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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]

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]

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 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]

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]

More than 100 years ago, Robert Millikan demonstrated the quantization of the electron using charged, falling droplets, but the statistical analysis on many falling droplets did not allow a direct visualization of the quantization of charge. Instead of letting the droplets fall, we have used optical levitation to create a single droplet version of Millikan's experiment where the effects of a single electron removal can be observed by the naked eye and measured with a ruler. As we added charges to the levitated droplet, we observed that its equilibrium position jumped vertically in quantized steps. The discrete nature of the droplet's jumps is a direct consequence of the single-electron changes in the charge on the droplet, and therefore clearly demonstrates the quantization of charge. The steps were optically magnified onto a wall and filmed. We anticipate that the video of these single electron additions can become a straightforward demonstration of the quantization of charge for a general audience. [ABSTRACT FROM AUTHOR]

The interplay between ferromagnetism and topological properties of electronic band structures leads to a precise quantization of Hall resistance without any external magnetic field. This so-called quantum anomalous Hall effect (QAHE) is born out of topological correlations, and is oblivious of low-sample quality. It was envisioned to lead towards dissipation-less and topologically protected electronics. However, no clear framework of how to design such an electronic device out of it exists. Here we construct an ultra-low power, non-volatile, cryogenic memory architecture leveraging the QAHE phenomenon. Our design promises orders of magnitude lower cell area compared with the state-of-the-art cryogenic memory technologies. We harness the fundamentally quantized Hall resistance levels in moiré graphene heterostructures to store non-volatile binary bits (1, 0). We perform the memory write operation through controlled hysteretic switching between the quantized Hall states, using nano-ampere level currents with opposite polarities. The non-destructive read operation is performed by sensing the polarity of the transverse Hall voltage using a separate pair of terminals. We custom design the memory architecture with a novel sensing mechanism to avoid accidental data corruption, ensure highest memory density and minimize array leakage power. Our design provides a pathway towards realizing topologically protected memory devices. [ABSTRACT FROM AUTHOR]

In this paper, a novel adaptive fuzzy controller is developed for the uncertain fractional-order switched nonlinear systems whose output is quantized by a class of sector-bounded quantizers. Since the states are not completely measurable, an observer with quantized output signal is designed to estimate the unknown system states. Meanwhile, based on the fractional Lyapunov stability criterion, the Lyapunov function with sum functions and the virtual control function with hyperbolic tangent functions are designed. Besides, in order to improve the approximation accuracy of the unknown nonlinear functions generated by fractional differential, the prediction errors and auxiliary variables of series-parallel estimation model are introduced in backstepping procedures. The simulation results show that the control scheme ensures that all the signals of the considered system remain semi-globally uniformly ultimately bounded, and the tracking error converges to a small neighborhood of the origin regardless of arbitrary switching. [ABSTRACT FROM AUTHOR]

This paper investigates the dissipative interval type-2 (IT2) fuzzy control issue for a group of uncertain nonlinear systems subject to randomly occurring sensor saturation and quantization. By utilizing the both lower and upper membership functions with relevant tradeoff moduli, uncertainties, which exist in the considered systems, can be captured effectively. During the design of the IT2 fuzzy controller, we take the actuator failure into consideration. Considering the randomicities for the occurrences of sensor saturation and quantization, two separate Bernoulli stochastic distributed courses are utilized to construct the corresponding complicated transmission route. In term of Lyapunov stability theory, sufficient criteria to design dissipative IT2 fuzzy controller are presented to assure the stochastic stability with strict dissipativity of resulting closed-loop systems. Finally, illustrative example verifies the effectiveness and merits of the control strategy proposed in this paper. [ABSTRACT FROM AUTHOR]

Effective indexing is a crucial need for large scale object matching and retrieval. In this work, a novel indexing scheme is presented, that exploits the advantages of hierarchical clustering and product quantization. First, the high dimensional feature space is decomposed into disjointed sub-spaces and the data belonging to each sub-space is separately represented by a hierarchical clustering tree. Second, each tree quantizes a distinct part of an input vector to the closest centroid of a leaf node and the distances for all the pairs of centroids are pre-computed and stored in a lookup table. Finally, searching for a given query is proceeded in parallel between the trees and is performed efficiently in the quantized space using the pre-computed lookup tables. The proposed method has been validated by a number of experiments, demonstrating significant improvements of search performance in comparison with other methods. [ABSTRACT FROM AUTHOR]

