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Journal articles on the topic 'Phase quantization'

Author: Grafiati

Published: 4 June 2021

Last updated: 19 June 2025

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1

Bergeron, Hervé, and Jean-Pierre Gazeau. "Variations à la Fourier-Weyl-Wigner on Quantizations of the Plane and the Half-Plane." Entropy 20, no. 10 (2018): 787. http://dx.doi.org/10.3390/e20100787.

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Any quantization maps linearly function on a phase space to symmetric operators in a Hilbert space. Covariant integral quantization combines operator-valued measure with the symmetry group of the phase space. Covariant means that the quantization map intertwines classical (geometric operation) and quantum (unitary transformations) symmetries. Integral means that we use all resources of integral calculus, in order to implement the method when we apply it to singular functions, or distributions, for which the integral calculus is an essential ingredient. We first review this quantization scheme before revisiting the cases where symmetry covariance is described by the Weyl-Heisenberg group and the affine group respectively, and we emphasize the fundamental role played by Fourier transform in both cases. As an original outcome of our generalisations of the Wigner-Weyl transform, we show that many properties of the Weyl integral quantization, commonly viewed as optimal, are actually shared by a large family of integral quantizations.

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2

Zhang, Qiu Ju, Yong Chang Wang, and Kai Liu. "The Theory of Using an Intensity-Correcting Algorithm to Overcome Quantization Error for Phase Measuring Profilometry." Advanced Materials Research 718-720 (July 2013): 1170–74. http://dx.doi.org/10.4028/www.scientific.net/amr.718-720.1170.

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In the image process, intensity differs from its true value because the quantization process restricts image pixels to lie on an integer grid, and phase quantization error is introduced. In this paper, we propose a theory of using an intensity-correcting to overcome phase quantization error. According to the distribution of the intensity error in some pixels, the mathematical model of the intensity error is reconstructed to correct intensity values and reduce phase quantization error. Using specific example deduct the intensity-correction algorithm. At last, we compare the uncorrected quantization error and the quantization error after correction, and prove that the principle of this algorithm is right.

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3

PLYUSHCHAY, MIKHAIL S., and ALEXANDER V. RAZUMOV. "DIRAC VERSUS REDUCED PHASE SPACE QUANTIZATION FOR SYSTEMS ADMITTING NO GAUGE CONDITIONS." International Journal of Modern Physics A 11, no. 08 (1996): 1427–62. http://dx.doi.org/10.1142/s0217751x96000663.

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The constrained Hamiltonian systems admitting no gauge conditions are considered. The methods for dealing with such systems are discussed and developed. As a concrete application, the relationship between the Dirac and reduced phase space quantizations is investigated for spin models belonging to the class of systems under consideration. It is found that the two quantization methods may give similar, or essentially different, physical results, and moreover a class of constrained systems, which can be quantized only by the Dirac method, is discussed. A possible interpretation of the gauge degrees of freedom is given.

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4

Doh-Suk Kim. "Perceptual phase quantization of speech." IEEE Transactions on Speech and Audio Processing 11, no. 4 (2003): 355–64. http://dx.doi.org/10.1109/tsa.2003.814409.

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5

Inoue, Akira, and Masayuki Nishiguchi. "Phase quantization method and apparatus." Journal of the Acoustical Society of America 111, no. 5 (2002): 1972. http://dx.doi.org/10.1121/1.1486356.

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6

Chaturvedi, S., A. K. Kapoor, and V. Srinivasan. "Stochastic quantization in phase space." Physics Letters B 157, no. 5-6 (1985): 400–402. http://dx.doi.org/10.1016/0370-2693(85)90388-0.

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7

Horowitz, A. M. "Stochastic quantization in phase space." Physics Letters B 156, no. 1-2 (1985): 89–92. http://dx.doi.org/10.1016/0370-2693(85)91360-7.

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8

He, Rui, Feng Chen та Hong-Yi Fan. "𝔓-quantization, 𝔔-quantization and Weyl quantization of a ray in classical phase space". Modern Physics Letters A 29, № 17 (2014): 1450069. http://dx.doi.org/10.1142/s0217732314500692.

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By examining three quantization schemes of a ray function in classical phase space (a geometric ray is expressed by δ(x-λq-νp)), we find that the Weyl quantization scheme can reasonably demonstrate the correspondence between classical functions and quantum mechanical operators, since δ(x-λq-νp) really maps onto the operator δ(x-λQ-νP), where [Q, P] = iℏ, and δ(x-λQ-νP) represents a pure state (the coordinate-momentum intermediate representation), while 𝔓-ordered, 𝔔-ordered quantization schemes δ(x-λq-νp) to two different Fresnel integration kernels in Weyl-ordered form. Thus, Weyl quantization is more reasonable and preferable.

