Quantization Theory Research Articles

Minimal length scale in quantum mechanics from a deformation quantization perspective

Abstract We develop a deformation quantization approach to quantum mechanics that exhibits a nonzero minimal uncertainty in position through the modification of commutation relations for the operators of position and momentum. Deformation quantization is a method of quantizing a classical Hamiltonian system by suitably deforming the Poisson algebra of the system. The developed theory of deformation quantization is non-formal. An appropriate integral formula for the star-product is introduced, along with a suitable space of functions on which the star-product is well defined. A C*-algebra of observables and a space of states are constructed. Moreover, an operator representation in momentum space is presented. Finally, an example of states of maximal localization is given in terms of generalized Wigner functions.

Theory of Space Quantization and the Quantum Level Understanding of the True Logics of the Principles of Thermodynamics and Heat Engines

The recently discovered Topological Theory of Quantum Gravity (TTQG) is basically a Theory of Space Quantization (TSQ) and in this article first of all it has been substantiated that though the laws of thermodynamics, the well-known thermodynamic principles, the operations of heat engines are very much intuitive but they, in their conventional representations, miserably lack the harmony to the quantized ‘space -time’ of the universe. The well-known thermodynamic parameters, e.g., pressure (P), volume (V), heat content (H), internal energy (U), entropy (S), Gibbs free energy (G),....etc. and the related physical variables like ‘time’ (t)and ‘mass’ (m) do exist in the form of ‘quantum’ or ‘packets’(referred as Gravitons in TTQG) and those are continuously being exchanged between the so called ‘thermodynamic systems’ and the ‘space-time’. It has been shown in this article that a ‘thermodynamic system’ and the above said ‘space quantums’ are very much complimentary and ‘part and parcel’ to each other and a quantum level ‘space-time’ rich understanding has been made through the TSQ of the true logic behind the standing of the thermodynamic laws and the operations of the heat engines.

Optimizing Cellular Networks for UAV Corridors via Quantization Theory

Optimizing Cellular Networks for UAV Corridors via Quantization Theory

Theory of size quantization in monolayers of transition metal dichalcogenides

A theory of size quantization has been developed for both one-dimensional and zero-dimensional nanostructures, grown from monolayers of transition metal dichalcogenides. Expressions for the energy spectra of charge carriers have been obtained for both even and odd (relative to coordinate inversion) states in the quantum-confined line and point of monolayers of transition metal dichalcogenides, depending on their geometric dimensions. A numerical analysis of the quantum-confined energy states of electrons in nanostructures of monolayers of transition metal dichalcogenides has been conducted.

Theory of Linear-Circular Dichroism in Monoatomic Layers of Transition Metal Dichalcogenides Taking into Account the Rabi Effect

We have developed a theory of dimensional quantization for nanostructures, both one-dimensional and zero-dimensional, constructed from monoatomic layers of transition metal dichalcogenides (TMDCs). This theory has enabled us to derive expressions for the energy spectra of charge carriers in both even and odd states (relative to coordinate inversion), as these states occur within quantum-confined lines and points of the TMDC monoatomic layers, dependent on their geometric dimensions. Our numerical analysis provides a detailed exploration of the quantum-confined energy states of electrons within these nanostructures, offering insights into their potential applications in advanced nanoelectronic devices. This work not only advances our understanding of the energy characteristics of TMDC monoatomic layers but also contributes to the broader field of material science by exploring the effects of dimensional quantization on electronic properties.

Adaptive step size quantized simulation method for gas–electricity integrated energy systems

Gas–electricity integrated energy systems (GE-IES) offers a promising solution for enhancing energy efficiency and accommodating renewable energy sources. Accurate dynamic simulation is essential for optimizing and controlling GE-IES. However, the presence of various local controllers introduces prominent discrete characteristics, posing challenges for the dynamic simulation of the GE-IES. This paper investigates the dynamic simulation method in GE-IES with discrete characteristics. Firstly, we propose an adaptive step size simulation method based on quantized state system theory. This method maintains the event-driven characteristics of the quantized state integration algorithms, while enhancing computational speed through adaptive step size adjustments. Secondly, we establish an event-driven simulation framework that facilitates interactions of different subsystems during the dynamic simulation, improving the compatibility with various models and solving algorithms. Finally, we validate the accuracy, efficiency, and scalability of the proposed method and the framework using two typical GE-IES cases with different scales. Simulation results demonstrate the effectiveness on the dynamic simulation of GE-IES and highlight the feasibility of natural gas networks in consuming and storing surplus renewable energy.

