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We study the spectral problem in deformed supersymmetric quantum mechanics with polynomial superpotential by using the exact WKB method and the TBA equations. We apply the ODE/IM correspondence to the Schrödinger equation with an effective potential deformed by integrating out the fermions, which admits a continuous deformation parameter. We find that the TBA equations are described by the ℤ4-extended ones. For cubic superpotential corresponding to the symmetric double-well potential, the TBA system splits into the two D3-type TBA equations. We investigate in detail this example based on the TBA equations and their analytic continuation as well as the massless limit. We find that the energy spectrum obtained from the exact quantization condition is in good agreement with the diagonalization approach of the Hamiltonian. [ABSTRACT FROM AUTHOR]

In information transfer, the dissipation of a signal is of crucial importance. The feasibility of reconstructing the distorted signal depends on the related permanent loss. Therefore, understanding the quantized dissipative transversal mechanical waves might result in deep insights. In particular, it may be valid on the nanoscale in the case of signal distortion, loss, or even restoration. Based on the description of the damped quantum oscillator, we generalize the canonical quantization procedure for the case of the transversal waves. Then, we deduce the related damped wave equation and the state function. We point out the two possible solutions of the propagating-damping wave equation. One involves the well-known Gaussian spreading solution superposed with the damping oscillation, in which the loss of information is complete. The other is the Airy function solution, which is non-spreading–propagating, so the information loss is only due to oscillation damping. However, the structure of the wave shape remains unchanged for the latter. Consequently, this fact may allow signal reconstruction, resulting in the capability of restoring the lost information. [ABSTRACT FROM AUTHOR]

With the rapid development of microtechnology, the low-dimensional materials are fabricated with nontrivial topological structures, and then the action of geometric properties on the effective dynamics receives increasing attention. It is an effective theory that the quantum mechanics of low-dimensional curved systems can be given by using the thin-layer quantization approach, in which the geometric potential and the geometric momentum have been demonstrated experimentally. In the present paper, the thin-layer quantization formalism is first recalled, its fundamental calculation framework is first clarified, and the geometric quantum effects result from the diffeomorphism transformation and the rotation transformation connecting the local frames of different points. The results are helpful to understand the gravitational gauge and emerging gauge, and to image the geometries implied in the artificial gauge. In the particular quantum systems, the novel physical phenomena are briefly recalled that are induced by geometry, such as resonation tunneling, quantum block, quantum Hall effect, quantum Hall viscosity, quantum spin Hall effect, effective monopole magnetic field and so on. The results will shed light from a different angle on the relationships between the geometry and the novel physical phenomenon. [ABSTRACT FROM AUTHOR]

The article discusses the possibility of breaking Penrose's weak cosmic censorship conjecture in black hole collisions in higher dimensions using the technique called large D. It is stated that in black hole collisions with sufficient angular momentum, the resulting black hole is unstable and can split into two, creating a divergent curvature throat. The relationship between physics at different scales in a physical system is also mentioned, as well as the need to quantize theories to understand physics at the microscopic scale. Additionally, the need for a quantum theory of gravity to make predictions at increasingly higher energies is mentioned. [Extracted from the article]

This paper discusses the introduction of quantum ideas in general physics and education. Considering the fragile environment of physics education, the paper suggests three possible ways to help teaching and learning of quantum physics, (1) quantum metrics (2) simple experiments demonstrating quantum quantities (3) fractal and quantum analogies between worlds. From this perspective, this paper is also meant to be a test indicator of quantum popularity in physics and education. [ABSTRACT FROM AUTHOR]

We apply the exact Wentzel–Kramers–Brillouin (WKB) analysis to a couple of 1D Schrödinger-type equations reduced from the Stark effect of hydrogen in a uniform electric field. By introducing Langer's modification and incorporating the Stokes graphs, we prove the exactness of the Bohr–Sommerfeld quantization conditions for the Borel-resummed quantum WKB periods in the specific parameter regions of the electric field intensity and magnetic quantum number. It is also found these quantization conditions get modified with an additional suppressed contribution when the parameters vary beyond the specific regions. We also present thermodynamic Bethe ansatz (TBA) equations governing the quantum periods in the absence of Langer's modification and discuss its wall-crossing and analytic continuation. Numerical calculations are conducted to compare the complex resonant frequencies from our quantization conditions against ones from the Riccati–Padé method; the TBA equations are also confirmed by comparing its expansions with all-order quantum periods. [ABSTRACT FROM AUTHOR]