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9

Kim, Han-Byul, Joo Hyung Lee, Sungjoo Yoo, and Hong-Seok Kim. "MetaMix: Meta-State Precision Searcher for Mixed-Precision Activation Quantization." Proceedings of the AAAI Conference on Artificial Intelligence 38, no. 12 (2024): 13132–41. http://dx.doi.org/10.1609/aaai.v38i12.29212.

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Mixed-precision quantization of efficient networks often suffer from activation instability encountered in the exploration of bit selections. To address this problem, we propose a novel method called MetaMix which consists of bit selection and weight training phases. The bit selection phase iterates two steps, (1) the mixed-precision-aware weight update, and (2) the bit-search training with the fixed mixed-precision-aware weights, both of which combined reduce activation instability in mixed-precision quantization and contribute to fast and high-quality bit selection. The weight training phase exploits the weights and step sizes trained in the bit selection phase and fine-tunes them thereby offering fast training. Our experiments with efficient and hard-to-quantize networks, i.e., MobileNet v2 and v3, and ResNet-18 on ImageNet show that our proposed method pushes the boundary of mixed-precision quantization, in terms of accuracy vs. operations, by outperforming both mixed- and single-precision SOTA methods.

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10

Yan, Zhaoyi, Yemin Shi, Yaowei Wang, et al. "Towards Accurate Low Bit-Width Quantization with Multiple Phase Adaptations." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 04 (2020): 6591–98. http://dx.doi.org/10.1609/aaai.v34i04.6134.

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Low bit-width model quantization is highly desirable when deploying a deep neural network on mobile and edge devices. Quantization is an effective way to reduce the model size with low bit-width weight representation. However, the unacceptable accuracy drop hinders the development of this approach. One possible reason for this is that the weights in quantization intervals are directly assigned to the center. At the same time, some quantization applications are limited by the various of different network models. Accordingly, in this paper, we propose Multiple Phase Adaptations (MPA), a framework designed to address these two problems. Firstly, weights in the target interval are assigned to center by gradually spreading the quantization range. During the MPA process, the accuracy drop can be compensated for the unquantized parts. Moreover, as MPA does not introduce hyperparameters that depend on different models or bit-width, the framework can be conveniently applied to various models. Extensive experiments demonstrate that MPA achieves higher accuracy than most existing methods on classification tasks for AlexNet, VGG-16 and ResNet.

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11

Smith, T. B., D. A. Dubin, and M. A. Hennings. "The Weyl Quantization of Phase Angle." Journal of Modern Optics 39, no. 8 (1992): 1603–8. http://dx.doi.org/10.1080/713823581.

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12

Zachos, Cosmas, and Thomas Curtright. "Phase-Space Quantization of Field Theory." Progress of Theoretical Physics Supplement 135 (1999): 244–58. http://dx.doi.org/10.1143/ptps.135.244.

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13

BANDYOPADHYAY, PRATUL, and KOHINUR HAJRA. "STOCHASTIC QUANTIZATION AND THE BERRY PHASE." International Journal of Modern Physics A 06, no. 17 (1991): 3061–80. http://dx.doi.org/10.1142/s0217751x91001490.

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We study here the Berry phase from the point of view of stochastic quantization. The relativistic generalization of Nelson’s stochastic quantization procedure can be achieved when the Brownian motion process is taken into account in the internal space (apart from that in the external space). This effectively considers the particle as one that is stochastically extended, and nonrelativistic quantum mechanics is obtained in the sharp point limit. This can be formulated in terms of a gauge-field-theoretical extension of the particle. This inherent gauge field gives rise to the holonomy in a Hermitian line bundle, which appears as an extra phase factor in the adiabatic limit for a parameter-dependent Hamiltonian, and determines a unique connection. When the Hamiltonian is degenerate, the holonomy is defined in a complex vector bundle. In the case of a fermion, this Berry connection is found to be related to the Wess-Zumino term and can be considered to be of topological origin.

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14

García de León, P. L., and J. P. Gazeau. "Coherent state quantization and phase operator." Physics Letters A 361, no. 4-5 (2007): 301–4. http://dx.doi.org/10.1016/j.physleta.2006.09.065.

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15

Ahmed, Zafar. "Novel phase-space orbits and quantization." Journal of Physics A: Mathematical and General 38, no. 43 (2005): L701—L706. http://dx.doi.org/10.1088/0305-4470/38/43/l01.

