤ 4 it should undergo a first order phase transition. We comment on the latter wrong result examining the approxi...
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In 1918, Hardy and Ramanujan wrote their landmark paper deriving the asymptotic formula for the partition function. The paper however was fundamental for another reason, namely for introducing the circle method in questions of additive number theory. Though this method is powerful, it is often difficult and technically complicated to employ. In 2011, Bruinier and Ono discovered a new algebraic ...
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Ramanujan also conjectured that congruences (1) exist for the cases A = 5 , 7 , or 11 . This conjecture was proved by Watson [17] for the cases of powers of 5 and 7 and Atkin [3] for the cases of powers of 11. Since then, the problem of finding more examples of such congruences has attracted a great deal of attention. However, Ramanujan-type congruences appear to be very sparse. Prior to the la...
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ژورنال
عنوان ژورنال: Brazilian Journal of Physics
سال: 1997
ISSN: 0103-9733
DOI: 10.1590/s0103-97331997000300006