论文标题
带有$ K $的量子多屈服系统中的波函数结构 - 条件$ q $ - 正常形式的强度功能
Wavefunction structure in quantum many-fermion systems with $k$-body interactions: conditional $q$-normal form of strength functions
论文作者
论文摘要
对于有限的量子，以$ n $ $ n $单粒子状态为$ m $ fermions并与$ k $ - 体相互作用（$ k \ leq m $）相互作用的许多粒子系统，使用随机矩阵理论研究了波函数结构。该系统的Hamiltonian被选为$ H = H_0（t） +λv（k）$，而不受干扰的$ H_0（t）$ Hamiltonian是$ t $ tuby-body-body-body-body-toperator和$ v（k）$ a $ a $ a $ a $ a $ a $ a $ k $ - 体内运算符，具有交互强度$λ$。代表独立高斯正交矩阵（$ t $和$ t $和$ k $ fermion spaces的随机矩阵）的$ h_0（t）$和$ v（k）$，前四个时刻，$ m $ $ $ - $ - $ $ - $ $ - $ - $ - $ - $ - $ -FERMIRS SPACES，其强度函数$F_κ（e）$是衍生的；强度函数包含有关波函数结构的所有信息。用$ e $表示$ h $ energies或eigenvalues，$κ$用能量$e_κ$表示不受干扰的基础状态，$f_κ（e）$，给出了$κ$ state的传播。结果表明，$f_κ（e）$的前四个矩与以下条件$ q $ - 正常分布的矩相同：这自然会使$f_κ（e）$不对称地相对于$ e $，$e_κ$增加，并且随着$e_κ$的峰值变化。因此，一般来说，具有$ k $ body交互的量子多屈光度系统中的波函数结构总体上遵循条件$ q $ - 正常的分布。
For finite quantum many-particle systems modeled with say $m$ fermions in $N$ single particle states and interacting with $k$-body interactions ($k \leq m$), the wavefunction structure is studied using random matrix theory. Hamiltonian for the system is chosen to be $H=H_0(t) + λV(k)$ with the unperturbed $H_0(t)$ Hamiltonian being a $t$-body operator and $V(k)$ a $k$-body operator with interaction strength $λ$. Representing $H_0(t)$ and $V(k)$ by independent Gaussian orthogonal ensembles (GOE) of random matrices in $t$ and $k$ fermion spaces respectively, first four moments, in $m$-fermion spaces, of the strength functions $F_κ(E)$ are derived; strength functions contain all the information about wavefunction structure. With $E$ denoting the $H$ energies or eigenvalues and $κ$ denoting unperturbed basis states with energy $E_κ$, the $F_κ(E)$ give the spreading of the $κ$ states over the eigenstates $E$. It is shown that the first four moments of $F_κ(E)$ are essentially same as that of the conditional $q$-normal distribution given in: P.J. Szabowski, Electronic Journal of Probability {\bf 15}, 1296 (2010). This naturally gives asymmetry in $F_κ(E)$ with respect to $E$ as $E_κ$ increases and also the peak value changes with $E_κ$. Thus, the wavefunction structure in quantum many-fermion systems with $k$-body interactions follows in general the conditional $q$-normal distribution.