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16

BANDYOPADHYAY, P. "AREA PRESERVING DIFFEOMORPHISM, QUANTUM GROUP AND BERRY PHASE." International Journal of Modern Physics A 14, no. 03 (1999): 409–28. http://dx.doi.org/10.1142/s0217751x99000208.

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We study here the relationship between the area preserving diffeomorphism and quantum group with the deformation of symplectic structure and Berry phase in the Landau problem of 2D electron gas in a magnetic field. It is argued that while the area preserving diffeomorphism leads to the quantization of the symmetry [Formula: see text], the deformation of the symplectic structure leads to the quantization of the system having the relation Δp. Δ q=2πnℏ, n being an odd integer giving rise to the Berry phase ei2πμ with n=2μ. A possible link between the deformation parameter q of the deformed algebra [Formula: see text] with the Berry phase factor arising out of the quantization procedure has been suggested. Finally, the latticization of space associated with the quantum group and its connection with the Zp spin system is discussed.

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17

Majeed, Muhammad Kashif, Muhammad Usman, Iqbal Hussain, et al. "Super Broad Non-Hermitian Line Shape from Out-of-Phase and In-Phase Photon-Phonon Dressing in Eu3+: NaYF4 and Eu3+: BiPO4." Photonics 11, no. 12 (2024): 1169. https://doi.org/10.3390/photonics11121169.

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We report super broad non-Hermitian line shape from out-of-phase and in-phase photon-phonon dressing (quantization) in Eu3+: NaYF4 and Eu3+: BiPO4 nanocrystals. The line shape is controlled by changing time gate position, time gate width, power, temperature, sample, photomultiplier tubes, and laser. We observed that the fluorescence (FL) line-shape contrasts are 69.23% for Eu3+: BiPO4 and 43.75% for Eu3+: NaYF4, owing to the stronger out-of-phase photon-phonon dressing (destructive quantization). Moreover, we observed that the spontaneous four-wave mixing (SFWM) line shape was approximately three times wider at 300 K than at 77 K for the [(12:1)-phase] Eu3+: NaYF4 due to more high-frequency in-phase phonon dressing (strong constructive quantization). Furthermore, we showed that the noise line-shape width remains unchanged for Eu3+: BiPO4 (16 nm) and Eu3+: NaYF4 (12 nm) due to out-of-phase and in-phase photon-phonon dressing balance. Such results have potential applications in multi-channel band stop filter.

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18

HAJRA, K., and P. BANDYOPADHYAY. "EQUIVALENCE OF STOCHASTIC, KLAUDER AND GEOMETRIC QUANTIZATION." International Journal of Modern Physics A 07, no. 06 (1992): 1267–85. http://dx.doi.org/10.1142/s0217751x92000545.

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The relativistic generalization of stochastic quantization helps us to introduce a stochastic-phase-space formulation when a relativistic quantum particle appears as a stochastically extended one. The nonrelativistic quantum mechanics is obtained in the sharp point limit. This also helps us to introduce a gauge-theoretical extension of a relativistic quantum particle when for a fermion the group structure of the gauge field is SU(2). The sharp point limit is obtained when we have a minimal contribution of the residual gauge field retained in the limiting procedure. This is shown to be equivalent to the geometrical approach to the phase-space quantization introduced by Klauder if it is interpreted in terms of a universal magnetic field acting on a free particle moving in a higher-dimensional configuration space when quantization corresponds to freezing the particle to its first Landau level. The geometric quantization then appears as a natural consequence of these two formalisms, since the Hermitian line bundle introduced there finds a physical meaning in terms of the inherent gauge field in stochastic-phase-space formulation or in the interaction with the magnetic field in Klauder quantization.

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19

KURATSUJI, HIROSHI, and KEN-ICHI TAKADA. "CANONICAL PHASE, TOPOLOGICAL INVARIANT AND REPRESENTATION THEORY." Modern Physics Letters A 05, no. 12 (1990): 917–25. http://dx.doi.org/10.1142/s0217732390001013.

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We show that the non-integrable phase defined over the generalized phase space, which is called the canonical phase, yields the topological quantization that reveals the connection with the irreducible representation of a certain class of compact Lie groups. Although this consequence by itself is already known in mathematics under the general scheme named geometric quantization, it has not yet been fully appreciated in physics except for some specific problems. The descriptive technique adopted here seems fresh enough to commit itself to the topological aspect of quantum mechanics even including quantum field theory.

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20

BOJOWALD, MARTIN, and THOMAS STROBL. "SYMPLECTIC CUTS AND PROJECTION QUANTIZATION FOR NON-HOLONOMIC CONSTRAINTS." International Journal of Modern Physics D 12, no. 04 (2003): 713–25. http://dx.doi.org/10.1142/s0218271803002810.