Berezin quantization and representation theory

We present an approach to Berezin quantization (a variant of quantization in the spirit of Berezin) on para-Hermitian symmetric spaces using the notion of an “overgroup”. This approach gives covariant and contravariant symbols and the Berezin transform in a natural and transparent way.

To the theory of dimensional quantization in crystals in the Kane approximation

The microscopic mechanism of size quantization of the conduction band and valence band of semiconductors of cubic and tetrahedral symmetry has been theoretically studied in the Kane approximation. It is shown that the matrix Schrödinger equation obtained on the basis of the Kane model cannot be solved analytically for a potential well of an arbitrary profile. Therefore, expressions for the energy spectrum are obtained depending on the two-dimensional wave vector directed along the interface of the heterostructure for various cases that differ in the range of current carrier energy values.

Embodying the Abstract ‘Time Variable’ of the Universe through Thermodynamics and the Theory of Space Quantization (TSQ)

The world of general physics, cosmology, astronomy, and space physics has progressed rapidly with diversity and multidisciplinary research discoveries and inventions over the last two centuries. However, despite this significant advancement in science, the mystery of the physical variable ‘time,’ or what ‘time’ truly is, remained unresolved until the discovery of the Theory of Space Quantization (TSQ) or the Topological Theory of Quantum Gravity (TTQG). In this short review article, the development of the concept of time in TSQ is discussed and explained from the perspectives of topology, geometry, and thermodynamics. The impact on traditional thoughts or concepts in physics after incorporating the ‘time variable’ is also highlighted.

Theory of Space Quantization (Tsq) Driven Version of the Conventional Theories of Physics, Relativity and Gravitation-A Concise Report

The global scientific community at the moment is awaiting passionately for a ‘Theory of Everything’ (TOE) and the level of expectation of the said community is, i) the Theory has to be very robust and versatile ii) the theory should be in a position to fully explain and connect all the happenings and aspects of the universe and iii) the said TOE has to be a multi block compatibilizing one (is in harmony with the existing theories of physics) and as well has to establish the fact that the theories of physics proposed so far, though have been presented in many different forms but they are inherently being identical by their origins or routes. In this small article it is being reported that the recently discovered ‘ Topological Theory of Quantum gravity (TTQG) or the ‘ Theory of Space Quantization’ (TSQ) has already unified the theories of ‘Newtonian physics or classical physics’, ‘thermodynamics’, ‘quantum mechanics’, ‘cosmological theories’ and the ‘theories of relativities’ under a single umbrella and revealed the dimensionalities of ‘time’ , ‘mass’, ‘space expansion-space inversion’ of the universe , geometries of ‘gravitation’ the ‘singularity’ and the dimensionality of the universe itself and as well presented an ‘Universal Graviton Cycle’ to explain most of the cosmic/astronomical phenomena of the universe in a single frame. It is a first foot step of TSQ or TTQG to ultimately converge to the ‘Theory of Everything’.

An empirical study of a simple incremental classifier based on vector quantization and adaptive resonance theory

An empirical study of a simple incremental classifier based on vector quantization and adaptive resonance theory

To the Theory of Dimensional Quantization in Narrow-Gap Crystals

This article discusses studies of size quantization phenomena in zero-, one-, and two-dimensional semiconductor structures. The main attention is paid to the mechanisms of photon-kinetic effects in these structures. Despite many studies of the physical properties of low-dimensional systems of current carriers, the size quantization of energy spectra in narrow-gap semiconductors and the associated photonic-kinetic effects are still insufficiently studied. Therefore, this study focuses on the quantum mechanical study of size quantization in certain cases using Kane's multiband model. The insolvability of the 8×8 matrix Schrödinger equation in the Kane model for a potential well of arbitrary shape is analyzed. The dependence of the energy spectrum on the two-dimensional wave vector is studied for various cases. In particular, the energy spectra for InSb and GaAs semiconductors are considered, depending on the band parameters and the size of the potential well. Conclusions are presented on the analysis of various cases of size quantization in narrow-gap crystals with cubic or tetrahedral symmetry in the three-band approximation. It is shown that the energy spectrum corresponds to a set of size-quantized levels that depend on the Rabi parameter, band gap, and well size. The size-quantized energy spectra of electrons and holes in InSb and GaAs semiconductors are analyzed in a multiband model.