Capacity crunch has become critical in recent years as commercial communication systems approach their theoretical data rate limits. This work presents a low‐complexity digital backpropagation (DBP) implementation approach based on step size distribution that uses a binary logarithmic step size method to achieve high data rate optical transmission. The proposed scheme shows performance improvements (∆Q) of 2.36, 1.19, and 0.71 dB over linear compensation, constant step size (CSS) DBP, and logarithmic step size DBP techniques in a 2400 km 112 Gbit/s DP‐16 quadrature amplitude modulation (QAM) system, respectively. At 13 dBm, a high performance (Q) of 10.9 dB (BER = 2.25 × 10−4) is achieved, above the 3.80 × 10−3 hard‐decision forward error correction (HD‐FEC) limit, using the proposed scheme. Also, the allowable transmission distance is extended by 960 km at the HD‐FEC limit over the linear compensation technique. The optimization achieves a 38% saving in the number of DBP calculation steps compared to the CSS DBP, which considerably reduces the computational cost since a few steps are required for effective non‐linearity compensation. [ABSTRACT FROM AUTHOR]

We report on a quantum mechanics popularisation software, Eigengame, developed to get general audiences to play with key concepts in quantum mechanics, i.e., the wave function, the quantization of energy, the probability density and, to some extent, the measurement problem. The software is developed in python and is available online at github. [ABSTRACT FROM AUTHOR]

We consider the Dirac quantization in the first-class formalism to investigate the hypersphere soliton model (HSM) defined on the S 3 hypersphere. To do this, we construct the first-class Hamiltonian possessing the Weyl ordering correction. In the HSM, we evaluate the baryon physical quantities such as the baryon masses, magnetic moments, axial coupling constant and charge radii, most predicted values of which are in good agreement with the corresponding experimental data. Moreover, shuffling the baryon and transition magnetic moments, we find the model independent sum rules. In the HSM we also evaluate the baryon intrinsic frequencies such as ω N = 0.87 × 10 23 s − 1 and ω Δ = 1.74 × 10 23 s − 1 of the nucleon and delta baryon, respectively, to yield the identity ω Δ = 2 ω N . Next, making use of the Nambu-Goto string action and its extended rotating bosonic string theory, we formulate the stringy photon model to obtain the energy of the string configuration, which consists of the rotational and vibrational energies of the open string. Exploiting this total string energy, we evaluate the photon intrinsic frequency ω γ = 9.00 × 10 23 s − 1 , which is comparable to the corresponding baryon intrinsic frequencies. We also predict the photon size 〈 r 2 〉 1 / 2 (photon) = 0.17 fm , which is approximately 21% of the proton magnetic charge radius. [ABSTRACT FROM AUTHOR]

We develop the theory of transformation of intensive initial nonlinear wave pulses to trains of solitons emerging at asymptotically large time of evolution. Our approach is based on the theory of dispersive shock waves in which the number of nonlinear oscillations in the shock becomes the number of solitons at the asymptotic state. We show that this number of oscillations, which is proportional to the classical action of particles associated with the small-amplitude edges of shocks, is preserved by the dispersionless flow. Then, the Poincaré–Cartan integral invariant is also constant, and therefore, it reduces to the quantization rule similar to the Bohr–Sommerfeld quantization rule for a linear spectral problem associated with completely integrable equations. This rule yields a set of "eigenvalues," which are related to the asymptotic solitons' velocities and their characteristics. It is implied that the soliton equations under consideration give modulationally stable solutions; therefore, these "eigenvalues" are real. Our analytical results agree very well with the results of numerical solutions of the generalized defocusing nonlinear Schrödinger equation. [ABSTRACT FROM AUTHOR]

To the existing list of alternative formulations of quantum mechanics, a new version of the non-Hermitian interaction picture is added. What is new is that, in contrast to the more conventional non-Hermitian model-building recipes, the primary information about the observable phenomena is provided not only by the Hamiltonian but also by an additional operator with a real spectrum (say, R (t) ) representing another observable. In the language of physics, the information carried by R (t) ≠ R † (t) opens the possibility of reaching the exceptional-point degeneracy of the real eigenvalues, i.e., a specific quantum phase transition. In parallel, the unitarity of the system remains guaranteed, as usual, via a time-dependent inner-product metric Θ (t) . From the point of view of mathematics, the control of evolution is provided by a pair of conjugate Schrödiner equations. This opens the possibility od an innovative dyadic representation of pure states, by which the direct use of Θ (t) is made redundant. The implementation of the formalism is illustrated via a schematic cosmological toy model in which the canonical quantization leads to the necessity of working with two conjugate Wheeler-DeWitt equations. From the point of view of physics, the "kinematical input" operator R (t) may represent either the radius of a homogeneous and isotropic expanding empty Universe or, if you wish, its Hubble radius, or the scale factor a (t) emerging in the popular Lemaitre-Friedmann-Robertson-Walker classical solutions, with the exceptional-point singularity of the spectrum of R (t) mimicking the birth of the Universe ("Big Bang") at t = 0 . [ABSTRACT FROM AUTHOR]