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Projection quantization, which is a method to quantize systems with non-holonomic constraints like the condition Det q > 0 in general relativity, is shown to coincide with a reduced phase space quantization in a class of cases which is specified in the main text. This is inferred in the context of geometric quantization using the symplectic cutting technique.

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21

Karasev, M. V., and T. A. Osborn. "Magnetic quantization over Riemannian manifolds." Canadian Journal of Physics 84, no. 6-7 (2006): 551–56. http://dx.doi.org/10.1139/p06-027.

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We demonstrate that Weyl's pioneering idea (1918) to intertwine metric and magnetic fields into a single joint connection can be naturally realized, on the phase space level, by the gauge-invariant quantization of the cotangent bundle with magnetic symplectic form. Quantization, for systems over a noncompact Riemannian configuration manifold, may be achieved by the introduction of a magneto-metric analog of the Stratonovich quantizer — a family of invertible, selfadjoint operators representing quantum δ functions. Based on the quantizer, we construct a generalized Wigner transform that maps Hilbert–Schmidt operators into L2 phase-space functions. The algebraic properties of the quantizer allow one to extract a family of symplectic reflections, which are then used to (i) derive a simple, explicit, and geometrically invariant formula for the noncommutative product of functions on phase space, and (ii) construct a magneto-metric connection on phase space. The classical limit of this product is given by the usual multiplication of functions (zeroth-order term), the magnetic Poisson bracket (first-order term), and by the magneto-metric connection (second-order term).PACS Nos.: 02.40.-k, 11.10.Nx

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22

Thiemann, T. "REDUCED PHASE SPACE QUANTIZATION OF SPHERICALLY SYMMETRIC EINSTEIN-MAXWELL THEORY INCLUDING A COSMOLOGICAL CONSTANT." International Journal of Modern Physics D 03, no. 01 (1994): 293–98. http://dx.doi.org/10.1142/s0218271894000496.

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We present here the canonical treatment of spherically symmetric (quantum) gravity coupled to spherically symmetric Maxwell theory with or without a cosmological constant. The quantization is based on the reduced phase space which is coordinatized by the mass and the electric charge as well as their canonically conjugate momenta, whose geometrical interpretation is explored. The dimension of the reduced phase space depends on the topology chosen, quite similar to the case of pure (2+1) gravity. We also compare the reduced phase space quantization to the algebraic quantization. Altogether, we observe that the present model serves as an interesting testing ground for full (3+1) gravity. We use the new canonical variables introduced by Ashtekar which simplifies the analysis tremendously.

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23

Brychkov, Yu A., and N. V. Savischenko. "Capacity of a communication channel with quadrature phase-shift keying and phase quantization." Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki 166, no. 3 (2024): 306–19. http://dx.doi.org/10.26907/2541-7746.2024.3.306-319.

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The influence of the number of phase quantization levels L on the capacity CM,L of a communication channel with additive white Gaussian noise (AWGN) was studied in a communication system using QPSK (4-PSK).

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24

Belmonte, Fabián. "Canonical quantization of constants of motion." Reviews in Mathematical Physics 32, no. 10 (2020): 2050030. http://dx.doi.org/10.1142/s0129055x20500300.

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We develop a quantization method, that we name decomposable Weyl quantization, which ensures that the constants of motion of a prescribed finite set of Hamiltonians are preserved by the quantization. Our method is based on a structural analogy between the notions of reduction of the classical phase space and diagonalization of selfadjoint operators. We obtain the spectral decomposition of the emerging quantum constants of motion directly from the quantization process. If a specific quantization is given, we expect that it preserves constants of motion exactly when it coincides with decomposable Weyl quantization on the algebra of constants of motion. We obtain a characterization of when such property holds in terms of the Wigner transforms involved. We also explain how our construction can be applied to spectral theory. Moreover, we discuss how our method opens up new perspectives in formal deformation quantization and geometric quantization.

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25

Huang, Qing Qing, and Jian Long Shao. "Fast Fourier Transform Measuring the Phase Difference Based on MATLAB." Applied Mechanics and Materials 556-562 (May 2014): 3035–38. http://dx.doi.org/10.4028/www.scientific.net/amm.556-562.3035.

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This paper expounded the principle of using Fast Fourier transform measuring the phase difference and completed the simulation of measuring the phase differences of a plurality of signal. The simulation results show that the method can rapidly and accurately realize the phase difference measurement without considering the AD quantization error and noise interference. In considering the AD quantization error and random noise, Fast Fourier transform measuring the phase difference still has high measurement accuracy, and the measurement error can be controlled within 0.01°. The method can be applied in practical engineering.

