The Experts below are selected from a list of 126 Experts worldwide ranked by ideXlab platform
Itzhak Roditi - One of the best experts on this subject based on the ideXlab platform.
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Bethe states for the two-site Bose-Hubbard model: a binomial approach
2020Co-Authors: G. Santos, Angela Foerster, Itzhak RoditiAbstract:Abstract: We calculate explicitly the Bethe vectors states by the algebraic Bethe ansatz method with the gl(2)-invariant R-matrix for the two-site Bose-Hubbard model. Using a binomial expansion of the n-th power of a sum of two operators we get and solve a Recursion Equation. We calculate the scalar product and the norm of the Bethe vectors states. The form factors of the imbalance current operator are also computed.
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Bethe states for the two-site Bose–Hubbard model: A binomial approach
Physics Letters B, 2015Co-Authors: G. Santos, Angela Foerster, Itzhak RoditiAbstract:Abstract We calculate explicitly the Bethe vectors states by the algebraic Bethe ansatz method with the gl ( 2 ) -invariant R -matrix for the two-site Bose–Hubbard model. Using a binomial expansion of the n -th power of a sum of two operators we get and solve a Recursion Equation. We calculate the scalar product and the norm of the Bethe vectors states. The form factors of the imbalance current operator are also computed.
Joseph B Keller - One of the best experts on this subject based on the ideXlab platform.
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Stirling's formula derived simply
arXiv: Combinatorics, 2007Co-Authors: Joseph B Keller, Jean-marc Vanden-broeckAbstract:Stirling's formula, the asymptotic expansion of $n!$ for $n$ large, or of $\Gamma(z)$ for $z\to \infty$, is derived directly from the Recursion Equation $\Gamma(z+1) =z \Gamma(s)$ and the normalization condition $\Gamma ({1/2}) =\sqrt{\pi}$.
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a Recursion Equation for prime numbers
arXiv: Number Theory, 2007Co-Authors: Joseph B KellerAbstract:It is shown that the first $n$ prime numbers $p_1,...,p_n$ determine the next one by the Recursion Equation $$ p_{n+1} =\lim\limits_{s\to +\infty} [\prod\limits^n_{k=1} (1-\frac{1}{p^s_k}) \sum\limits^\infty_{j=1} \frac{1}{j^s} -1]^{-1/s}. $$ The upper limit on the sum can be replaced by $2p_n -1$, and the result still holds.
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Partition asymptotics from Recursion Equations
Siam Journal on Applied Mathematics, 1990Co-Authors: Charles Knessl, Joseph B KellerAbstract:A new method is presented for obtaining the asymptotic behavior, for both n and s large, of the number of partitions of an integer n into s parts of various kinds. It involves solving a Recursion Equation satisfied by the number of partitions, using asymptotic methods of applied mathematics such as the WKB method, the ray method, and the method of matched asymptotic expansions. It is applied to partitions of n into s parts, into s distinct parts, into srth powers, and into s parts which differ by at least d. The method can be applied to many other problems in partition theory and in combinatorics.
Andreas Langousis - One of the best experts on this subject based on the ideXlab platform.
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Break of temporal symmetry in a stationary Markovian setting: evidencing an arrow of time, and parameterizing linear dependencies using fractional low-order joint moments
Stochastic Environmental Research and Risk Assessment, 2020Co-Authors: Alin Andrei Carsteanu, Andreas LangousisAbstract:We demonstrate that “an arrow of time” that is being determined by the joint distributions of successive process variables, or equivalently a break of temporal symmetry (i.e. a symmetry/asymmetry dichotomy), can be evidenced solely on probabilistic grounds, on the basis of structural dependencies and statistical attributes of observed quantities, without the intervention of any symmetric or asymmetric physical laws. We do so for the simplest case of stable Markovian Recursions, and show that a break of temporal symmetry can occur as the combined effect of lack of Gaussianity and statistical dependencies, even in the case when the increments of the generated process are independent and identically distributed with symmetric marginal. This striking result occurs under conditions of stationarity, without any changes in the dynamic Recursion Equation of the process, allowing for statistical characterization of temporal symmetries versus asymmetries. To that end, we introduce and exemplify the use of an estimator based on fractional low-order joint moments, which exists for all stationary stochastic processes with strictly stable symmetric marginals, and can be used to parameterize their dependence structure in a linear setting.
G. Santos - One of the best experts on this subject based on the ideXlab platform.
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Bethe states for the two-site Bose-Hubbard model: a binomial approach
2020Co-Authors: G. Santos, Angela Foerster, Itzhak RoditiAbstract:Abstract: We calculate explicitly the Bethe vectors states by the algebraic Bethe ansatz method with the gl(2)-invariant R-matrix for the two-site Bose-Hubbard model. Using a binomial expansion of the n-th power of a sum of two operators we get and solve a Recursion Equation. We calculate the scalar product and the norm of the Bethe vectors states. The form factors of the imbalance current operator are also computed.
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Bethe states for the two-site Bose–Hubbard model: A binomial approach
Physics Letters B, 2015Co-Authors: G. Santos, Angela Foerster, Itzhak RoditiAbstract:Abstract We calculate explicitly the Bethe vectors states by the algebraic Bethe ansatz method with the gl ( 2 ) -invariant R -matrix for the two-site Bose–Hubbard model. Using a binomial expansion of the n -th power of a sum of two operators we get and solve a Recursion Equation. We calculate the scalar product and the norm of the Bethe vectors states. The form factors of the imbalance current operator are also computed.
Alin Andrei Carsteanu - One of the best experts on this subject based on the ideXlab platform.
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Break of temporal symmetry in a stationary Markovian setting: evidencing an arrow of time, and parameterizing linear dependencies using fractional low-order joint moments
Stochastic Environmental Research and Risk Assessment, 2020Co-Authors: Alin Andrei Carsteanu, Andreas LangousisAbstract:We demonstrate that “an arrow of time” that is being determined by the joint distributions of successive process variables, or equivalently a break of temporal symmetry (i.e. a symmetry/asymmetry dichotomy), can be evidenced solely on probabilistic grounds, on the basis of structural dependencies and statistical attributes of observed quantities, without the intervention of any symmetric or asymmetric physical laws. We do so for the simplest case of stable Markovian Recursions, and show that a break of temporal symmetry can occur as the combined effect of lack of Gaussianity and statistical dependencies, even in the case when the increments of the generated process are independent and identically distributed with symmetric marginal. This striking result occurs under conditions of stationarity, without any changes in the dynamic Recursion Equation of the process, allowing for statistical characterization of temporal symmetries versus asymmetries. To that end, we introduce and exemplify the use of an estimator based on fractional low-order joint moments, which exists for all stationary stochastic processes with strictly stable symmetric marginals, and can be used to parameterize their dependence structure in a linear setting.