PDM Damped-Driven Oscillators: Exact Solvability, Classical States Crossings, and Self-Crossings

Within the standard Lagrangian and Hamiltonian setting, we consider a position-dependent mass (PDM) classical particle performing a damped driven oscillatory (DDO) motion under the influence of a conservative harmonic oscillator force field $V\left( x\right) =\frac{1}{2}\omega ^{2}Q\left( x\right) x^{2}$ and subjected to a Rayleigh dissipative force field $\mathcal{R}\left( x,\dot{x}\right) =\frac{1}{2}b\,m\left( x\right) \dot{x}^{2}$ in the presence of an external periodic (non-autonomous) force $F\left( t\right) =F_{\circ }\,\cos \left( \Omega t\right) $. Where, the correlation between the coordinate deformation $\sqrt{Q(x)}$ and the velocity deformation $\sqrt{m(x)}$ is governed by a point canonical transformation $q\left( x\right) =\int \sqrt{m\left( x\right) }dx=\sqrt{%Q\left( x\right) }x$. Two illustrative examples are used: a non-singular PDM-DDO, and a power-law PDM-DDO models. Classical-states $\{x(t),p(t)\}$ crossings are analysed and reported. Yet, we observed/reported that as a classical state $\{x_{i}(t),p_{i}(t)\}$ evolves in time it may cross itself at an earlier and/or a later time/s.

Fundamental sensitivity bounds for quantum enhanced optical resonance sensors based on transmission and phase estimation

Quantum states of light can enable sensing configurations with sensitivities beyond the shot-noise limit (SNL). In order to better take advantage of available quantum resources and obtain the maximum possible sensitivity, it is necessary to determine fundamental sensitivity limits for different possible configurations for a given sensing system. Here, due to their wide applicability, we focus on optical resonance sensors, which detect a change in a parameter of interest through a resonance shift. We compare their fundamental sensitivity limits set by the quantum Cramér-Rao bound (QCRB) based on the estimation of changes in transmission or phase of a probing bright two-mode squeezed state (bTMSS) of light. We show that the fundamental sensitivity results from an interplay between the QCRB and the transfer function of the system. As a result, for a resonance sensor with a Lorentzian lineshape a phase-based scheme outperforms a transmission-based one for most of the parameter space; however, this is not the case for lineshapes with steeper slopes, such as higher order Butterworth lineshapes. Furthermore, such an interplay results in conditions under which the phase-based scheme provides a higher sensitivity but a smaller degree of quantum enhancement than the transmission-based scheme. We also study the effect of losses external to the sensor on the degree of quantum enhancement and show that for certain conditions, probing with a classical state can provide a higher sensitivity than probing with a bTMSS. Finally, we discuss detection schemes, namely optimized intensity-difference and optimized homodyne detection, that can achieve the fundamental sensitivity limits even in the presence of external losses.

Toolbox for non-classical state calculations

Computational challenges associated with the use of Wigner functions to identify non-classical properties of states are addressed with the aid of generating functions. It allows the computation of the Wigner functions of photon-subtracted states for an arbitrary number of subtracted photons. Both the formal definition of photon-subtracted states in terms of ladder operators and the experimental implementation with heralded photon detections are analyzed. These techniques are demonstrated by considering photon subtraction from squeezed thermal states as well as squeezed Fock states. Generating functions are also used for the photon statistics of these states. These techniques reveal various aspects of the parameter dependences of these states.

Confucianism and Philosophy of a Shared-Future Global Community in an Inter-civilisational World Order: Comparative Analysis of Their Relationships and Prospects

The Western-initiating international relations theoretical framework plays a fairly dominant role in analysing and initiating the prospects and scenarios of international order. However, with the peaceful rise of China, whose civlisation sustains almost 5000 years, China is playing a more proactive role in inter-civilisational international order; thus, in-depth explorations into Confucianism as the core element of Han Chinese Civilisation have been resurgent on the world stage, and it is indispensable for relevant scholars, intellectuals and strategists to closely evaluate unexploited implications and demystify the sustainability and intrinsic dynamism of Confucianism-themed Han Chinese Civilisation, and its implicit ties with a comparable philosophical concept of a global community of shared future. Through historical-studies approaches and comparative methodologies, the primary purpose of this paper seeks to crucially investigate a potential relationship between Confucianism and the philosophical concept of a global community of shared future ranging from the perspectives of historical origin, context, substance and so forth. It can be argued that the philosophical standpoint of a community of shared future for humankind bears historical significance and merits that Confucian thoughts somehow generate. This paper of research findings meanwhile predicts that China’s inter-civlisational international engagement as part of China’s soft-power strategy will proceed beyond classical state-based theoretic framework and the Confucian thoughts of the prevalence of public spirit and harmony without homogeneity will grow as an alternative guiding international norm in better services of rebuilding normative, inter-civilisational international order that a global community demands.

Quantum algorithms for escaping from saddle points

We initiate the study of quantum algorithms for escaping from saddle points with provable guarantee. Given a function f:Rn→R, our quantum algorithm outputs an ϵ-approximate second-order stationary point using O~(log2⁡(n)/ϵ1.75) queries to the quantum evaluation oracle (i.e., the zeroth-order oracle). Compared to the classical state-of-the-art algorithm by Jin et al. with O~(log6⁡(n)/ϵ1.75) queries to the gradient oracle (i.e., the first-order oracle), our quantum algorithm is polynomially better in terms of log⁡n and matches its complexity in terms of 1/ϵ. Technically, our main contribution is the idea of replacing the classical perturbations in gradient descent methods by simulating quantum wave equations, which constitutes the improvement in the quantum query complexity with log⁡n factors for escaping from saddle points. We also show how to use a quantum gradient computation algorithm due to Jordan to replace the classical gradient queries by quantum evaluation queries with the same complexity. Finally, we also perform numerical experiments that support our theoretical findings.