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COSTA DIAS, N., and J. N. PRATA. "DEFORMATION QUANTIZATION AND WIGNER FUNCTIONS." Modern Physics Letters A 20, no. 17n18 (2005): 1371–85. http://dx.doi.org/10.1142/s0217732305017822.

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We review the Weyl-Wigner formulation of quantum mechanics in phase space. We discuss the concept of Narcowich-Wigner spectrum and use it to state necessary and sufficient conditions for a phase space function to be a Wigner distribution. Based on this formalism we analize the modifications introduced by the presence of boundaries. Finally, we discuss the concept of environment-induced decoherence in the context of the Weyl-Wigner approach.

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27

FLORATOS, EMMANUEL. "MATRIX QUANTIZATION OF TURBULENCE." International Journal of Bifurcation and Chaos 22, no. 09 (2012): 1250213. http://dx.doi.org/10.1142/s0218127412502136.

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Based on our recent work on Quantum Nambu Mechanics [Axenides & Floratos 2009], we provide an explicit quantization of the Lorenz chaotic attractor through the introduction of noncommutative phase space coordinates as Hermitian N × N matrices in R3. For the volume preserving part, they satisfy the commutation relations induced by one of the two Nambu Hamiltonians, the second one generating a unique time evolution. Dissipation is incorporated quantum mechanically in a self-consistent way having the correct classical limit without the introduction of external degrees of freedom. Due to its volume phase space contraction, it violates the quantum commutation relations. We demonstrate that the Heisenberg–Nambu evolution equations for the Matrix Lorenz system develop fast decoherence to N independent Lorenz attractors. On the other hand, there is a weak dissipation regime, where the quantum mechanical properties of the volume preserving nondissipative sector survive for long times.

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28

Zhang, Jie, and Jiudong Zheng. "Prototype Verification of Self-Interference Suppression for Constant-Amplitude Full-Duplex Phased Array with Finite Phase Shift." Electronics 11, no. 3 (2022): 295. http://dx.doi.org/10.3390/electronics11030295.

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In view of the strong self-interference problem when the practical phased array system is simultaneously applied for transmission and reception, under the constraints including limited quantization number, constant envelope amplitude, scanning mode, wideband signal mode, etc., this work studies it and proposes the amplitude-phase joint adjustment method and the phase-only method for beamforming optimization. Through digital simulation design, electromagnetic simulation evaluation and principle test verification, under the actual array system conditions, including 6-bit phase quantization or phase step size of 5.625° and amplitude 0.5 dB quantization step, when the transmitting beam is pointing (0°, 0°), the research has achieved a performance of 11.9~14.4 dB for self-interference suppression; at the same time, the optimized beam shape is maintained well, and the ratio of the main lobe to the side lobes does not change significantly, but the beam gain has a loss of about 2~3 dB. In addition, we studied the interference suppression performance and beam feature retention performance of the optimized beamforming weights in the case of array scanning and broadband signals, and analyzed the influence of the changes in the mutual coupling characteristics between elements caused by scanning and frequency changes on the cancellation performance. This provides a reference for the application research of the simultaneous transmitting and receiving self-interference suppression technology in the actual array system state.

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Gazeau, Jean-Pierre, and Romain Murenzi. "Covariant Integral Quantization of the Semi-Discrete SO(3)-Hypercylinder." Symmetry 15, no. 11 (2023): 2044. http://dx.doi.org/10.3390/sym15112044.

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Covariant integral quantization with rotational SO(3) symmetry is established for quantum motion on this group manifold. It can also be applied to Gabor signal analysis on this group. The corresponding phase space takes the form of a discrete-continuous hypercylinder. The central tool for implementing this procedure is the Weyl–Gabor operator, a non-unitary operator that operates on the Hilbert space of square-integrable functions on SO(3). This operator serves as the counterpart to the unitary Weyl or displacement operator used in constructing standard Schrödinger–Glauber–Sudarshan coherent states. We unveil a diverse range of properties associated with the quantizations and their corresponding semi-classical phase-space portraits, which are derived from different weight functions on the considered discrete-continuous hypercylinder. Certain classes of these weight functions lead to families of coherent states. Moreover, our approach allows us to define a Wigner distribution, satisfying the standard marginality conditions, along with its related Wigner transform.

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Grewe, Adrian, and Stefan Sinzinger. "Efficient quantization of tunable helix phase plates." Optics Letters 41, no. 20 (2016): 4755. http://dx.doi.org/10.1364/ol.41.004755.