Following our previous study of the Bohr–Sommerfeld (BS) quantization condition for one-dimensional case [J. C. del Valle and A. V. Turbiner, Int. J. Mod. Phys. A36, 2150221 (2021)], we extend it to d -dimensional power-like radial potentials. The BS quantization condition for S -states of the d -dimensional radial Schrödinger equation is proposed. Based on numerical results obtained for the spectra of power-like potentials, V (r) = r m with m ∈ [ − 1 , ∞) , the correctness of the proposed BS quantization condition is established for various dimensions d. It is demonstrated that by introducing the WKB correction γ into the right-hand side of the BS quantization condition leads to the so-called exact WKB quantization condition, which reproduces the exact energies, while γ remains always very small. For m = 2 (any integer d) and for m = − 1 (at d = 2) the WKB correction γ = 0 : for S states the BS spectra coincides with the exact ones. Concrete calculations for physically important cases of linear, cubic, quartic and sextic oscillators, as well as Coulomb and logarithmic potentials in dimensions d = 2 , 3 , 6 are presented. Radial quartic anharmonic oscillator is considered briefly. [ABSTRACT FROM AUTHOR]

The angular momentum of any quantum system should be unambiguously quantized. We show that such a quantization fails for a pure Dirac monopole due to a previously overlooked field angular momentum from the monopole-electric charge system coming from the magnetic field of the Dirac string and the electric field of the charge. Applying the point-splitting method to the monopole-charge system yields a total angular momentum which obeys the standard angular momentum algebra, but which is gauge variant. In contrast it is possible to properly quantize the angular momentum of a topological 't Hooft–Polyakov monopole plus charge. This implies that pure Dirac monopoles are not viable – only 't Hooft–Polyakov monopoles are theoretically consistent with angular momentum quantization and gauge invariance. [ABSTRACT FROM AUTHOR]

In the current article, utilizing the theory of quantization of time and space and the internal structure of elementary particles, the radiation spectrum of the excited hydrogen atom is calculated theoretically. By doing this, the electron movement parameters in the hydrogen atom have been stated in a novel way, and via generalizing these calculations, the excited states of other atoms can be calculated. It can be shown that during the transfer of the electron from a higher level to a lower one, what is the state of the electron in terms of momentum, energy, time, and length. [ABSTRACT FROM AUTHOR]

Using the thin-layer quantization, we formulate the problem of a Schrödinger particle constrained to move along a coordinate surface of the bi-spherical coordinate system. In three-dimensional space, the free Schrödinger equation is not separable in this coordinate system. However, when we consider the equation for a particle constrained to a given surface, there are only two degrees of freedom. One has to introduce a geometrical potential to attach the particle to the surface. This well-known potential has two contributions: one from Gauss' curvature and the other from the mean curvature. The Schrödinger equation leads to a general Heun equation. We solve it exactly and present the eigenfunctions and plots of the probability densities, and, as an application of this methodology, we study the problem of an electric charge propagating along these coordinate surfaces in the presence of a uniform magnetic field. [ABSTRACT FROM AUTHOR]

We show that the strongly coupled field theory holographically dual to the Gubser-Rocha anti-de-Sitter Einstein-Maxwell-Dilaton theory describes not a single non-trivial AdS2 IR fixed point, but a one-parameter family. It is dual to a local quantum critical phase instead of a quantum critical point. This result follows from a detailed analysis of the possible quantizations of the gravitational theory that is consistent with the thermodynamics of the analytical Gubser-Rocha black hole solution. The analytic Gubser-Rocha black hole is only a 2-parameter subset of all possible solutions, and we construct other members numerically. These new numerical solutions correspond to turning on an additional scalar charge. Moreover, each solution has multiple holographic interpretations depending on the quantization chosen. In one particular quantization involving a multitrace deformation the scalar charge is a marginal operator. In other quantizations where the marginal multitrace operator is turned off, the analytic Gubser-Rocha black hole does not describe a finite temperature conformal fluid. [ABSTRACT FROM AUTHOR]

In the present review of the author's works, the calculation of the radiation spectrum of a hydrogen-like atom is described in detail using the principle of commensurability of conserved quantities, which is introduced by the author. The result obtained allows us to give a clear physical interpretation of Bohr's quantum hypothesis. It follows from the data obtained that the "resolved" states of quantum systems are the result of the need to fulfill the requirement of having a common measure of conserved quantities for all participants in physical interaction before and after interaction. [ABSTRACT FROM AUTHOR]