A Sign Logic-Based Method of Current Sensor Fault Detection for PMSM Drivers

A simplified method of current sensor fault detection and isolation (FDI) for permanent magnet synchronous motor (PMSM) drives, which only requires to collect the information of motor positions and currents of the measured phases, has been proposed in this paper. Compared with the classical state-observer-based approaches, the calculations needed in the new method only involve a few addition and logical operations. The simplicity and reliability of the new method makes itself especially useful for fault detection of current sensors in real-time control systems with limited computational capability, e.g., single-chip microcomputers (SCM) or field programmable gate arrays (FPGA). The experimental results on the basis of a FPGA controller have validated the feasibility and robustness of the proposed FDI approach.

Experimental localisation of quantum entanglement through monitored classical mediator

Quantum entanglement is a form of correlation between quantum particles that cannot be increased via local operations and classical communication. It has therefore been proposed that an increment of quantum entanglement between probes that are interacting solely via a mediator implies non-classicality of the mediator. Indeed, under certain assumptions regarding the initial state, entanglement gain between the probes indicates quantum coherence in the mediator. Going beyond such assumptions, there exist other initial states which produce entanglement between the probes via only local interactions with a classical mediator. In this process the initial entanglement between any probe and the rest of the system "flows through" the classical mediator and gets localised between the probes. Here we theoretically characterise maximal entanglement gain via classical mediator and experimentally demonstrate, using liquid-state NMR spectroscopy, the optimal growth of quantum correlations between two nuclear spin qubits interacting through a mediator qubit in a classical state. We additionally monitor, i.e., dephase, the mediator in order to emphasise its classical character. Our results indicate the necessity of verifying features of the initial state if entanglement gain between the probes is used as a figure of merit for witnessing non-classical mediator. Such methods were proposed to have exemplary applications in quantum optomechanics, quantum biology and quantum gravity.

Fractional data-driven control for a rotary flexible joint system

As one of the most promising topics in complex control processes, data-driven techniques have been widely used in numerous industrial sectors and have developed over the past two decades. In addition, the fractional-order controller has become more attractive in applied studies. In this article, a fractional integral control is implemented for a rotary flexible joint system. Moreover, an adjusted virtual reference feedback tuning (VRFT) technique is used to tune the fractional-order integrator. In this method, fractional integral control is designed based on state feedback control. Then, VRFT is adjusted and applied to the fractional integral controller. The effectiveness of the proposed adjusted VRFT method is discussed and presented through simulation and experimental results. The tracking performance of the rotary arm and the minimization of the vibration tip is evaluated based on the proposed method. In this article, the comparison of our proposed VRFT fractional scheme is made with the classical state feedback as well as a recently developed state feedback-based fractional order integral (SF-FOI) controller. The current investigations determine the performance improvement of our proposed scheme of comparable structure to the recent SF-FOI, with the introduction of the VRFT to the SF-FOI scheme.

The world experience of state support for the hotel business

The investigation of the world experience of state support for the hotel business is carried out in this paper. In the course of scientific research, the methods of analysis and synthesis are used in order to describe the forms and methods of state support for the hotel business; inductions and deductions in order to formulate the relevance, results and conclusions; method of analogy to highlight the features and peculiarities; schematic and tabular presentation of information to visualize the results of the investigation. In the study, the features of classical state support in leading countries have been presented. It is determined that in accordance with the international experience, the important and effective means of regulating the development of the hotel business are as follows: the implementation of legal methods (development of regulatory framework), implementation of strategic programs, innovative projects of hotel construction and similar accommodation facilities. Under COVID-19 conditions, a number of European governments developed unique assistance programs for various business sectors and plans for assisting the hotel business. It is defined that measures directed to support the hotel business include: direct grants or tax benefits; subsidized state guarantees for bank loans; public and private loans with subsidized interest rates; deferred payment of taxes and / or deferred social security contributions; wage subsidies to employees in order to avoid layoffs during the virus outbreak. It is established that in Ukraine the government has provided the program to support hotel business because of COVID-19 pandemic. However, such assistance lags far behind the hotel business support and promotion offered by developed foreign countries. It is reasonable for the government of Ukraine to monitor the methods of international state support for hotel business development and to introduce them in the national environment making it possible to keep them at the level of functioning without reducing the competitiveness of the national hotel business, to develop directions for their further strategic development, to find optimal methods of hotel business management under crisis conditions.

A trade-off between classical and quantum circuit size for an attack against CSIDH

We propose a heuristic algorithm to solve the underlying hard problem of the CSIDH cryptosystem (and other isogeny-based cryptosystems using elliptic curves with endomorphism ring isomorphic to an imaginary quadratic order 𝒪). Let Δ = Disc(𝒪) (in CSIDH, Δ = −4p for p the security parameter). Let 0 < α < 1/2, our algorithm requires:A classical circuit of size $2^{\tilde{O}\left(\log(|\Delta|)^{1-\alpha}\right)}.$A quantum circuit of size $2^{\tilde{O}\left(\log(|\Delta|)^{\alpha}\right)}.$Polynomial classical and quantum memory.Essentially, we propose to reduce the size of the quantum circuit below the state-of-the-art complexity $2^{\tilde{O}\left(\log(|\Delta|)^{1/2}\right)}$ at the cost of increasing the classical circuit-size required. The required classical circuit remains subexponential, which is a superpolynomial improvement over the classical state-of-the-art exponential solutions to these problems. Our method requires polynomial memory, both classical and quantum.