To locate the tampered region of double compressed JPEG images, one of the most effective methods is based on the statistical characteristic of the images. After tampering operation, the tampered region and the original region will have different statistical distributions. And according to this cue, the histogram of DCT coefficients can be moded as the mixture of the distributions of DCT coefficients in tampered and untampered regions. By estimating each distribution of the mixture model, the probability of being tampered of each DCT block can be calculated and the final localization result can be obtained. Thus the mixture model will significant impact the result. In this paper, a novel mixture model based on normalized gray level co-occurrence matrix (NGLCM) is proposed for tampering localization in JPEG images. Firstly, NGLCM is used to measure the conditional probabilities of being tampered regions and being untampered regions for each 8 × 8 DCT coefficient block, which can take advantage of both the statistical characteristic of double quantization effect and the relationship among neighboring blocks. Then the Bayesian posterior probability map is generated by the conditional probabilities, which indicates the tampering probability of each block. Finally, the map is refined based on a inter-block connectivity and Gaussian weighted filter strategy to determine the final tampered region location. Experimental results demonstrate that the proposed approach can localize the tampered region of JPEG images with a satisfactory performance and outperforms the state-of-the-art methods. [ABSTRACT FROM AUTHOR]

This paper proposes a novel robust image watermarking scheme in Discrete Cosine Transform (DCT) domain for active forensics. We investigate the relation between the positions and the modification magnitudes of DCT coefficients and directions of texture blocks. By exploring such relation, a direction-coefficient mapping is designed. First, the texture direction of each image block is estimated by Gabor filter. And then, according to the direction-coefficient mapping, one watermark bit is embedded into each block along its texture direction. Compared with existing schemes, the proposed method utilizes the direction features of texture blocks better. Therefore, the improvements in watermarked image quality and the robustness of watermark signal against image processing attacks are both achieved. [ABSTRACT FROM AUTHOR]

Recently, the methods of quantum theory, especially quantum information, started to be widely applied outside of physics: in cognitive, social sciences, economics, finance, decision making and biology. We propose a quantum-like model: the "information laser". The basic assumption is the discrete structure of state spaces related to the quantization of information. The information field acts in the form of indistinguishable quanta of "social energy" analogue to photons. The massive flow of information acts as a laser pump. In this framework, an information selection process by agents under constant pressure of massive repeated information leads to collective "resonance" effects in analogy with laser cavity and stimulated emission. In order to make operational parallels between physical lasers and the information laser we identify the essential features of laser operation. An application to the analysis of recent disruptive social events (colour revolutions) is discussed. Social analogues to the laser are also considered through the model of Echo Chambers induced by the Internet and Adam Smith's invisible hand. [ABSTRACT FROM AUTHOR]

Inverted indexing based on vector quantization has been a popular technique in large scale information retrieval. With vector quantization based on a certain similarity metric, the sample space is partitioned into some voronoi cells, and samples in each cell are indexed by an inverted list. The nearest neighbors of a query are efficiently identified by looking up the cell where the query is located. To improve the recall, the sample space partitioning has been performed multiple times with different initializations of k-means to build multiple inverted indexes. While with the single similarity metric, e.g., Euclidean distance, high correlation may exist between multiple inverted indexes, which constrains the possible gain in recall. A new multiple inverted indexing method based on multiple sample space partitioning with multiple different similarity metrics is presented in this paper. Furthermore, several techniques for defining multiple metrics are investigated empirically. Experiments are conducted on 3 representative datasets, million-scale SIFT and GIST feature sets and a deep-learning-produced feature set, to properly evaluate the effectiveness of the proposed method. Experiment results show that the proposed method has competitive performance compared with the state-of-the-art inverted indexing methods in terms of recall and retrieval time, and the Latin-Hypercube weighting method can generate better diverse multiple metrics and get better gain in recall. [ABSTRACT FROM AUTHOR]

We propose a simple approach to formal deformations of associative algebras. It exploits the machinery of multiplicative coresolutions of an associative algebra A in the category of A-bimodules. Specifically, we show that certain first-order deformations of A extend to all orders and we derive explicit recurrent formulas determining this extension. In physical terms, this may be regarded as the deformation quantization of noncommutative Poisson structures on A. [ABSTRACT FROM AUTHOR]