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Gosson, Maurice de. "The symplectic camel and phase space quantization." Journal of Physics A: Mathematical and General 34, no. 47 (2001): 10085–96. http://dx.doi.org/10.1088/0305-4470/34/47/313.

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BARONE, V., and V. PENNA. "GROUP THEORY OF THE NUMBER-PHASE QUANTIZATION." Modern Physics Letters B 09, no. 11n12 (1995): 685–92. http://dx.doi.org/10.1142/s0217984995000620.

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A formalism for the number-phase quantization, based on the doubting of the degrees of freedom, is studied from a group-theoretical viewpoint. The so-called relative number states are shown to be a standard basis of unitary irreducible representations of both SU(2) and SU(1, 1). The algebraic meaning of the relevant operators is elucidated and their eigenstates are constructed. As an example, the dynamics of the quantum-damped harmonic oscillator is worked out.

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33

Amemiya, Fumitoshi, and Tatsuhiko Koike. "Reduced phase space quantization of FRW universe." Journal of Physics: Conference Series 314 (September 22, 2011): 012053. http://dx.doi.org/10.1088/1742-6596/314/1/012053.

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Thiemann, T. "Reduced phase space quantization and Dirac observables." Classical and Quantum Gravity 23, no. 4 (2006): 1163–80. http://dx.doi.org/10.1088/0264-9381/23/4/006.

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35

de Gosson, Maurice A. "Phase space quantization and the uncertainty principle." Physics Letters A 317, no. 5-6 (2003): 365–69. http://dx.doi.org/10.1016/j.physleta.2003.09.008.

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36

Kuratsuji, Hiroshi, and Shinji Iida. "Semiclassical quantization with a quantum adiabatic phase." Physics Letters A 111, no. 5 (1985): 220–22. http://dx.doi.org/10.1016/0375-9601(85)90248-8.

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37

Kiukas, J. "Phase space quantization as a moment problem." Optics and Spectroscopy 103, no. 3 (2007): 429–33. http://dx.doi.org/10.1134/s0030400x07090123.

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Luan, Yuchen, Yuyang Lu, Jian Ren, and Fukun Sun. "Design of 2.5 Bit Programmable Metasurface Unit Cell for Electromagnetic Manipulation." Electronics 13, no. 9 (2024): 1648. http://dx.doi.org/10.3390/electronics13091648.

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Programmable metasurfaces are two-dimensional electromagnetic structures characterized by a low profile, conformability, and the ability to flexibly manipulate the amplitude and phase of electromagnetic waves. For high-quality beam scanning with the metasurface, it is essential that the metasurface possesses high-precision phase response quantization characteristics. This paper constructs a reflection-type metasurface unit cell featuring four P-I-N diodes and six operating states. To address the unit cell’s complexity and optimization challenges, we developed an automatic optimization algorithm, derived from the genetic optimization algorithm, for the metasurface unit cell. This algorithm was used to optimize a six-phase reflective 2.5 bit programmable metasurface cell operating at 5 GHz. The unit cell’s prototype was fabricated and measured to verify the design. Additionally, a metasurface comprising 16 × 16 unit cells was designed and simulated. The results highlight the metasurface unit cell’s excellent phase response quantization characteristics, and investigate the impact of quantization accuracy on beam scanning.

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39

Fu, Xin. "Noninterferometric optical phase-shifter module in phase-shifted optical quantization." Optical Engineering 48, no. 3 (2009): 034301. http://dx.doi.org/10.1117/1.3089884.

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ASHTEKAR, ABHAY, RANJEET TATE, and CLAES UGGLA. "MINISUPERSPACES: OBSERVABLES AND QUANTIZATION." International Journal of Modern Physics D 02, no. 01 (1993): 15–50. http://dx.doi.org/10.1142/s0218271893000039.

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A canonical transformation is performed on the phase space of a number of homogeneous cosmologies to simplify the form of the scalar (or Hamiltonian) constraint. Using the new canonical coordinates, it is then easy to obtain explicit expressions of Dirac observables, i.e. phase-space functions which commute weakly with the constraint. This, in turn, enables us to carry out a general quantization program to completion. We are also able to address the issue of time through “deparametrization” and discuss physical questions such as the fate of initial singularities in the quantum theory. We find that they persist in the quantum theory in spite of the fact that the evolution is implemented by a one-parameter family of unitary transformations. Finally, certain of these models admit conditional symmetries which are explicit already prior to the canonical transformation. These can be used to pass to the quantum theory following an independent avenue. The two quantum theories — based, respectively, on Dirac observables in the new canonical variables and conditional symmetries in the original ADM variables — are compared and shown to be equivalent.