It is well known that designing mode-dependent event-triggered control (MDETC) brings challenging difficulties to theoretical analysis, especially for two-dimensional (2-D) switched systems. Therefore, for 2-D switched Fornasini-Marchesini local state-space (FMLSS) systems, this paper designs a MDETC to investigate global exponential stabilization almost surely (GES a.s.). A MDETC based on dynamic output quantization control scheme is designed, which not only has a wide range of practicability, but also greatly saves network bandwidth resources. By constructing mode-dependent Lyapunov functions that include two time directions, some novel sufficient conditions are provided such that the switched FMLSS system achieves GES a.s. Unlike most previous results, our results do not require each mode to be stable, not even after adding control. Finally, numerical experiments are provided to verify the validity of our main theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we address the design of multi-user multiple-input single-output (MU-MISO) precoders for indoor visible light communication (VLC) systems. The goal is to minimize the transmitted optical power per light emitting diode (LED) under imperfect channel state information (CSI) at the transmitter side. Robust precoders for imperfect CSI available in the literature include noisy and outdated channel estimation cases. However, to the best of our knowledge, no work has considered adding robustness against channel quantization. In this paper, we fill this gap by addressing the case of imperfect CSI due to the quantization of VLC channels. We model the quantization errors in the CSI through polyhedric uncertainty regions. For polyhedric uncertainty regions and positive real channels, as is the case of VLC channels, we show that the robust precoder against channel quantization errors that minimizes the transmitted optical power while guaranteeing a target signal to noise plus interference ratio (SNIR) per user is the solution of a second order cone programming (SOCP) problem. Finally, we evaluate its performance under different quantization levels through numerical simulations. [ABSTRACT FROM AUTHOR]

Recently, deep learning-based Quantization Index Modulation (QIM) steganalysis algorithms have achieved great success. However, most of them are supervised learning algorithms that rely on a large number of labeled samples and have poor generalization performance. Towards addressing the challenge, we present a novel semi-supervised ladder network, termed SSLadNet, for weak signal detection in QIM steganalysis of VoIP streams. In particular, we integrate supervised learning and unsupervised learning into an end-to-end learning architecture via a ladder network, and achieve joint optimization for semi-supervised learning by backpropagation to minimize the sum of supervised and unsupervised cost functions. To the best of our knowledge, this is the first deep learning-based semi-supervised detection model applied to QIM steganalysis that can effectively extract rich features reflecting the correlation changes between codewords caused by QIM steganography. Experimental results showed that even for the labeled samples with a number of 512, SSLadNet can achieve a detection accuracy of around 96.09% for 1000 ms long samples and 100% embedding rate, and outperforms the state-of-the-art methods based on semi-supervised learning. • We propose a QIM steganalysis method based on the semi-supervised ladder network. • We design a RNN-based DAE to integrate supervised and unsupervised learning. • We conduct comprehensive experiments to evaluate SSLadNet's performance. [ABSTRACT FROM AUTHOR]

[Display omitted] • An approximate entropy algorithm enabling quantitative evaluation of non-synchronous sampling is proposed. • A harmonic frequency and amplitude correction method based on the all-phase FFT is developed. • A spectrum folding identification method using relative height analysis of harmonic amplitudes is designed. • Efficient and correct multi-surface phases demodulation combined with the above advantages is realized. As a non-destructive detection technique for measuring parallel transparent optics, wavelength-shifting interferometry provides a separation basis for multiple measured surfaces by assigning different frequencies to the interference harmonics based on their optical-path-difference. However, the non-synchronous sampling and spectral aliasing can decrease the measurement accuracy. Therefore, an approximate entropy algorithm is utilized to determine the sampling performance. Then the frequency search accuracy is guaranteed by the zero-padding method, and the all-phase Fourier transform method is introduced to correct the harmonic frequencies and amplitudes, where the spectral aliasing problem is solved by the relative amplitude analysis. So efficient surface measurement combining the above advantages is realized, and the validity is verified by simulation analysis of different profile features and de-tuning errors. The effectiveness of the proposed method is fully confirmed by the repetitive measurements on two parallel plates in the experiments. [ABSTRACT FROM AUTHOR]

In this article, mode‐reconfigurable orbit angular momentum (OAM) waves is developed by mechanically rotating a 2 bit phase quantization (0°, 90°, 180°, and 270°) transmitarray (TA) with size 6.2λ0 × 6.2λ0 × 0.98λ0 (λ0 wavelength in free space). The TA consists of three‐layer metasurfaces (MSs), which are in the top, middle, and bottom layers, respectively. The TA is excited by a horn. The top layer MS converts the spherical wave from the horn into plane wave. The middle and bottom layers are same, and they together convert the plane wave into OAM wave with mode l, and then reconfigurable mode can be achieved by rotating the bottom layer MS. To the knowledge of the authors, it is the first time to design mechanical OAM mode reconfigurability by phase quantization TA. As example, two TAs are designed for reconfigurable modes at 15.5 GHz: (1) Among l = 1, 0, −1. (2) Among l = 2, 0, −2. The TAs have the following advantages: high gain (15.1–21.5 dBi), high aperture efficiency (the highest up to 29.2%), high purity (92.67%–98.93%), and small size (6.2λ0 × 6.2λ0). The measured and simulated results agree well, and validate the design method. The developed OAM mode reconfigurable TAs have potential application for future high capacity communication. [ABSTRACT FROM AUTHOR]

