Proper Quantization Research Articles

Black hole interior quantization: a minimal uncertainty approach

In a previous work we studied the interior of the Schwarzschild black hole implementing an effective minimal length, by applying a modification to the Poisson brackets of the theory. In this work we perform a proper quantization of such a system. Specifically, we quantize the interior of the Schwarzschild black hole in two ways: once by using the standard quantum theory, and once by following a minimal uncertainty approach. Then, we compare the obtained results from the two approaches. We show that, as expected, the wave function in the standard approach diverges in the region where classical singularity is located and the expectation value of the Kretschmann scalar also blows up on this state in that region. On the other hand, by following a minimal uncertainty quantization approach, we obtain 5 new and important results as follows. (1) All the interior states remain well-defined and square-integrable. (2) The expectation value of the Kretschmann scalar on the states remains finite over the whole interior region, particularly where used to be the classical singularity, therefore signaling the resolution of the black hole singularity. (3) A new quantum number is found which plays a crucial role in determining the convergence of the norm of states, as well as the convergence and finiteness of the expectation value of the Kretschmann scalar. (4) A minimum for the radius of the (2-spheres in the) black holes is found (5) By demanding square-integrability of states in the whole interior region, an exact relation between the Barbero-Immirzi parameter and the minimal uncertainty scale is found.

Thermodynamic properties and superstatistics analysis of particle in the non-relativistic system under the influence of trigonometric scarf potential using Dong proper quantization

There has been an intense study on the eigenvalue and eigenfunction of the nonrelativistic quantum system. The Schrodinger equation is important in the nonrelativistic quantum system that is used to analyze the quantum information of the system, so it attached the interest of the researchers to conduct the exploration on it. In most of the studies, the researchers expand the study of the solution of the Schrodinger equation to the physical properties of the system. The thermodynamical property is one of the physical properties and key to analyzing the characteristic of materials. It needs more investigation since it has the potential to form a new design of the material. In this study, the Schrodinger equation with trigonometric Scarf potential was solved using the Supersymmetry WKB quantization condition scheme, where the variable of trigonometric Scarf potential was transformed into the Poschl-Teller potential. The energy spectra were obtained by comparing the constant parameters between Trigonometric Scarf potential and Poschl-Teller potential and by using Dong proper quantization condition of transformed Supersymmetry WKB for trigonometric Scarf potential. The result shows that the energy spectra are influenced by the radial quantum number and the potential width, and the energy increase by the increase of the radial quantum number and the potential width. The thermodynamic properties of the system were obtained approximately using the energy spectra equation and were expressed in the erf function. The superstatistics mechanics was approximately obtained by using modified Delta Dirac function distribution for the Boltzmann factor. These properties are important to analyze the characteristic of the designed solids.

Proper time quantization of a thin shell

“Time” has different meanings in classical general relativity and in quantum theory. While all choices of a time function yield the same local classical geometries, quantum theories built on different time functions are not unitarily equivalent. This incompatibility is most vivid in model systems for which exact quantum descriptions in different time variables are available. One such system is a spherically symmetric, thin dust shell. In this paper, we will compare the quantum theories of the shell built on proper time and on a particular coordinate time. We find wholly incompatible descriptions: whereas the shell quantum mechanics in coordinate time admits no solutions when the mass is greater than the Planck mass, its proper time quantum mechanics only admits solutions when the mass is greater than the Planck mass. The latter is in better agreement with what is expected from observation. We argue that proper time quantization provides a superior approach to the problem of time in canonical quantization.

Selective mode excitations and spontaneous emission engineering in quantum emitter-photonic structure coupled systems.

We study the excitation conditions of the supported field modes, as well as the spontaneous decay property of a two-level quantum emitter coupled to photonic structures containing topological insulators (TIs) and left-handed materials. Within the proper field quantization scheme, the spontaneous decay rates of dipoles with different polarizations are expressed in forms of the Green's functions. We find that in the proposed structure, the variation in the topological magnetoelectric polarizability (TMP) has a deterministic effect on the excitation of different field modes. As the result, the spontaneous decay property of the quantum emitter can be engineered. For a dipole placed in different spatial regions, the spontaneous decay feature indicates a dominant contribution from the waveguide modes, the surface plasmon modes or the free vacuum modes. Moreover, a special kind of the surface plasmon modes displaying asymmetric density of states at the interfaces, becomes legal in the presence of nontrivial TIs. These phenomena manifest the feasibility in controlling dipole emissions via manipulations of the topological magnetoelectric (TME) effect. Our results have potential applications in quantum technologies relied on the accurate control over light-matter interactions.

