Pseudo-Hermitian ensemble of random Gaussian matrices.
نویسندگان
چکیده
It is shown how pseudo-Hermiticity, a necessary condition satisfied by operators of PT symmetric systems can be introduced in the three Gaussian classes of random matrix theory. The model describes transitions from real eigenvalues to a situation in which, apart from a residual number, the eigenvalues are complex conjugate.
منابع مشابه
A pseudo-unitary ensemble of random matrices, PT-symmetry and the Riemann Hypothesis
An ensemble of 2 × 2 pseudo-Hermitian random matrices is constructed that possesses real eigenvalues with level-spacing distribution exactly as for the Gaussian unitary ensemble found by Wigner. By a re-interpretation of Connes’ spectral interpretation of the zeros of Riemann zeta function, we propose to enlarge the scope of search of the Hamiltonian connected with the celebrated Riemann Hypoth...
متن کاملua nt - p h / 04 07 15 4 v 1 2 0 Ju l 2 00 4 Gaussian - random Ensembles of Pseudo - Hermitian Matrices ∗
Attention has been brought to the possibility that statistical fluctuation properties of several complex spectra, or, well-known number sequences may display strong signatures that the Hamiltonian yielding them as eigenvalues is PT-symmetric (Pseudo-Hermitian). We find that the random matrix theory of pseudo-Hermitian Hamiltonians gives rise to new universalities of levelspacing distributions o...
متن کاملThe pseudo-Wishart distribution and its application to MIMO systems
The pseudo-Wishart distribution arises when a Hermitian matrix generated from a complex Gaussian ensemble is not full-rank. It plays an important role in the analysis of communication systems using diversity in Rayleigh fading. However, it has not been extensively studied like the Wishart distribution. Here, we derive some key aspects of the complex pseudo-Wishart distribution. Pseudo-Wishart a...
متن کاملEstimates for moments of random matrices with Gaussian elements
We describe an elementary method to get non-asymptotic estimates for the moments of Hermitian random matrices whose elements are Gaussian independent random variables. We derive a system of recurrent relations for the moments and the covariance terms and develop a triangular scheme to prove the recurrent estimates. The estimates we obtain are asymptotically exact in the sense that they give exa...
متن کاملPseudounitary symmetry and the Gaussian pseudounitary ensemble of random matrices.
Employing the currently discussed notion of pseudo-Hermiticity, we define a pseudounitary group. Further, we develop a random matrix theory that is invariant under such a group and call this ensemble of pseudo-Hermitian random matrices the pseudounitary ensemble. We obtain exact results for the nearest-neighbor level-spacing distribution for (2 x 2) PT-invariant Hamiltonian matrices that have f...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Physical review. E
دوره 94 1-1 شماره
صفحات -
تاریخ انتشار 2016