By virtue of the Weyl ordering method,we find a new formalism of optical field operator expansion in number state representation.Miscellaneous optical fields＇（coherent state,squeezed field,Wigner operator,etc.） new...By virtue of the Weyl ordering method,we find a new formalism of optical field operator expansion in number state representation.Miscellaneous optical fields＇（coherent state,squeezed field,Wigner operator,etc.） new expansions are therefore exhibited.Some new generating functions of special polynomials are derived herewith.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
Letf(x,y)=ax2+bxy+cy2,g(x,y)=Ax2+Bxy+Cy2,be two binary quadratic forms with real coefficients.A real number m is said to be represented by fif f(x,y)=m has a(rational)integer solution(x,y).We say f and g are equivalen...Letf(x,y)=ax2+bxy+cy2,g(x,y)=Ax2+Bxy+Cy2,be two binary quadratic forms with real coefficients.A real number m is said to be represented by fif f(x,y)=m has a(rational)integer solution(x,y).We say f and g are equivalent if there exists aninteger matrlx(r s t u)with determinant±1 such that f(x′,y′)=g(x,y),where展开更多
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10975125 and 11175113)
文摘By virtue of the Weyl ordering method,we find a new formalism of optical field operator expansion in number state representation.Miscellaneous optical fields＇（coherent state,squeezed field,Wigner operator,etc.） new expansions are therefore exhibited.Some new generating functions of special polynomials are derived herewith.
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Letf(x,y)=ax2+bxy+cy2,g(x,y)=Ax2+Bxy+Cy2,be two binary quadratic forms with real coefficients.A real number m is said to be represented by fif f(x,y)=m has a(rational)integer solution(x,y).We say f and g are equivalent if there exists aninteger matrlx(r s t u)with determinant±1 such that f(x′,y′)=g(x,y),where