The Particle in a Box Warrants an Examination

The particle in a box is a simple model that has a classical Hamiltonian H = p2 (using 2m = 1), with a limited coordinate space, -b q b, where 0 b < ∞. Using canonical quantization, this example has been fully studied thanks to its simplicity, and it is a common example for beginners to understand. Despite its repeated analysis, there is a feature that puts the past results into question. In addition to pointing out the quantization issue, the procedures of affine quantization can lead to a proper quantization that necessarily points toward more complicated eigenfunctions and eigenvalues, which deserve to be solved.

Energy and momentum eigenspectrum of the Hulthén-screened cosine Kratzer potential using proper quantization rule and SUSYQM method.

Using the Qiang-Dong proper quantization rule (PQR) and the supersymmetric quantum mechanics approach, we obtain the eigenspectrum of the energy and momentum for time-independent and time-dependent Hulth'en-screened cosine Kratzer potentials. For the suggested time-independent Hulthén-screened cosine Kratzer potential (HSCKP), we solve the Schrödinger equation in D dimensions. The Feinberg-Horodecki equation for time-dependent Hulth'en-screened cosine Kratzer potential (tHSCKP) also solves. To address the inverse square term in the time-independent and time-dependent equations, we employed the Greene-Aldrich approximation approach. We were able to extract time-independent and time-dependent potentials, as well as their accompanying energy and momentum spectra. In three-dimensional space, we estimate the rotational vibrational (RV) energy spectrum for many homodimers (H2, I2, O2) and heterodimers (MnH, ScN, LiH, HCl). We also use the recently introduced formula approach to obtain the relevant eigen function. We also calculate momentum spectra for the dimers MnH and ScN. The method is compared to prior methodologies for accuracy and validity using numerical data for heterodimer LiH, HCl and homodimer I2, O2, H2. The calculated energy and momentum spectra are tabulated and analyzed.

Determination of Energy Spectra By Using Proper Quantization Rule of Woods-Saxon Potential

In this study, the energy spectra of Schrodinger equation for non-zero l values considering Woods Saxon potential (WSP) is calculated using proper quantization rule, then the binding energies (BE) of random light nuclei is obtained and the optimized potential parameters such as potential depth (V0) and surface thickness (a) are found. In order to calculate the energy levels of the nuclei with WSP, the PQR method was used, which has not been considered before. In quantum mechanics, the exact solution of energy systems, momentum, and quantum states can be found using the proper quantization rule(PQR) method.Using the Matlab calculation program, we have achieved numerical values of the energy spectrum for random light nuclei and compared the result with the experimental Nuclear Data Center (NDC) values. In addition, we found potential depth and surface thickness for four light nuclei. Correlations between the light nuclei show the facts about the nuclear structure characteristics, origin, and energies of these nuclei. Pearson’s correlation coefficient is accepted as the most common correlation coefficient. According to the values of Pearson correlation coefficients, it is observed that there is a significant positive correlation between the nucleons examined. Finally, we plot the E-V0-a diagrams for those values to optimize and provide the appropriate coefficients. It is shown that there is a good agreement between the results of this work and experimental values.

Bound states of Dirac equation using the proper quantization rule

Using the proper quantization rule, we investigate the exact solution of Dirac equation for Hartmann and the ring-shaped non-spherical harmonic oscillator potentials under the condition of equal scalar and vector potentials. By considering the proper quantization condition within angular and radial variables, the exact relativistic energy spectra are obtained for each system. Then by the mean of suitable changes of variables, the corresponding spinor wave-functions are constructed where the normalization constants are exactly calculated. We also derived the non-relativistic limit of energy spectra.