In this article, I discuss the criticisms raised against Thomas Kuhn's Black-Body Theory. These criticisms concern two issues: how to understand Planck's position with regards to the quantization of energy in 1901, and how to understand the book's relation to The Structure of Scientific Revolutions. Both criticisms, I argue, concern the notion of a paradigm: the first concerns how Boltzmann acted as an exemplar for Planck, and the second whether the book provides a paradigm change. I will then argue that both criticisms presume a conceptualization of paradigms that does not align well with Kuhn's conceptualization of it in both Structure and later work: they assume, more specifically, that sharing a paradigm presupposes sharing an interpretation of it, and that paradigm changes are essentially identical to gestalt switches. On the basis of this, I will then argue that the criticisms are misguided, that Kuhn's position regarding Planck's work is in fact quite close to the indetermination-view developed by some of his critics, and that the book fits Structure quite well. In conclusion, I will then reflect on how the narrative provided in Black-Body Theory connects with Kuhn's views on the relation between history and philosophy of science. [ABSTRACT FROM AUTHOR]

The close-in weapon system (CIWS) is a combat system that faces a complex environment full of dynamic and unknown challenges, whose construction and planning require a systematic design method. Multiliving agent (MLA) theory is a methodology for the combat system design, which uses the livelihood degree to evaluate the multi-dimensional long-term operational effectiveness of the system; whereas, there is still no uniform quantization framework for the livelihood degree, and the adjustment methods of livelihood degree need to be further improved. In this paper, we propose the uniform quantization framework for the livelihood degree and detailed discuss the methods of livelihood adjustment. Based on the MLA theory, the multi-dimensional operational effectiveness of the missile-gun integrated weapon system (MGIWS) is analyzed, and the long-term combat effectiveness against the saturation attack is assessed. Furthermore, the planning problem of the equipment deployment and configuration is investigated. Two objectives, including the overall livelihood degree and cost-effectiveness (CE), are proposed, and the optimization method based on genetic algorithm (GA) is studied for the planning problem. [ABSTRACT FROM AUTHOR]

Deploying convolutional neural networks to mobile or embedded devices is often prohibited by limited memory and computational resources. This is particularly problematic for the most successful networks, which tend to be very large and require long inference times. Many alternative approaches have been developed for compressing neural networks based on pruning, regularization, quantization or distillation. In this paper, we propose the "Knowledge Distillation with Dynamic Pruning" (KDDP), which trains a dynamically pruned compact student network under the guidance of a large teacher network. In KDDP, we train the student network with supervision from the teacher network, while applying L1 regularization on the neuron activations in a fully-connected layer. Subsequently, we prune inactive neurons. Our method automatically determines the final size of the student model. We evaluate the compression rate and accuracy of the resulting networks on an image classification dataset, and compare them to results obtained by Knowledge Distillation (KD). Compared to KD, our method produces better accuracy and more compact models. [ABSTRACT FROM AUTHOR]

On the basis of revising the quantum concept and reinterpreting Bohr's hydrogen atom structure model in classical physics, this paper deduces the elliptical orbital energy level formula of electrons in hydrogen like atoms in detail. When the electron transition time is taken as unit time (1 s), the energy level formula is completely consistent with Bohr Sommerfeld's atomic structure Theory. [ABSTRACT FROM AUTHOR]

We consider the well-known Lieb-Liniger (LL) model for N N bosons interacting pairwise on the line via the δ δ potential in the mean-field scaling regime. Assuming suitable asymptotic factorization of the initial wave functions and convergence of the microscopic energy per particle, we show that the time-dependent reduced density matrices of the system converge in trace norm to the pure states given by the solution to the one-dimensional cubic nonlinear Schrödinger equation (NLS) with an explict rate of convergence. In contrast to previous work [ 3 ] relying on the formalism of second quantization and coherent states and without an explicit rate, our proof is based on the counting method of Pickl [ 65 , 66 , 67 ] and Knowles and Pickl [ 44 ]. To overcome difficulties stemming from the singularity of the δ δ potential, we introduce a new short-range approximation argument that exploits the Hölder continuity of the N N -body wave function in a single particle variable. By further exploiting the L 2 L 2 -subcritical well-posedness theory for the 1D cubic NLS, we can prove mean-field convergence when the limiting solution to the NLS has finite mass, but only for a very special class of N N -body initial states. [ABSTRACT FROM AUTHOR]