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SAHOO, DEBENDRANATH, and M. C. VALSAKUMAR. "NONEXISTENCE OF QUANTUM NAMBU MECHANICS." Modern Physics Letters A 09, no. 29 (1994): 2727–32. http://dx.doi.org/10.1142/s0217732394002574.

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We investigate the problem of quantization of Nambu mechanics — a problem posed by Nambu [Phys. Rev.D7, 2405 (1973)] — along the line of Wigner–Weyl–Moyal (WWM) phase-space quantization of classical mechanics and show that the quantum analog of Nambu mechanics does not exist.

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42

Liu, Yue, Jifang Qiu, Chang Liu, Yan He, Ran Tao, and Jian Wu. "An Optical Analog-to-Digital Converter with Enhanced ENOB Based on MMI-Based Phase-Shift Quantization." Photonics 8, no. 2 (2021): 52. http://dx.doi.org/10.3390/photonics8020052.

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An optical analog-to-digital converter (OADC) scheme with enhanced bit resolution by using a multimode interference (MMI) coupler as optical quantization is proposed. The mathematical simulation model was established to verify the feasibility and to investigate the robustness of the scheme. Simulation results show that 20 quantization levels (corresponding to 4.32 of effective number of bits (ENOB)) are realized by using only 6 channels, which indicates that the scheme requires much fewer quantization channels or modulators to realize the same amount of ENOB. The scheme is robust and potential for integration.

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43

Gazeau, Jean-Pierre, and Romain Murenzi. "Integral Quantization for the Discrete Cylinder." Quantum Reports 4, no. 4 (2022): 362–79. http://dx.doi.org/10.3390/quantum4040026.

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Covariant integral quantizations are based on the resolution of the identity by continuous or discrete families of normalized positive operator valued measures (POVM), which have appealing probabilistic content and which transform in a covariant way. One of their advantages is their ability to circumvent problems due to the presence of singularities in the classical models. In this paper, we implement covariant integral quantizations for systems whose phase space is Z×S1, i.e., for systems moving on the circle. The symmetry group of this phase space is the discrete & compact version of the Weyl–Heisenberg group, namely the central extension of the abelian group Z×SO(2). In this regard, the phase space is viewed as the right coset of the group with its center. The non-trivial unitary irreducible representation of this group, as acting on L2(S1), is square integrable on the phase space. We show how to derive corresponding covariant integral quantizations from (weight) functions on the phase space and resulting resolution of the identity. As particular cases of the latter we recover quantizations with de Bièvre-del Olmo–Gonzales and Kowalski–Rembielevski–Papaloucas coherent states on the circle. Another straightforward outcome of our approach is the Mukunda Wigner transform. We also look at the specific cases of coherent states built from shifted gaussians, Von Mises, Poisson, and Fejér kernels. Applications to stellar representations are in progress.

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Xiao, Yang, Zhiguo Cao, Li Wang, and Tao Li. "Local phase quantization plus: A principled method for embedding local phase quantization into Fisher vector for blurred image recognition." Information Sciences 420 (December 2017): 77–95. http://dx.doi.org/10.1016/j.ins.2017.08.059.

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KALINOWSKI, M. W., and W. PIECHOCKI. "GEOMETRIC QUANTIZATION OF FIELD THEORY ON CURVED SPACE–TIME." International Journal of Modern Physics A 14, no. 07 (1999): 1087–110. http://dx.doi.org/10.1142/s0217751x99000543.

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A symplectic structure of classical field theory and its application to the canonical geometric quantization procedure are presented. The developed formalism can be treated in two ways: as a prequantization procedure in the usual sense or as a quantization procedure in a stochastic quantum mechanics approach on a phase space.

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46

Park, Sungkyung, and Chester Sungchung Park. "Quantization Noise Analysis of Time-to-Digital-Converter-Based All-Digital Phase-Locked Loop and Frequency Discriminators." Journal of Circuits, Systems and Computers 25, no. 11 (2016): 1650131. http://dx.doi.org/10.1142/s0218126616501310.

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All-digital phase-locked loops (ADPLLs) based on the time-to-digital converter (TDC) and the frequency discriminator (FD) are modeled and analyzed in terms of quantization effects. Using linear models with quantization noise sources, theoretical analysis and simulation are carried out to obtain the output phase noise of each building block of the TDC-based ADPLL. It is newly derived that the TDC noise component caused by the delta-sigma modulator (DSM) and the finite resolution of the digitally controlled oscillator is not white. Namely, the in-band phase noise caused by the DSM-induced TDC is not white, which is due to the integrate-and-dump and subsampling operations of the TDC. This can give some insight into the design of low-noise ADPLLs. Some structures of delta-sigma FDs, which can serve as an alternative to the TDC, are also newly analyzed in terms of quantization noise, using the derived linear noise model.