J—state solutions and thermodynamic properties of the Tietz oscillator

In this work, we have solved the radial part of the Schrödinger equation with Tietz potential to obtain explicit expressions for bound state ro-vibrational energies and radial eigenfunctions. The proper quantization rule and ansatz solution technique were used to arrive at the solutions. In modeling the pseudo-spin–orbit term of the effective potential, the Pekeris-like and the Greene-Aldrich approximation recipes were applied. Using our equation for eigen energies, we have deduced expression for bound state energy eigenvalues of Deng-Fan oscillator. The result obtained agrees with available literature data for this potential. Also, for arbitrary values of rotational and vibrational quantum numbers, we have calculated bound state energies for the Tietz oscillator. Our computed results are in excellent agreement with those in the literature. Furthermore, the result showed that unlike Greene-Aldrich approximation, energies computed based on Pekeris-like approximation are better and almost indistinguishable from numerically obtained energies of the Tietz oscillator in the literature. With the help of our formula for ro-vibrational energy, analytical expressions for some important thermodynamic relations were also derived for the Tietz oscillator. The derived thermal functions which include ro-vibrational: partition function, free energy, mean energy, entropy and specific heat capacity were subsequently applied to the spectroscopic data of KI diatomic molecule. Studies of the thermal functions indicated that the partition function decreases monotonically as the temperature is raised and increases linearly for increase in the upper bound vibrational quantum number. On the other hand, increase in either temperature or upper bound vibrational quantum number amounts to monotonic rise in the entropy of the KI molecules

Deep Task-Based Quantization.

Quantizers play a critical role in digital signal processing systems. Recent works have shown that the performance of acquiring multiple analog signals using scalar analog-to-digital converters (ADCs) can be significantly improved by processing the signals prior to quantization. However, the design of such hybrid quantizers is quite complex, and their implementation requires complete knowledge of the statistical model of the analog signal. In this work we design data-driven task-oriented quantization systems with scalar ADCs, which determine their analog-to-digital mapping using deep learning tools. These mappings are designed to facilitate the task of recovering underlying information from the quantized signals. By using deep learning, we circumvent the need to explicitly recover the system model and to find the proper quantization rule for it. Our main target application is multiple-input multiple-output (MIMO) communication receivers, which simultaneously acquire a set of analog signals, and are commonly subject to constraints on the number of bits. Our results indicate that, in a MIMO channel estimation setup, the proposed deep task-bask quantizer is capable of approaching the optimal performance limits dictated by indirect rate-distortion theory, achievable using vector quantizers and requiring complete knowledge of the underlying statistical model. Furthermore, for a symbol detection scenario, it is demonstrated that the proposed approach can realize reliable bit-efficient hybrid MIMO receivers capable of setting their quantization rule in light of the task.

Background dominant colors extraction method based on color image quick fuzzy c-means clustering algorithm

A quick and accurate extraction of dominant colors of background images is the basis of adaptive camouflage design. This paper proposes a Color Image Quick Fuzzy C-Means (CIQFCM) clustering algorithm based on clustering spatial mapping. First, the clustering sample space was mapped from the image pixels to the quantized color space, and several methods were adopted to compress the amount of clustering samples. Then, an improved pedigree clustering algorithm was applied to obtain the initial class centers. Finally, CIQFCM clustering algorithm was used for quick extraction of dominant colors of background image. After theoretical analysis of the effect and efficiency of the CIQFCM algorithm, several experiments were carried out to discuss the selection of proper quantization intervals and to verify the effect and efficiency of the CIQFCM algorithm. The results indicated that the value of quantization intervals should be set to 4, and the proposed algorithm could improve the clustering efficiency while maintaining the clustering effect. In addition, as the image size increased from 128 × 128 to 1024 × 1024, the efficiency improvement of CIQFCM algorithm was increased from 6.44 times to 36.42 times, which demonstrated the significant advantage of CIQFCM algorithm in dominant colors extraction of large-size images.