We study charge transport in the Peierls-Harper model with a quasi-periodic cosine potential. We compute the Landauer-type conductance of the wire. Our numerical results show the following: (i) When the Fermi energy lies in the absolutely continuous spectrum that is realized in the regime of the weak coupling, the conductance is quantized to the universal conductance. (ii) For the regime of localization that is realized for the strong coupling, the conductance is always vanishing irrespective of the value of the Fermi energy. Unfortunately, we cannot make a definite conclusion about the case with the critical coupling. We also compute the conductance of the Thue-Morse model. Although the potential of the model is not quasi-periodic, the energy spectrum is known to be a Cantor set with zero Lebesgue measure. Our numerical results for the Thue-Morse model also show the quantization of the conductance at many locations of the Fermi energy, except for the trivial localization regime. Besides, for the rest of the values of the Fermi energy, the conductance shows a similar behavior to that of the Peierls-Harper model with the critical coupling. [ABSTRACT FROM AUTHOR]

Following the lines of the recent papers (Daneshmand and Tavassoly, Int. J. Theor. Phys. 56, 1218 (2017)), we study quantum mechanical treatments of an interaction between a two-level atom with a single-mode field in the two-photon Jaynes-Cummings model, where the Hamiltonian of the field is considered to be the quantized Caldirola-Kanai (CK) Hamiltonian. As a result, we would expect that the quantum dynamics of the two-photon JCM in terms of the CK Hamiltonian is qualitatively different from that of the usual one-photon case. We analytically calculate the explicit form of the atom-field entangled state and numerically evaluate the dynamics of its physical properties. The degree of entanglement, atomic population as well as sub-Poissonian statistics and quadrature squeezing of the field are analyzed. We adjust the latter evolved parameters by appropriately tuning the damping parameter within the CK Hamiltonian and detuning factor. Finally, we report a field detuning asymmetry in the collective statistical behavior. [ABSTRACT FROM AUTHOR]

In this paper, an improved wavelet based medical image watermarking algorithm is proposed. Initially, the proposed technique decomposes the cover medical image into ROI and NROI regions and embedding three different watermarks into the non-region of interest (NROI) part of the transformed DWT cover image for compact and secure medical data transmission in E-health environment. In addition, the method addressing the problem of channel noise distortion may lead to faulty watermark by applying error correcting codes (ECCs) before embedding them into the cover image. Further, the bit error rates (BER) performance of the proposed method is determined for different kind of attacks including 'Checkmark' attacks. Experimental results indicate that the Turbo code performs better than BCH (Bose-Chaudhuri-Hochquenghem) error correction code. Furthermore, the experimental results validate the effectiveness of the proposed framework in terms of BER and embedding capacity compared to other state-of-the-art methods. Therefore, the proposed method finds potential application in prevention of patient identity theft in e-health applications. [ABSTRACT FROM AUTHOR]

This work develops a new method to calculate non-perturbative corrections in one-dimensional Quantum Mechanics, based on trans-series solutions to the refined holomorphic anomaly equations of topological string theory. The method can be applied to traditional spectral problems governed by the Schrödinger equation, where it both reproduces and extends the results of well-established approaches, such as the exact WKB method. It can be also applied to spectral problems based on the quantization of mirror curves, where it leads to new results on the trans-series structure of the spectrum. Various examples are discussed, including the modified Mathieu equation, the double-well potential and the quantum mirror curves of local P2 and local F0. In all these examples, it is verified in detail that the trans-series obtained with this new method correctly predict the large-order behavior of the corresponding perturbative sectors. [ABSTRACT FROM AUTHOR]

Among the existing lossy compression methods, the transform coding is one of the most effective strategies. The Discrete Wavelet Transform (DWT) can be efficiently used in image coding applications because of its advantages as compared to the other transforms. A typical wavelet image compression system is composed of three connected components namely transformation, quantization and coding. In this paper, we review the recent improvements of each component. We present a detailed study of the recent implementation of the DWT as well as of its improvements. In addition, we describe the main principles of the wavelet-based compression schemes such as EZW, SPIHT, SPECK and EBCOT. We review the advantages and shortcomings of each of these algorithms. Also, we provide a survey of the recent improvements of the different coding schemes. Moreover, a comparative analysis of the recent enhancement and compression techniques is carried out in terms of visual quality and encoding time. We conclude by some guidelines which concern the design of an efficient codec for wavelet image compression using spline transform and improved coding scheme. [ABSTRACT FROM AUTHOR]

