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Abhishek Dhar - One of the best experts on this subject based on the ideXlab platform.
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Generating Function Formula of heat transfer in harmonic networks
Physical Review E, 2011Co-Authors: Keiji Saito, Abhishek DharAbstract:We consider heat transfer across an arbitrary classical harmonic network connected to two heat baths at different temperatures. The network has N positional degrees of freedom, of which N(L) are connected to a bath at temperature T(L) and N(R) are connected to a bath at temperature T(R). We derive an exact Formula for the cumulant Generating Function for heat transfer between the two baths. The Formula is valid even for N(L)≠N(R) and satisfies the Gallavotti-Cohen fluctuation symmetry. Since harmonic crystals in three dimensions are known to exhibit different regimes of transport such as ballistic, anomalous, and diffusive, our result implies validity of the fluctuation theorem in all regimes. Our exact Formula provides a powerful tool to study other properties of nonequilibrium current fluctuations.
Keiji Saito - One of the best experts on this subject based on the ideXlab platform.
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Generating Function Formula of heat transfer in harmonic networks
Physical Review E, 2011Co-Authors: Keiji Saito, Abhishek DharAbstract:We consider heat transfer across an arbitrary classical harmonic network connected to two heat baths at different temperatures. The network has N positional degrees of freedom, of which N(L) are connected to a bath at temperature T(L) and N(R) are connected to a bath at temperature T(R). We derive an exact Formula for the cumulant Generating Function for heat transfer between the two baths. The Formula is valid even for N(L)≠N(R) and satisfies the Gallavotti-Cohen fluctuation symmetry. Since harmonic crystals in three dimensions are known to exhibit different regimes of transport such as ballistic, anomalous, and diffusive, our result implies validity of the fluctuation theorem in all regimes. Our exact Formula provides a powerful tool to study other properties of nonequilibrium current fluctuations.
Fan Hongyi - One of the best experts on this subject based on the ideXlab platform.
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application of eigenkets of bosonic creation operator in deriving some new Formulas of associated laguerre polynomials
Communications in Theoretical Physics, 2008Co-Authors: Fan Hongyi, Wang TongtongAbstract:Using the resolution of unity composed of bosonic creation operator's eigenkets and annihilation operator's un-normalized eigenket, which is a new quantum mechanical representation in contour integration form, we derive new contour integration expression of associated Laguerre polynomials L?m(|z|2) and its generalized Generating Function Formula. A series of recursive relations regarding to L?m(|z|2) are also deduced in the context of the Fock representation by algebraic method.
Wang Tongtong - One of the best experts on this subject based on the ideXlab platform.
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application of eigenkets of bosonic creation operator in deriving some new Formulas of associated laguerre polynomials
Communications in Theoretical Physics, 2008Co-Authors: Fan Hongyi, Wang TongtongAbstract:Using the resolution of unity composed of bosonic creation operator's eigenkets and annihilation operator's un-normalized eigenket, which is a new quantum mechanical representation in contour integration form, we derive new contour integration expression of associated Laguerre polynomials L?m(|z|2) and its generalized Generating Function Formula. A series of recursive relations regarding to L?m(|z|2) are also deduced in the context of the Fock representation by algebraic method.
Doris D M Sang - One of the best experts on this subject based on the ideXlab platform.
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the rogers ramanujan gordon theorem for overpartitions
Proceedings of The London Mathematical Society, 2013Co-Authors: William Y C Chen, Doris D M SangAbstract:Let $B_{k,i}(n)$ be the number of partitions of $n$ with certain difference condition and let $A_{k,i}(n)$ be the number of partitions of $n$ with certain congruence condition. The Rogers-Ramanujan-Gordon theorem states that $B_{k,i}(n)=A_{k,i}(n)$. Lovejoy obtained an overpartition analogue of the Rogers-Ramanujan-Gordon theorem for the cases $i=1$ and $i=k$. We find an overpartition analogue of the Rogers-Ramanujan-Gordon theorem in the general case. Let $D_{k,i}(n)$ be the number of overpartitions of $n$ satisfying certain difference condition and $C_{k,i}(n)$ be the number of overpartitions of $n$ whose non-overlined parts satisfy certain congruences condition. We show that $C_{k,i}(n)=D_{k,i}(n)$. By using a Function introduced by Andrews, we obtain a recurrence relation which implies that the Generating Function of $D_{k,i}(n)$ equals the Generating Function of $C_{k,i}(n)$. We also find a Generating Function Formula of $D_{k,i}(n)$ by using Gordon marking representations of overpartitions, which can be considered as an overpartition analogue of an identity of Andrews for ordinary partitions.