Non-Abelian extension of the aether term and the Gribov problem

In this paper, we treat the proper path integral quantization of the Yang–Mills-aether (YM-aether) system by dealing with the extra gauge copies in the Landau gauge. Within Gribov’s prescription to get rid of such remaining gauge copies, we explicitly derive the Gribov parameter dependence of the coupling constant and of the Lorentz violation aether term. The ultraviolet limit is investigated under the light of recent bounds on the magnitude of the non-Abelian aether parameter, and we show that the Gribov parameter can be disregarded in that limit.

A frame-level MLP-based bit-rate controller for real-time video transmission using VVC standard

Real-time video transmission is one of the most popular applications that are included in the versatile video coding (VVC) standard. However, real-time applications are encountered with practical limitations, including the buffer size and available bandwidth. In these applications, the buffer overflow and underflow should be strictly prevented and also the bit-rate fluctuation should be suppressed. In this paper, a video bit-rate controller is proposed that completely conforms with the constraints of real-time applications. The proposed controller is based on a multi-layer perceptron (MLP) neural network which estimates the proper quantization parameter (QP) modification at the frame level. The buffer occupancy is directly included in the QP derivation process for robust buffer control. Experimental results show that the proposed bit-rate controller fulfils the buffering constraints and controls the bit-rate accurately. The average bit-rate error of the proposed method is 0.29% while providing a low initial buffering delay of about 0.21 s. Also, the rate-distortion analysis shows that the performance of the proposed method is close to those of the conventional algorithms.

A perceptual rate control algorithm based on luminance adaptation for HEVC encoders

This paper proposes a rate control algorithm by selecting a proper quantization parameter (QP) based on perceptual luminance adaptation in a single-loop encoding fashion. In this paper, the proposed algorithm uses the visual characteristics of humans to adaptively decide the number of bits available for a pixel. Then, a base QP is selected based on the proposed R–λ model. The proposed rate control determines the range of QP based on the base QP and calculates the maximum and minimum bpps within that range. The optimal bpp is obtained from the bpp range by considering the visual characteristics of the human being, and the QP value is determined by the optical bpp through the proposed R–λ model. In the proposed rate control algorithm, the QP value is selected based on the R–λ model by considering the perceptual luminance adaptation model at the CTU level. The number of target bits is decided to decide the QP, subject to visual sensitivity based on JND thresholds. With the use of the proposed rate control algorithm, bits for non-noticeable regions can be saved, and the remaining bits can be consumed for perceptually noticeable regions to enhance the overall subjective quality with the similar amount of total bits. The proposed method shows lower average variances of bits and PSNR fluctuations. Also, the proposed method achieves an approximately 0.19 higher MOS value on average under DSCQS test, compared with the conventional R–λ model-based rate control algorithm.

Model-Based Deep Learning for One-Bit Compressive Sensing

In this work, we consider the problem of one-bit deep compressive sensing from both a system design and a signal recovery perspective. In particular, we develop hybrid model-based deep learning architectures based on the deep unfolding methodology. We further interpret the overall data-acquisition and signal recovery modules as an auto-encoder structure allowing for learning task-specific sensing matrix, quantization thresholds, as well as the latent-parameters of iterative first-order optimization algorithms specifically designed for the problem of one-bit sparse signal recovery. The proposed model-based deep architectures have the ability to adaptively learn the proper quantization thresholds, paving the way for amplitude recovery in one-bit compressive sensing. We further show that the proposed methodology implicitly learns task-specific sensing matrices with very low coherence, which is highly desirable in a compressive sensing setting. Due to the model-based nature of the proposed deep architecture, it enjoys from the interpretability and versatility of model-based techniques as well as benefiting from the expressive power of data-driven methods. Specifically, owing to its model-based nature, it has far fewer parameters and requires far less samples for training as compared to black-box machine learning models. Our results demonstrate a significant improvement compared to state-of-the-art algorithms.