In this study, two effective approaches are combined which are implemented at the element design level and system design level to simultaneously improve the frequency bandwidth and aperture efficiency of a dual-polarized single-layer reflecting metasurface. At the element design level, a broadband behavior is realized by using the polarization conversion technique (PCT) which is a novel technique to enhance the bandwidth of the element. To this end, an anisotropic metasurface with the I-shaped metal patch is proposed for rotating the polarization of the wave emitted from a point source by 90 ∘ and making a continuous phase shift in a full range of 360 ∘ within 8-18 GHz. Therefore, a completely equiphase aperture is achieved leading to enhancing the metasurface performance such as directivity and aperture efficiency and reducing the sidelobe level compared to reflecting metasurface developed by 1-bit phase quantization technique. At the system design level, the three-frequency phase synthesis (TFPS) method, which is based on determining the best constant reference phase for the aperture, is used and the corresponding constant reference phases are optimized to minimize the phase error in the whole band. The combination of TFPS and PCT enhances the effectiveness of the TFPS method considerably. An 841 element reflecting metasurface with aperture dimensions of 290 cm × 290 cm is designed, simulated, and fabricated in Ku-band to verify the concept. The measurement results show that the 1-dB gain bandwidth before and after combining PCT and TFPS techniques are 17.47% (14.1–16.8 GHz) and 30.3% (14–19 GHz), respectively. In addition, the maximum aperture efficiency of the proposed metasurface is 63.62% which occurs at 14.5 GHz. [ABSTRACT FROM AUTHOR]

An approach of the proper quantization rule to find exact solution of radial Schrödinger equation for non-polynomial potentials, which are quasi exactly solvable, is developed in this work. Using this rule, the determination of the energy spectrum En for non-pollynomialy potentials is somewhat impossible and limited, which provides their energy at ground state only. To overcome this difficulty, we devised in this approach the potential into two potentials: an exact potential Ve(r) and a non-linear extension Va(r), the potential will be expressed as:V (r) = Ve(r)+Va(r), then calculate the energy level εn and the ground state ε0 energy for exactly solvable potential Ve(r) using the proper quantization rule, from which an analytical expression of energie En for non-polynomial potential V (r) related with the ground level energy E0 is found easily. We conclude that the study of non-exactly potential remain to the study of the first exactly solvable potential. [ABSTRACT FROM AUTHOR]

The hybrid beamforming can significantly improve the spectral and energy efficiencies of the millimeter‐wave (mmWave) massive multiple input multiple output (MIMO) systems without obvious performance loss. However, the fundamental limitation of existing hybrid beamforming is that they include high‐resolution analog‐to‐digital converters (ADCs) which consume high power. To overcome this fundamental limitation, in this paper, spectrum and energy efficient mmWave massive MIMO transmission scheme is proposed that jointly optimizes the hybrid combiner and the number of ADC bits. Particularly, the hybrid combiner is presented as a combination of three parts: the analog combiner matrix, the quantization matrix, and the digital baseband matrix which is based on the Kalman filter. Unlike most existing works that rely on sumrate optimization to design the hybrid combiner, in this work, the mean square error (MSE) is chosen as the main performance metric to describe the reliability of the system. Simulations results confirm that the proposed Kalman based hybrid combiner exhibits the best performance in terms of spectral and energy efficiencies compared to minimum mean square error (MMSE) and zero forcing (ZF) receivers. [ABSTRACT FROM AUTHOR]

Efficient quantizer design is vital in high‐speed optical receivers. In this paper, the authors propose a three‐level (1.5‐bit) reliability‐based quantizer for low‐complexity soft decoding of low‐density parity‐check (LDPC) codes, and show that it outperforms a conventional quantizer employing eight levels (3 bits). Different approaches for obtaining the quantization thresholds are discussed, and it is shown that the achievable channel capacity with the proposed quantizer is within 0.4 dB of the Shannon limit of the unquantized channel. Rate‐compatible LDPC codes are also designed tailored to the asymmetric optical channel terminated with the proposed reliability‐based quantizer, and it is shown that the resulting quantizer‐aware LDPC codes significantly outperform other existing codes of similar rates. [ABSTRACT FROM AUTHOR]

Quantization provides a very natural way to preserve the convex order when approximating two ordered probability measures by two finitely supported ones. Indeed, when the convex order dominating original probability measure is compactly supported, it is smaller than any of its dual quantizations while the dominated original measure is greater than any of its stationary (and therefore any of its quadratic optimal) primal quantization. Moreover, the quantization errors then correspond to martingale couplings between each original probability measure and its quantization. This permits to prove that any martingale coupling between the original probability measures can be approximated by a martingale coupling between their quantizations in Wassertein distance with a rate given by the quantization errors but also in the much finer adapted Wassertein distance. As a consequence, while the stability of (Weak) Martingale Optimal Transport problems with respect to the marginal distributions has only been established in dimension 1 so far, their value function computed numerically for the quantized marginals converges in any dimension to the value for the original probability measures as the numbers of quantization points go to ∞. [ABSTRACT FROM AUTHOR]