Transform/quantization (T/Q) is one of the high complex modules in high efficiency video coding (HEVC). In this paper, all zero block (AZB) detection algorithm for HEVC is proposed to reduce the complexity of T/Q. The proposed AZB detection algorithm is based on the quantization level of the maximum transform coefficient, which is suitable for both uniform quantizer (UQ) and rate-distortion optimized quantizer (RDOQ). Experimental results show that 46% complexity of T/Q for UQ and 42% for RDOQ can be reduced with negligible loss of video quality and compression efficiency, outperforming the state-of-the-art methods. [ABSTRACT FROM AUTHOR]

We develop a new approach to deformation quantizations of Lie bialgebras and Poisson structures which goes in two steps. In the first step one associates to any Poisson (resp. Lie bialgebra) structure a so called quantizable Poisson (resp. Lie bialgebra) structure. We give explicit transcendental formulae for this correspondence. In the second step one deformation quantizes a quantizable Poisson (resp. Lie bialgebra) structure. We show again explicit transcendental formulae for this second step correspondence (as a byproduct we obtain configuration space models for biassociahedron and bipermutohedron). In the Poisson case the first step is the most non-trivial one and requires a choice of an associator while the second step quantization is essentially unique, it is independent of a choice of an associator and can be done by a trivial induction. We conjecture that similar statements hold true in the case of Lie bialgebras. The main new result is a surprisingly simple explicit universal formula (which uses only smooth differential forms) for universal quantizations of finite-dimensional Lie bialgebras. [ABSTRACT FROM AUTHOR]

We give a closed formula for the Rankin-Cohen formal covariant quantization in terms of generating functions of Jacobi polynomials. [ABSTRACT FROM AUTHOR]

Structures and objects used in Hamiltonian secondary quantization are discussed. By the secondary quantization of a Hamiltonian system ℋ, we mean the Schrödinger quantization of another Hamiltonian system ℋ1 for which the Hamiltonian equation is the Schrödinger one obtained by the quantization of the original Hamiltonian system ℋ. The phase space of ℋ1 is the realification ℍR of the complex Hilbert space ℍ of the quantum analogue of ℋ equipped with the natural symplectic structure. The role of a configuration space is played by the maximal real subspace of ℍ. [ABSTRACT FROM AUTHOR]

In physics, one is often misled in thinking that the mathematical model of a system is part of or is that system itself. Think of expressions commonly used in physics like "point" particle, motion "on the line", "smooth" observables, wave function, and even "going to infinity", without forgetting perplexing phrases like "classical world" versus "quantum world".... On the other hand, when a mathematical model becomes really inoperative in regard with correct predictions, one is forced to replace it with a new one. It is precisely what happened with the emergence of quantum physics. Classical models were (progressively) superseded by quantum ones through quantization prescriptions. These procedures appear often as ad hoc recipes. In the present paper, well defined quantizations, based on integral calculus and Weyl-Heisenberg symmetry, are described in simple terms through one of the most basic examples of mechanics. Starting from (quasi-) probability distribution(s) on the Euclidean plane viewed as the phase space for the motion of a point particle on the line, i.e., its classical model, we will show how to build corresponding quantum model(s) and associated probabilities (e.g. Husimi) or quasi-probabilities (e.g. Wigner) distributions. We highlight the regularizing rôle of such procedures with the familiar example of the motion of a particle with a variable mass and submitted to a step potential. [ABSTRACT FROM AUTHOR]

The quasi-classical approximation is used to determine the positions of the classical turning points upon motion of an electron that is bound by an image field and a constant homogeneous electric field of the same direction. Power expansions of the coordinates of the turning points in a wide range of electron energies and field strengths are obtained. The mechanism of one-dimensional confinement of an electron, which determines a completely discrete spectrum of states, is described. The dependence of the spatial width of the confinement region on the field strength and electron energy is determined. The dependences of the electron energy in different states on the external field strength are calculated numerically. Quasi-classical quantization is performed, and the dependence of the electron energy on the width of the confinement region is determined. The energy interval of a maximum density of electron states is found, which is determined by the dependence of the width of the confinement region on the electric field strength. [ABSTRACT FROM AUTHOR]

The problem of elastic scattering of particles has been considered by the potential quantization method. The properties of the eigenfunctions ϕν(+)(r) and eigenvalues αν(+) of this method for states with positive energies (continuous spectrum) have been studied. Under the assumption of the completeness of the set {ϕν(+)(r)}, the problem has been solved by expanding the desired wavefunction in this set. The proposed approach reproduces known results in all considered limiting cases. At the same time, it gives a more detailed description of the scattering amplitude than the standard phase theory. [ABSTRACT FROM AUTHOR]