The impact of quantized magnetic pressure on the stimulated Brillouin scattering of electromagnetic waves

Within the frame work of Landau quantization theory of Fermi gas, we formulate here the exotic physics of magnetic stimulated Brillouin scattering instability (MSBS) arising due to the nonlinear interaction of high frequency electromagnetic waves (EMWs) with degenerate, strongly magnetized electron-ion plasma. Quantum magneto hydrodynamic model (QMHD) is followed to develop the basic differential equations of quantized magnetosonic waves (QMWs) in the presence of super strong magnetic (SSH) field, whereas Maxwell equations are used to derive the governing differential equation of pump EMWs. The nonlinear interaction of EMWs and QMWs is addressed by employing the phasor matching technique. The obtained dispersion relation of MSBS shows that for a fixed density of fermions, the SSH field alone suppresses the MSBS instability as a function of quantized magneto ion velocity (C He ) and the Alfven speed (V A ) via three-wave decay and modulational instabilities. However, for particular condition the MSBS instability is found to increase as a function of SSH field. Next, the analytical results are verified numerically and graphically for soft x-rays in the environment of neutron star. The present MSBS analysis may be critical in neutron stars, radio pulsars and magnetars having super strong magnetic field i.e. even larger than the quantum threshold value i.e, H ∼ 4.4 × 1013 G, or in any application where the enhancement or suppression of SBS may be important.

Signatures of quantized magnetic field on the nonlinear Landau damping of transverse electromagnetic waves

A quantum kinetic approach alongwith the Landau theory of quantization (LQ) is utilized to study the impact of the magnetic field on the nonlinear Landau damping (NLD) of transverse electromagnetic (EM) waves in a degenerate electron-ion plasma. The gyratory motion of fermions around the magnetic field (H) lines gets quantized into the Landau levels and consequently the associated Fermi–Dirac distribution function becomes modified with the fermion cyclotron frequency under the limit l ℏ ω ce − ε Fe ≫ k B T e , where l is the orbital quantum number with all other standard notations. In this context, the density oscillations due to electrons are calculated in the presence of the LQ parameter η( = ℏ ω ce /ε Fe < 1) and ion density perturbations are computed using the framework of Maxwell distribution. A new type of kinetic nonlinear Shrödinger equation is derived in the presence of η, which involves nonlocal nonlinear term responsible for the NLD of EM waves. Furthermore, longitudinal wave modes are investigated to account for quantization parameter η. The LQ is also shown to absorb oscillation spectra of the linear ion-acoustic mode. The present findings might be helpful to understand the impact of the H field on the nonlinear interaction of EM waves with astrophysical plasmas, e.g., in the atmosphere of neutron star the presence of quantized magnetic field is more common.

Anomalous conductance quantization of a one-dimensional channel in monolayer WSe2

Among quantum devices based on 2D materials, gate-defined quantum confined 1D channels are much less explored, especially in the high-mobility regime where many-body interactions play an important role. We present the results of measurements and theory of conductance quantization in a gate-defined one-dimensional channel in a single layer of transition metal dichalcogenide material WSe2. In the quasi-ballistic regime of our high-mobility sample, we report conductance quantization steps in units of e2/h for a wide range of carrier concentrations. Magnetic field measurements show that as the field is raised, higher conductance plateaus move to accurate quantized values and then shift to lower conductance values while the e2/h plateau remains locked. Based on microscopic atomistic tight-binding theory, we show that in this material, valley and spin degeneracies result in 2 e2/h conductance steps for noninteracting holes, suggesting that symmetry-breaking mechanisms such as valley polarization dominate the transport properties of such quantum structures.