Higher-spin diffeomorphisms are to higher-order differential operators what diffeomorphisms are to vector fields. Their rigorous definition is a challenging mathematical problem which might predate a better understanding of higher-spin symmetries and interactions. Several yes-go and no-go results on higher-spin diffeomorphisms are collected from the mathematical literature in order to propose a generalisation of the algebra of differential operators on which higher-spin diffeomorphisms are well-defined. This work is dedicated to the memory of Christiane Schomblond, who taught several generations of Belgian physicists the formative rigor and delicate beauty of theoretical physics. [ABSTRACT FROM AUTHOR]

The system under study is the Λ -Kantowski–Sachs universe. Its canonical quantization is provided based on a recently developed method: the singular minisuperspace Lagrangian describing the system, is reduced to a regular (by inserting into the dynamical equations the lapse dictated by the quadratic constraint) possessing an explicit (though arbitrary) time dependence; thus a time-covariant Schrödinger equation arises. Additionally, an invariant (under transformations t = f (t ~) ) decay probability is defined and thus "observers" which correspond to different gauge choices obtain, by default, the same results. The time of decay for a Gaussian wave packet localized around the point a = 0 (where a the radial scale factor) is calculated to be of the order ∼ 10 - 42 - 10 - 41 s . The acquired value is near the end of the Planck era (when comparing to a FLRW universe), during which the quantum effects are most prominent. Some of the results are compared to those obtained by following the well known canonical quantization of cosmological systems, i.e. the solutions of the Wheeler–DeWitt equation. [ABSTRACT FROM AUTHOR]

To model a true three-dimensional (3D) display system, we introduced the method of voxel molding to obtain the stereoscopic imaging space of the system. For the distribution of each voxel, we proposed a four-dimensional (4D) Givone-Roessor (GR) model for state-space representation--that is, we established a local state-space model with the 3D position and one-dimensional time coordinates to describe the system. First, we extended the original elementary operation approach to a 4D condition and proposed the implementation steps of the realization matrix of the 4D GR model. Then, we described the working process of a true 3D display system, analyzed its real-time performance, introduced the fixed-point quantization model to simplify the system matrix, and derived the conditions for the global asymptotic stability of the system after quantization. Finally, we provided an example to prove the true 3D display system's feasibility by simulation. The GR-model-representation method and its implementation steps proposed in this paper simplified the system's mathematical expression and facilitated the microcontroller software implementation. Real-time and stability analyses can be used widely to analyze and design true 3D display systems. [ABSTRACT FROM AUTHOR]

Gravity is perturbatively renormalizable for the physical states which can be conveniently defined via foliation-based quantization. In recent sequels, one-loop analysis was explicitly carried out for Einstein-scalar and Einstein-Maxwell systems. Various germane issues and all-loop renormalizability have been addressed. In the present work we make further progress by carrying out several additional tasks. Firstly, we present an alternative 4D-covariant derivation of the physical state condition by examining gauge choice-independence of a scattering amplitude. To this end, a careful dichotomy between the ordinary, and large gauge symmetries is required and appropriate gauge-fixing of the ordinary symmetry must be performed. Secondly, vacuum energy is analyzed in a finite-temperature setup. A variant optimal perturbation theory is implemented to two-loop. The renormalized mass determined by the optimal perturbation theory turns out to be on the order of the temperature, allowing one to avoid the cosmological constant problem. The third task that we take up is examination of the possibility of asymptotic freedom in finite-temperature quantum electrodynamics. In spite of the debates in the literature, the idea remains reasonable. [ABSTRACT FROM AUTHOR]

On the basis of the intimate relation between Nambu dynamics and hydrodynamics, hydrodynamics on a non-commutative space (obtained by the quantization of space), proposed by Nambu in his last work, is formulated as hydrodynamics of granular material. In Sect. 2 , the quantization of space is done using a Moyal product, and the hydrodynamic simulation is performed for the thus-obtained 2D fluid, which flows inside a channel with an obstacle. The obtained results differ between two cases in which the size of a fluid particle is zero and finite. The difference seems to come from the behavior of vortices generated by an obstacle. In Sect. 3 , considering a vortex as a string, two models are examined; one is the hybrid model in which vortices interact with each other by exchanging Kalb–Ramond fields (a generalization of stream functions), and the other is the more general string field theory in which the Kalb–Ramond field is one of the excitation modes of string oscillations. In the string field theory, an Altarelli–Parisi-type evolution equation is introduced. This is expected to describe the response of the distribution function of a vortex inside turbulence, when the energy scale is changed. The behavior of viscosity differs in string theory compared with particle theory, so that the Landau theory of fluids to introduce viscosity may be modified. In conclusion, hydrodynamics and string theory are almost identical theories. It should be noted, however, that the string theory needed to reproduce a given hydrodynamics is not the usual string theory. [ABSTRACT FROM AUTHOR]