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Pang, Jing, Wei Hua Mou, Xiao Mei Tang, and Gang Ou. "Effects of Phase Jitter on the Navigation Signal Simulator." Applied Mechanics and Materials 602-605 (August 2014): 2781–84. http://dx.doi.org/10.4028/www.scientific.net/amm.602-605.2781.

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As the measuring equipment of the navigation receivers, high precision pseudorange signal is generated by navigation signal simulator. Pseudorange error is mainly from modeling error in high dynamic scenarios, but it is mainly from phase quantization error of digital implementation process in high precision scenarios of evaluating receiver’s pseudorange accuracy. Is this paper, according to the implementation principle of carrier and code DDS, the causes of the phase quantization error is analyzed and the pseudorange error formula is derived and the simulation results are given. Analysis and simulation results show that phase critter originated by carry phase truncation effects measurement result of zero value and cannot be ignored. The conclusion can guide the design of navigation signal simulator.

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48

Mena-Parra, J., K. Bandura, M. A. Dobbs, J. R. Shaw, and S. Siegel. "Quantization Bias for Digital Correlators." Journal of Astronomical Instrumentation 07, no. 02n03 (2018): 1850008. http://dx.doi.org/10.1142/s2251171718500083.

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In radio interferometry, the quantization process introduces a bias in the magnitude and phase of the measured correlations which translates into errors in the measurement of source brightness and position in the sky, affecting both the system calibration and image reconstruction. In this paper, we investigate the biasing effect of quantization in the measured correlation between complex-valued inputs with a circularly symmetric Gaussian probability density function (PDF), which is the typical case for radio astronomy applications. We start by calculating the correlation between the input and quantization error and its effect on the quantized variance, first in the case of a real-valued quantizer with a zero mean Gaussian input and then in the case of a complex-valued quantizer with a circularly symmetric Gaussian input. We demonstrate that this input-error correlation is always negative for a quantizer with an odd number of levels, while for an even number of levels, this correlation is positive in the low signal level regime. In both cases, there is an optimal interval for the input signal level for which this input-error correlation is very weak and the model of additive uncorrelated quantization noise provides a very accurate approximation. We determine the conditions under which the magnitude and phase of the measured correlation have negligible bias with respect to the unquantized values: we demonstrate that the magnitude bias is negligible only if both unquantized inputs are optimally quantized (i.e. when the uncorrelated quantization error model is valid), while the phase bias is negligible when (1) at least one of the inputs is optimally quantized, or when (2) the correlation coefficient between the unquantized inputs is small. Finally, we determine the implications of these results for radio interferometry.

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49

Rosati, Giacomo. "The Duflo non-commutative Fourier transform for the Lorentz group." International Journal of Geometric Methods in Modern Physics 17, supp01 (2020): 2040011. http://dx.doi.org/10.1142/s0219887820400113.

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For a quantum system whose phase space is the cotangent bundle of a Lie group, like for systems endowed with particular cases of curved geometry, one usually resorts to a description in terms of the irreducible representations of the Lie group, where the role of (non-commutative) phase space variables remains obscure. However, a non-commutative Fourier transform can be defined, intertwining the group and (non-commutative) algebra representation, depending on the specific quantization map. We discuss the construction of the non-commutative Fourier transform and the non-commutative algebra representation, via the Duflo quantization map, for a system whose phase space is the cotangent bundle of the Lorentz group.

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Yuan, Y., S. Cheung, T. Van Vaerenbergh, et al. "Low-phase quantization error Mach–Zehnder interferometers for high-precision optical neural network training." APL Photonics 8, no. 4 (2023): 040801. http://dx.doi.org/10.1063/5.0146062.

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A Mach–Zehnder interferometer is a basic building block for linear transformations that has been widely applied in optical neural networks. However, its sinusoidal transfer function leads to the inevitable dynamic phase quantization error, which is hard to eliminate through pre-calibration. Here, a strongly overcoupled ring is introduced to compensate for the phase change without adding perceptible loss. Two full-scale linearized Mach–Zehnder interferometers are proposed and experimentally validated to improve the bit precision from 4-bit to 6- and 7-bit, providing ∼3.5× to [Formula: see text] lower phase quantization errors while maintaining the same scalability. The corresponding optical neural networks demonstrate higher training accuracy.

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