With the help of the time-dependent Lagrangian for a damped harmonic oscillator, the quantization of mesoscopic RLC circuit in the context of a number-phase quantization scheme is realized and the corresponding Hamilt...With the help of the time-dependent Lagrangian for a damped harmonic oscillator, the quantization of mesoscopic RLC circuit in the context of a number-phase quantization scheme is realized and the corresponding Hamiltonian operator is obtained. Then the evolution of the charge number and phase difference across the capacity are obtained. It is shown that the number-phase analysis is useful to tackle the quantization of some mesoscopic circuits and dynamical equations of the corresponding operators.展开更多
A packing of the complete directed symmetric graph DK v with m circuits, denoted by ( v,m) DCP, is defined to be a family of arc disjoint m circuits of DK v such that any one arc of DK v \ occurs...A packing of the complete directed symmetric graph DK v with m circuits, denoted by ( v,m) DCP, is defined to be a family of arc disjoint m circuits of DK v such that any one arc of DK v \ occurs in at most one m circuit. The packing number P(v,m) is the maximum number of m circuits in such a packing. The packing problem is to determine the value P(v,m) for every integer v≥m. In this paper, the problem is reduced to the case m+6≤v≤2m- 4m-3+12 , for any fixed even integer m≥4 . In particular, the values of P(v,m) are completely determined for m=12 , 14 and 16.展开更多
We discuss quantum fluctuation in excited states （named thermo number states） of mesoscopic LC circuits at a finite temperature. By introducing the coherent thermo state into the thermo field dynamics pioneered by U...We discuss quantum fluctuation in excited states （named thermo number states） of mesoscopic LC circuits at a finite temperature. By introducing the coherent thermo state into the thermo field dynamics pioneered by Umezawa and using the natural representation of thermo squeezing operator we can concisely derive the fluctuation. The result shows that the noise becomes larger when either temperature or the excitation number increases.展开更多
在过去10年里,基于量子力学的量子信号表示研究已经出现一些重要结果.然而,关于量子信号处理方面的研究却相对滞后,其中就包括量子信号的滤波处理.首先,改进了现有的数字信号的量子表示模型(quantum representation of digital signals,...在过去10年里,基于量子力学的量子信号表示研究已经出现一些重要结果.然而,关于量子信号处理方面的研究却相对滞后,其中就包括量子信号的滤波处理.首先,改进了现有的数字信号的量子表示模型(quantum representation of digital signals,QRDS),使其适用于任意长度的时间信号,同时还修改了QRDS模型中二补码的编码方法,使得新的编码更符合实际问题.然后,基于改进的模型引入了中值滤波方案,该方案回避了量子计算不能直接实现卷积运算的缺陷.为了实现该滤波方案的量子电路,又给出了基本量子运算模块:比较器模块、交换模块和中值计算模块.最后,通过实例验证了文中所提滤波方案的有效性和合理性.展开更多
Woodall 所引入的一个图 G 的联结数 bind(G)是|ΓG(×)|/|×|的最小值,其中×遍取V(G)的所有子集(×≠φ).ΓG(×)表示 G 中×的邻点集(ΓG(×)≠V(G)).本文得到了θ图θ_(r,s,t)及其线圈的联结数:(1)若 n...Woodall 所引入的一个图 G 的联结数 bind(G)是|ΓG(×)|/|×|的最小值,其中×遍取V(G)的所有子集(×≠φ).ΓG(×)表示 G 中×的邻点集(ΓG(×)≠V(G)).本文得到了θ图θ_(r,s,t)及其线圈的联结数:(1)若 n=r+s+t-1是偶数,则 bind(θ_(r,s,t)=1.(2)若 n 是奇数:当 r,s,t 均为偶数时,bind(θ_(r,s,t))=(r+s+t-2)/r+s+t;否则,bind(θ_(r,s,t,)=(r+s+t-2)/r+s+t-3.(3)若 r,s,t 中至少有一个大于2,则 bind(L(θ_(r,s,t,)=(r+s+t-1)/r+s+t-2.展开更多
文摘With the help of the time-dependent Lagrangian for a damped harmonic oscillator, the quantization of mesoscopic RLC circuit in the context of a number-phase quantization scheme is realized and the corresponding Hamiltonian operator is obtained. Then the evolution of the charge number and phase difference across the capacity are obtained. It is shown that the number-phase analysis is useful to tackle the quantization of some mesoscopic circuits and dynamical equations of the corresponding operators.
文摘A packing of the complete directed symmetric graph DK v with m circuits, denoted by ( v,m) DCP, is defined to be a family of arc disjoint m circuits of DK v such that any one arc of DK v \ occurs in at most one m circuit. The packing number P(v,m) is the maximum number of m circuits in such a packing. The packing problem is to determine the value P(v,m) for every integer v≥m. In this paper, the problem is reduced to the case m+6≤v≤2m- 4m-3+12 , for any fixed even integer m≥4 . In particular, the values of P(v,m) are completely determined for m=12 , 14 and 16.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10574060 and 10775097)the Natural Science Foundation of Shandong Province of China (Grant No. Y2008A23)the Shandong Province Higher Educational Science and Technology Program (Grant No. J09LA07)
文摘We discuss quantum fluctuation in excited states （named thermo number states） of mesoscopic LC circuits at a finite temperature. By introducing the coherent thermo state into the thermo field dynamics pioneered by Umezawa and using the natural representation of thermo squeezing operator we can concisely derive the fluctuation. The result shows that the noise becomes larger when either temperature or the excitation number increases.
文摘在过去10年里,基于量子力学的量子信号表示研究已经出现一些重要结果.然而,关于量子信号处理方面的研究却相对滞后,其中就包括量子信号的滤波处理.首先,改进了现有的数字信号的量子表示模型(quantum representation of digital signals,QRDS),使其适用于任意长度的时间信号,同时还修改了QRDS模型中二补码的编码方法,使得新的编码更符合实际问题.然后,基于改进的模型引入了中值滤波方案,该方案回避了量子计算不能直接实现卷积运算的缺陷.为了实现该滤波方案的量子电路,又给出了基本量子运算模块:比较器模块、交换模块和中值计算模块.最后,通过实例验证了文中所提滤波方案的有效性和合理性.