We review some aspects of Nambu mechanics on the basis of works previously published separately by the present author. The main focuses are on three themes: the various symmetry structures, their possible relevance to string/M-theory, and a Hamilton–Jacobi-like reformulation. We try to elucidate the basic ideas, most of which were rooted in more or less the same ground, and to explain the motivations behind these works from a unified and vantage viewpoint. Various unsolved questions are mentioned. We also include a historical account of the genesis of Nambu mechanics, and discuss (in the appendix) some parallelism of various ideas behind Nambu's paper with Dirac's old works which are related to the description of vortical flows in terms of gauge potentials. [ABSTRACT FROM AUTHOR]

We reviewed the canonical quantisation of the geometry of the spacetime in the cases of a simply and a non-simply connected manifold. In the former, we analysed the information contained in the solutions of the Wheeler--DeWitt equation and showed their interpretation in terms of the customary boundary conditions that are typically imposed on the semiclassical wave functions. In particular, we reviewed three different paradigms for the quantum creation of a homogeneous and isotropic universe. For the quantisation of a non-simply connected manifold, the best framework is the third quantisation formalism, in which the wave function of the universe is seen as a field that propagates in the space of Riemannian 3-geometries, which turns out to be isomorphic to a (part of a) 1 + 5 Minkowski spacetime. Thus, the quantisation of the wave function follows the customary formalism of a quantum field theory. A general review of the formalism is given, and the creation of the universes is analysed, including their initial expansion and the appearance of matter after inflation. These features are presented in more detail in the case of a homogeneous and isotropic universe. The main conclusion in both cases is that the most natural way in which the universes should be created is in entangled universe--antiuniverse pairs. [ABSTRACT FROM AUTHOR]

The main aim of this article is to characterize inner Poisson structure on a quantum cluster algebra without coefficients. Mainly, we prove that inner Poisson structure on a quantum cluster algebra without coefficients is always a standard Poisson structure. We introduce the concept of so-called locally inner Poisson structure on a quantum cluster algebra and then show it is equivalent to locally standard Poisson structure in the case without coefficients. Based on the result from [7] we obtain finally the equivalence between locally inner Poisson structure and compatible Poisson structure in this case. [ABSTRACT FROM AUTHOR]

This paper presents an effective machine learning-based depth selection algorithm for CTU (Coding Tree Unit) in HEVC (High Efficiency Video Coding). Existing machine learning methods are limited in their ability in handling the initial depth decision of CU (Coding Unit) and selecting the proper set of input features for the depth selection model. In this paper, we first propose a new classification approach for the initial division depth prediction. In particular, we study the correlation of the texture complexity, QPs (quantization parameters) and the depth decision of the CUs to forecast the original partition depth of the current CUs. Secondly, we further aim to determine the input features of the classifier by analysing the correlation between depth decision of the CUs, picture distortion and the bit-rate. Using the found relationships, we also study a decision method for the end partition depth of the current CUs using bit-rate and picture distortion as input. Finally, we formulate the depth division of the CUs as a binary classification problem and use the nearest neighbor classifier to conduct classification. Our proposed method can significantly improve the efficiency of interframe coding by circumventing the traversing cost of the division depth. It shows that the mentioned method can reduce the time spent by 34.56% compared to HM-16.9 while keeping the partition depth of the CUs correct. [ABSTRACT FROM AUTHOR]

Quantum computers that process information by harnessing the remarkable power of quantum mechanics are increasingly being put to practical use. In the future, their impact will be felt in numerous fields, including in online casino games. This is one of the reasons why quantum gambling theory has garnered considerable attention. Studies have shown that quantum gambling theory often yields nontrivial consequences that classical theory cannot interpret. We have formulated blackjack, one of the most famous card games, as a quantum game and found possible quantum entanglement between strategies. We also devised a quantum circuit reproducing classical blackjack. This circuit can be realized in the near future when quantum computers are commonplace. Furthermore, we showed that the player's expectation increases compared to the classical game using quantum basic strategy , which is a quantum version of the popular basic strategy of blackjack. [ABSTRACT FROM AUTHOR]

We experimentally demonstrated 16384-ary quadrature amplitude modulation (16384QAM) mobile fronthaul based on 3-amplitude quantization high-pass Delta-sigma Modulation (DSM) in the O band intensity-modulated direct detection (IM/DD) system. By using 3-amplitude quantized high-pass DSM, we successfully quantize the analog waveform of intermediate frequency (IF) Orthogonal Frequency Division Multiplexing (OFDM) signal into 3-Level Pulse Amplitude Modulation (PAM3) signal, and 1 GHz bandwidth 16384-QAM and 1024QAM are successful transmission in 20Gb/s IM/DD link. 0.63% Error Vector Magnitude (EVM) of 16384QAM and 0.7% EVM of 2048QAM are achieved after 25km SSMF and 50km SSMF transmission, respectively. The signal-to-noise ratio (SNR) of the retrieved OFDM signal is 43 dB, which shows that the proposed scheme can support 16384QAM mobile fronthaul network. [ABSTRACT FROM AUTHOR]