Detailed Balance and Intermediate Statistics

Higher Order Squeezing and Higher Order Subpoissonian Photon Statistics in Intermediate States

Recently simpler criteria for the Hong-Mandel higher order squeezing (HOS) and higher order subpossonian photon statistics (HOSPS) are provided by us [Phys. Lett. A 374 (2010) 1009]. Here we have used these simplified criteria to study the possibilities of observing HOSPS and HOS in different intermediate states, such as generalized binomial state, hypergeometric state, negative binomial state and photon added coherent state. It is shown that these states may satisfy the condition of HOS and HOSPS. It is also shown that the depth and region of nonclassicality can be controlled by controlling v…

利用含噪声中等规模量子器件获取经典非线性动力系统的稳态统计量

Steady-State Statistics of Classical Nonlinear Dynamical Systems from Noisy Intermediate-Scale Quantum Devices

本文探索用NISQ量子计算机经QPE和VQE求解FPE零模，以获取经典非线性动力系统的稳态PDF，并在一维Ornstein-Uhlenbeck问题上验证其与经典结果吻合。

On intermediate statistics across many-body localization transition

The level statistics in the transition between delocalized and localized {phases of} many body interacting systems is {considered}. We recall the joint probability distribution for eigenvalues resulting from the statistical mechanics for energy level dynamics as introduced by Pechukas and Yukawa. The resulting single parameter analytic distribution is probed numerically {via Monte Carlo method}. The resulting higher order spacing ratios are compared with data coming from different {quantum many body systems}. It is found that this Pechukas-Yukawa distribution compares favorably with {$β$--Gaus…

Detailed balance and entanglement

We study a connection between quantum detailed balance, which is a concept of importance in statistical mechanics, and entanglement. We also explore how this connection fits into thermofield dynamics.

The intermediate level statistics in dynamically localized chaotic eigenstates

We demonstrate that the energy or quasienergy level spacing distribution in dynamically localized chaotic eigenstates is excellently described by the Brody distribution, displaying the fractional power law level repulsion. This we show in two paradigmatic systems, namely for the fully chaotic eigenstates of the kicked rotator at K=7, and for the chaotic eigenstates in the mixed-type billiard system (Robnik 1983), after separating the regular and chaotic eigenstates by means of the Poincaré Husimi function, at very high energies with great statistical significance (587654 eigenstates, starting …

Permutation Phase and Gentile Statistics

This paper presents a new way to construct single-valued many-body wavefunctions of identical particles with intermediate exchange phases between Fermi and Bose statistics. It is demonstrated that the exchange phase is not a representation character but the \textit{word metric} of the permutation group, beyond the anyon phase from the braiding group in two dimensions. By constructing this type of wavefunction from the direct product of single-particle states, it is shown that a finite \textit{capacity q} -- the maximally allowed particle occupation of each quantum state, naturally arises. The …

Spectral statistics of Toeplitz matrices

Spectral statistics of hermitian random Toeplitz matrices with independent identically distributed elements is investigated numerically. It is found that the eigenvalue statistics of complex Toeplitz matrices is surprisingly well approximated by the semi-Poisson distribution belonging to intermediate-type statistics observed in certain pseudo-integrable billiards. The origin of intermediate behaviour could be attributed to the fact that Fourier transformed random Toeplitz matrices have the same slow decay outside the main diagonal as critical random matrix ensembles. The statistical properties…

Intermediate quantum maps for quantum computation

We study quantum maps displaying spectral statistics intermediate between Poisson and Wigner-Dyson. It is shown that they can be simulated on a quantum computer with a small number of gates, and efficiently yield information about fidelity decay or spectral statistics. We study their matrix elements and entanglement production, and show that they converge with time to distributions which differ from random matrix predictions. A randomized version of these maps can be implemented even more economically, and yields pseudorandom operators with original properties, enabling for example to produce …

Statistical properties of structured random matrices

Spectral properties of Hermitian Toeplitz, Hankel, and Toeplitz-plus-Hankel random matrices with independent identically distributed entries are investigated. Combining numerical and analytic arguments it is demonstrated that spectral statistics of all these random matrices is of intermediate type, characterized by (i) level repulsion at small distances, (ii) an exponential decrease of the nearest-neighbor distributions at large distances, (iii) a non-trivial value of the spectral compressibility, and (iv) the existence of non-trivial fractal dimensions of eigenvectors in Fourier space. Our fi…