Efficient Hardware for Generalized Turbo Signal Recovery in Compressed Sensing

Compressed sensing (CS) is becoming a hot topic in recent years for its advantages such as low-power consumption, low memory requirement, and low sampling frequency. However, high-dimensional nonlinear signals will inevitably introduce notable complexity and low efficiency in signal recovery. Generalized turbo signal recovery (G-Turbo-SR) is a cutting-edge method, which efficiently reduces complexity with a partial discrete Fourier transform (DFT) sensing matrix. However, in practical applications, G-Turbo-SR still suffers from high complexity for probability computations and matrix multiplications. This article optimizes the algorithm of G-Turbo-SR in scheduling to reduce the matrix multiplications by half. High-precision numerical approximation method is proposed to replace the complex integral calculation, which efficiently reduces the hardware cost with acceptable performance degradation. Based on the data-flow graph (DFG) analysis, detailed hardware architecture is proposed with module designs. Proper quantization scheme is selected according to the mean square error (MSE) performance. Pipelining, folding, and variable precision quantization (VPQ) scheme are employed for higher hardware efficiency. FPGA implementation on Xilinx 7k325tffg900-2 shows a higher throughput and hardware efficiency compared to existing recovery methods for CS.

Approximate solution of the Schrödinger equation with Manning-Rosen plus Hellmann potential and its thermodynamic properties using the proper quantization rule

We obtained, by using the proper quantization rule, the approximate solutions of the Schrodinger equation with Manning-Rosen plus Hellmann potential for any l-state. Furthermore, thermodynamic properties, such as the vibrational mean U , specific heat C, free energy F and entropy S for the pure vibrational state in the classical limit for these energy eigenvalues, are studied.

On the Performance of Cell-Free Massive MIMO With Low-Resolution ADCs

This paper considers an uplink cell-free massive multi-input multi-output (mMIMO) system with multi-antenna access points (APs) and users, assuming low-resolution analog-to-digital converter (ADC) architecture is employed at the APs. Leveraging on the additive quantization noise model (AQNM), we derive a tight approximate expression for uplink spectral efficiency (SE). This trackable finding provides us with a tool for easily quantifying the impacts of the number of antenna arrays and the number of quantization bit of low-resolution ADCs. We find 5-bit is required in a cell-free mMIMO with low-resolution ADCs to achieve the same SE as a cell-free mMIMO with full-precision ADCs. Besides, when the number of antennas of the user is small, deploying more antennas at the users can boost the sum SE. Then, to further highlight the potential of low-resolution ADCs architecture, we also investigate the tradeoff between the SE and energy efficiency (EE) with design issues surrounding the quantization bit of low-resolution ADCs and the number of antenna arrays. The resulting observations reveal that by choosing a proper quantization bit, the cell-free mMIMO with low-resolution ADCs has the capability to enjoy a better SE-EE tradeoff compared to the perfect ADCs counterpart.

Energy spectra and the expectation values of diatomic molecules confined by the shifted Deng-Fan potential

The approximate bound state solutions of the Schrodinger equation with the shifted Deng-Fan potential was obtained via a proper quantization rule. The energy spectra for the homogenous diatomic molecules (H2, I2); the heterogeneous diatomic molecules (CO, HCl, LiH); the neutral transition metal hydrides (ScH, TiH, VH, CrH); the transition-metal lithide (CuLi); the transition-metal carbides (TiC, NiC); the transition metal nitrite (ScN) and the transition metal fluoride (ScF) were calculated. By applying the Hellmann-Feynman theorem, the expression for the expectation values of the square of inverse of position r-2, potential energy V, kinetic energy T and the square of momentum p2 were derived and the numerical values for diatomic molecules were presented. The result is reliable and very consistent with the available ones in the literature.

3DoF+ 360 Video Location-Based Asymmetric Down-Sampling for View Synthesis to Immersive VR Video Streaming.

Recently, with the increasing demand for virtual reality (VR), experiencing immersive contents with VR has become easier. However, a tremendous amount of calculation and bandwidth is required when processing 360 videos. Moreover, additional information such as the depth of the video is required to enjoy stereoscopic 360 contents. Therefore, this paper proposes an efficient method of streaming high-quality 360 videos. To reduce the bandwidth when streaming and synthesizing the 3DoF+ 360 videos, which supports limited movements of the user, a proper down-sampling ratio and quantization parameter are offered from the analysis of the graph between bitrate and peak signal-to-noise ratio. High-efficiency video coding (HEVC) is used to encode and decode the 360 videos, and the view synthesizer produces the video of intermediate view, providing the user with an immersive experience.