S-duality in Toverline{T} -deformed CFT

Toverline{T} deformed conformal field theories can be reformulated as worldsheet theories of non-critical strings. We use this correspondence to compute and study the Toverline{T} deformed partition sum of a symmetric product CFT. We find that it takes the form of a partition sum of a second quantized string theory with a worldsheet given by the product of the seed CFT and a gaussian sigma model with the two-torus as target space. We show that deformed symmetric product theory admits a natural UV completion that exhibits a strong weak coupling ℤ2 duality that interchanges the momentum and winding numbers and maps the Toverline{T} -coupling λ to its inverse 1/λ. The ℤ2 duality is part of a full O(2, 2, ℤ)-duality group that includes a PSL(2, ℤ) acting on the complexified Toverline{T} coupling. The duality symmetry eliminates the appearance of complex energies at strong coupling for all seed CFTs with central charge c ≤ 6.

Privacy-preserving federated learning on lattice quantization

Federated learning (FL) is an important approach to cooperate with multiple devices for learning without exchanging data between devices and central server. However, due to bandwidth and other reasons, the communication efficiency should be considered when the volume of information transmitted is limited. In this paper, we utilize the tool of lattice quantization form quantization theory and the variable intercommunication interval to improve communication efficiency. Meanwhile, to make strong privacy guarantee, we incorporate the notion of differential privacy (DP) to the FL framework with local SGD algorithm. By adding calibrated noises, we propose a universal lattice quantization for differentially private federated averaging algorithm (ULQ-DP-FedAvg). We provide tight privacy bound by using some privacy techniques. We also analyze the convergence bound of ULQ-DP-FedAvg based on bits rate constraints and the growing inter-communication interval as well as the data are non-independent identically distribution (Non-IID). It turns out that the algorithm converges and preserves that the privacy has scarcely influenced on the convergence rate. The effectiveness of our algorithm is demonstrated by synthetic and real datasets.

Vertex algebras and quantum master equation

We contribute to study the two dimensional chiral conformal field theories that arise from chiral deformations of free theories such as the $\beta \gamma$‑system, bc‑system and chiral bosons. Our method is based on the effective Batalin–Vilkovisky quantization theory. We establish an exact correspondence between renormalized quantum master equations for chiral deformations and Maurer–Cartan equations for the Lie algebra of modes of chiral vertex algebras. The generating functions on the torus are proven to have modular property with mild holomorphic anomaly. As an application, we construct an exact solution of quantum B‑model (BCOV theory) in complex one dimension that solves the full higher genus mirror symmetry conjecture on elliptic curves.

Setting method of exit advance guide signs in mountainous expressway tunnel based on information quantization theory.

Driving behavior in expressway tunnels is more complicated than in common roadbed sections because of differences in illuminance, visual range, speed perception, and reaction time. To explore the setting method of exit advance guide signs in expressway tunnels and improve the effectiveness of drivers' recognition of them, we propose 12 layout forms based on information quantification theory. In experiments, UC-win/Road was used to build a simulation scene, and the recognition reaction time of 12 element combinations of exit advance guide signs of different subjects was collected through an E-Prime simulation experiment. The loading effectiveness of the signs was analyzed based on the subjective workload and comprehensive evaluation scores of different subjects. The results are the following. The width of the exit advance guide sign layout in the tunnel is negatively correlated with the height of Chinese characters and the distance between the characters and the edge of the sign. The larger the height of Chinese characters and the distance between them and the edge of the sign, the smaller the maximum layout width of the sign. Considering the driver's reaction time, subjective workload, sign recognition, amount of sign information, sign accuracy, and sign safety of 12 different information combinations, we suggest that exit advance guide signs in tunnels should be laid out as Chinese/English place name + distance + guide arrow.

Voros Coefficients for the Hypergeometric Differential Equations and Eynard–Orantin’s Topological Recursion: Part I—For the Weber Equation

We develop the theory of quantization of spectral curves via the topological recursion. We formulate a quantization scheme of spectral curves which is not necessarily admissible in the sense of Bouchard and Eynard. The main result of this paper and the second part (Iwaki et al. in Voros coefficients for the hypergeometric differential equations and Eynard–Orantin’s topological recursion, part II: for the confluent family of hypergeometric equations, preprint; arXiv:1810.02946 ) establishes a relation between the Voros coefficients for the quantum curves and the free energy for spectral curves associated with the confluent family of Gauss hypergeometric differential equations. We focus on the Weber equation in this article and generalize the result for the other members of the confluent family in the second part. We also find explicit formulas of free energy for those spectral curves in terms of the Bernoulli numbers.