PT-symmetry entails pseudo-Hermiticity regardless of diagonalizability

We prove that in finite dimensions, a Parity-Time (PT)-symmetric Hamiltonian is necessarily pseudo-Hermitian regardless of whether it is diagonalizable or not. This result is different from Mostafazadeh's, which requires the Hamiltonian to be diagonalizable. PT-symmetry breaking often occurs at exceptional points where the Hamiltonian is not diagonalizable. Our result implies that PT-symmetry breaking is equivalent to the onset of instabilities of pseudo-Hermitian systems, which was systematically studied by Krein et al. in 1950s. In particular, we show that the mechanism of PT-symmetry breaking is the resonance between eigenmodes with different Krein signatures.Comment: 11pages, 1 figure. arXiv admin note: text overlap with arXiv:1801.0167

Semiquantum key distribution with secure delegated quantum computation

Semiquantum key distribution allows a quantum party to share a random key with a "classical" party who only can prepare and measure qubits in the computational basis or reorder some qubits when he has access to a quantum channel. In this work, we present a protocol where a secret key can be established between a quantum user and an almost classical user who only needs the quantum ability to access quantum channels, by securely delegating quantum computation to a quantum server. We show the proposed protocol is robust even when the delegated quantum server is a powerful adversary, and is experimentally feasible with current technology. As one party of our protocol is the most quantum-resource efficient, it can be more practical and significantly widen the applicability scope of quantum key distribution.Comment: 7 pages, 2 figure

What breaks parity-time-symmetry? -- pseudo-Hermiticity and resonance between positive- and negative-action modes

It is generally believed that Parity-Time (PT)-symmetry breaking occurs when eigenvalues or both eigenvalues and eigenvectors coincide. However, we show that this well-accepted picture of PT-symmetry breaking is incorrect. Instead, we demonstrate that the physical mechanism of PT-symmetry breaking is the resonance between positive- and negative-action modes. It is proved that PT-symmetry breaking occurs when and only when this resonance condition is satisfied, and this mechanism applies to all known PT-symmetry breakings observed in different branches of physics. The result is achieved by proving a remarkable fact that in finite dimensions, a PT-symmetric Hamiltonian is necessarily pseudo-Hermitian, regardless whether it is diagonalizable or not.Comment: 15 pages, 3 figure

Lattice complexity and fine graining of symbolic sequence

A new complexity measure named as Lattice Complexity is presented for finite symbolic sequences. This measure is based on the symbolic dynamics of one-dimensional iterative maps and Lempel-Ziv Complexity. To make Lattice Complexity distinguishable from Lempel-Ziv Complexity, an approach called fine-graining process is also proposed. When the control parameter fine-graining order is small enough, the two measures are almost equal. While the order increases, the difference between the two measures becomes more and more significant. Applying Lattice Complexity to logistic map with a proper order, we find that the sequences that are regarded as complex are roughly at the edges of chaotic regions. Further derived properties of the two measures concerning the fine-graining process are also discussed.Comment: 16 page, 8 figures,a revised English version of a article published in Chines

Kelvin-Helmholtz instability is the result of parity-time symmetry breaking

Parity-Time (PT)-symmetry is being actively investigated as a fundamental property of observables in quantum physics. We show that the governing equations of the classical two-fluid interaction and the incompressible fluid system are PT-symmetric, and the well-known Kelvin-Helmholtz instability is the result of spontaneous PT-symmetry breaking. It is expected that all classical conservative systems governed by Newton's law admit PT-symmetry, and the spontaneous breaking thereof is a generic mechanism for classical instabilities. Discovering the PT-symmetry of systems in fluid dynamics and plasma physics and identifying the PT-symmetry breaking responsible for instabilities enable new techniques to classical physics and enrich the physics of PT-symmetry.Comment: 11 pages, 1 figur

Understanding the Temporal Fading in Wireless Industrial Networks: Measurements and Analyses

The wide deployment of wireless industrial networks still faces the challenge of unreliable service due to severe multipath fading in industrial environments. Such fading effects are not only caused by the massive metal surfaces existing within the industrial environment but also, more significantly, the moving objects including operators and logistical vehicles. As a result, the mature analytical framework of mobile fading channel may not be appropriate for the wireless industrial networks especially the majority fixed wireless links. In this paper, we propose a qualitative analysis framework to characterize the temporal fading effects of the fixed wireless links in industrial environments, which reveals the essential reason of correlated temporal variation of both the specular and scattered power. Extensive measurements with both the envelop distribution and impulse response from field experiments validate the proposed qualitative framework, which will be applicable to simulate the industrial multipath fading characteristics and to derive accurate link quality metrics to support reliable wireless network service in various industrial applications

On the physical mechanism of three-wave instabilities -- resonance between positive- and negative-action modes

Three-wave instability is a fundamental process that has important applications in many branches of physics. It is widely accepted that the resonant condition $\omega_{z}\approx\omega_{x}+\omega_{y}$ for participating waves is the criteria for the onset of the instability. We show that this condition is neither sufficient nor necessary, instead, the exact criteria for the onset of the instability is that a positive-action mode resonates with a negative-action mode. This mechanism is imposed by the topology and geometry of the spectral space. Guided by this new theory, additional instability bands previously unknown are discovered.Comment: 14 pages, 4 figure

A lattice Maxwell system with discrete space-time symmetry and local energy-momentum conservation

A lattice Maxwell system is developed with gauge-symmetry, symplectic structure and discrete space-time symmetry. Noether's theorem for Lie group symmetries is generalized to discrete symmetries for the lattice Maxwell system. As a result, the lattice Maxwell system is shown to admit a discrete local energy-momentum conservation law corresponding to the discrete space-time symmetry. These conservative properties make the discrete system an effective algorithm for numerically solving the governing differential equations on continuous space-time. Moreover, the lattice model, respecting all conservation laws and geometric structures, is as good as and probably more preferable than the continuous Maxwell model. Under the simulation hypothesis by Bostrom and in consistent with the discussion on lattice QCD by Beane et al., the two interpretations of physics laws on space-time lattice could be essentially the same.Comment: 12 page

ηc\eta_c production associated with light hadrons at the B-factories and the future super B-factories

We present a complete study of the associated production of the $\eta_c$ meson with light hadrons in $e^+e^-$ collisions at the B-factory energy, which is demonstrated to be one of the best laboratories for testing the colour-octet (CO) mechanism. The colour-siglet contributions are evaluated up to $O(\alpha^2\alpha_s^3)$ while the CO ones are evaluated up to $O(\alpha^2\alpha_s^2)$. For the first time, the angular distribution of the $^1S_0^{[8]}$ production is studied at QCD next-to-leading order. We find that the $^1S_0^{[8]}$ channel dominate the total cross section, while the $^1P_1^{[8]}$ one exhibit its importance in the angular distribution, which turns out to be downward going with respect to $\mathrm{cos}\theta$. This can be considered as the most distinct signal for the CO mechanism

Fidelity susceptibility and geometric phase in critical phenomenon

Motivated by recent development in quantum fidelity and fidelity susceptibility, we study relations among Lie algebra, fidelity susceptibility and quantum phase transition for a two-state system and the Lipkin-Meshkov-Glick model. We get the fidelity susceptibility for SU(2) and SU(1,1) algebraic structure models. From this relation, the validity of the fidelity susceptibility to signal for the quantum phase transition is also verified in these two systems. At the same time, we obtain the geometric phase in these two systems in the process of calculating the fidelity susceptibility. In addition, the new method of calculating fidelity susceptibility has been applied to explore the two-dimensional XXZ model and the Bose-Einstein condensate(BEC).Comment: 12 pages, 4 figure