本文我们引进了拟乘法分拆函数的概念,并证明了下述:定理 B 设 h(n)是拟乘法分拆函数,如果0<q<2,则 h(n)<n/logkn,对每个正整数 k 和充分大的 n。定理 C 设 h(n)是拟乘法分拆函数,则(i)若 d=0,则 h(n)≡0,对一切 n∈N。(ii)若2...本文我们引进了拟乘法分拆函数的概念,并证明了下述:定理 B 设 h(n)是拟乘法分拆函数,如果0<q<2,则 h(n)<n/logkn,对每个正整数 k 和充分大的 n。定理 C 设 h(n)是拟乘法分拆函数,则(i)若 d=0,则 h(n)≡0,对一切 n∈N。(ii)若2~m<q<2^(m+1),其中 m 是正整数,则存在某个0<ε<1,使得h(n)≤dn^(m+ε),对一切 n 成立。(iii)若 q=2~m,其中 m 是某个正整数,则h(n)≤dn^m,对一切展开更多
The imaginary time path integral formalism offers a powerful numerical tool for simulating thermodynamic properties of realistic systems.We show that,when second-order and fourth-order decompositions are employed,they...The imaginary time path integral formalism offers a powerful numerical tool for simulating thermodynamic properties of realistic systems.We show that,when second-order and fourth-order decompositions are employed,they share a remarkable unified analytic form for the partition function of the harmonic oscillator.We are then able to obtain the expression of the thermodynamic property and the leading error terms as well.In order to obtain reasonably optimal values of the free parameters in the generalized symmetric fourth-order decomposition scheme,we eliminate the leading error terms to achieve the accuracy of desired order for the thermodynamic property of the harmonic system.Such a strategy leads to an efficient fourth-order decomposition that produces thirdorder accurate thermodynamic properties for general systems.展开更多
文摘本文我们引进了拟乘法分拆函数的概念,并证明了下述:定理 B 设 h(n)是拟乘法分拆函数,如果0<q<2,则 h(n)<n/logkn,对每个正整数 k 和充分大的 n。定理 C 设 h(n)是拟乘法分拆函数,则(i)若 d=0,则 h(n)≡0,对一切 n∈N。(ii)若2~m<q<2^(m+1),其中 m 是正整数,则存在某个0<ε<1,使得h(n)≤dn^(m+ε),对一切 n 成立。(iii)若 q=2~m,其中 m 是某个正整数,则h(n)≤dn^m,对一切
基金supported by the National Natural Science Foundation of China(No.21961142017,No.22073009 and No.21421003)the Ministry of Science and Technology of China(No.2017YFA0204901)。
文摘The imaginary time path integral formalism offers a powerful numerical tool for simulating thermodynamic properties of realistic systems.We show that,when second-order and fourth-order decompositions are employed,they share a remarkable unified analytic form for the partition function of the harmonic oscillator.We are then able to obtain the expression of the thermodynamic property and the leading error terms as well.In order to obtain reasonably optimal values of the free parameters in the generalized symmetric fourth-order decomposition scheme,we eliminate the leading error terms to achieve the accuracy of desired order for the thermodynamic property of the harmonic system.Such a strategy leads to an efficient fourth-order decomposition that produces thirdorder accurate thermodynamic properties for general systems.