We consider the relationship between the unitary quantization scheme and the para-Fermi statistics of order 2. We propose an appropriate generalization of Green’s ansatz, which has made it possible to transform bilinear and trilinear commutation relations for the creation and annihilation operators for two different para-Fermi fields φa and φb into identities. We also propose a method for incorporating para-Grassmann numbers ξk into the general unitary quantization scheme. For the parastatistics of order 2, a new fact has been revealed: the trilinear relations containing both para-Grassmann variables ξk and field operators ak and bm are transformed under a certain reversible mapping into unitary equivalent relations in which commutators are replaced by anticommutators, and vice versa. It is shown that this leads to the existence of two alternative definitions of the coherent state for para-Fermi oscillators. The Klein transformation for Green’s components of operators ak and bm is constructed in explicit form, which enabled us to reduce the initial commutation rules for the components to the normal commutation relations for ordinary Fermi fields. We have analyzed a nontrivial relationship between the trilinear commutation relations of the unitary quantization scheme and the so-called Lie supertriple system. The possibility of incorporating the Duffin-Kemmer-Petiau theory into the unitary quantization scheme is discussed briefly. [ABSTRACT FROM AUTHOR]

In the first part of the paper we introduce a new parametrization for the manifold underlying quadratic analogue of the usual Heisenberg group introduced in Accardi et al. (Infin Dimens Anal Quantum Probab Relat Top 13:551-587, 2010) which makes the composition law much more transparent. In the second part of the paper the new coordinates are used to construct an inductive system of ∗-algebras each of which is isomorphic to a finite tensor product of copies of the one-mode quadratic Weyl algebra. We prove that the inductive limit ∗-algebra is factorizable and has a natural localization given by a family of ∗-sub-algebras each of which is localized on a bounded Borel subset of R. Moreover, we prove that the family of quadratic analogues of the Fock states, defined on the inductive family of ∗-algebras, is projective hence it defines a unique state on the limit ∗-algebra. Finally we complete this ∗-algebra under the (minimal regular) C∗-norm thus obtaining a C∗-algebra. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the κ-deformed boson algebra. We present the infinite dimensional representation of this algebra. Assuming that the photon obeys the κ-deformed algebra instead of the ordinary boson algebra, we discuss the κ-deformed quantum optical electromagnetic field whose classical Hamiltonian is written in terms of an infinite set of real harmonic oscillators. We also discuss the second quantization of light when we regard the photon as the quantum particle obeying the κ-deformed boson algebra. Finally we discuss the interaction between a two-level atom coupled to a single κ-photon. [ABSTRACT FROM AUTHOR]

Observables have a dual nature in both classical and quantum kinematics: they are at the same time quantities, allowing to separate states by means of their numerical values, and generators of transformations, establishing relations between different states. In this work, we show how this twofold role of observables constitutes a key feature in the conceptual analysis of classical and quantum kinematics, shedding a new light on the distinguishing feature of the quantum at the kinematical level. We first take a look at the algebraic description of both classical and quantum observables in terms of Jordan-Lie algebras and show how the two algebraic structures are the precise mathematical manifestation of the twofold role of observables. Then, we turn to the geometric reformulation of quantum kinematics in terms of Kähler manifolds. A key achievement of this reformulation is to show that the twofold role of observables is the constitutive ingredient defining what an observable is. Moreover, it points to the fact that, from the restricted point of view of the transformational role of observables, classical and quantum kinematics behave in exactly the same way. Finally, we present Landsman’s general framework of Poisson spaces with transition probability, which highlights with unmatched clarity that the crucial difference between the two kinematics lies in the way the two roles of observables are related to each other. [ABSTRACT FROM AUTHOR]

Abstract: A technique for quantization of the electromagnetic field in photonic nanostructures with three-dimensional modulation of the dielectric constant is developed on the basis of the scattering matrix formalism (S quantization in the three-dimensional case). Quantization is based on equating the eigenvalues of the scattering matrix to unity, which is equivalent to equating each other the sets of Fourier expansions for the fields of the waves incident on the structure and propagating away from the structure. The spatial distribution of electromagnetic fields of the modes in a photonic nanostructure is calculated on the basis of the R and T matrices describing the reflection and transmission of the Fourier components by the structure. To calculate the reflection and transmission coefficients of individual real-space and Fourier-space components, the structure is divided into parallel layers within which the dielectric constant varies as a function of two-dimensional coordinates. Using the Fourier transform, Maxwell’s equations are written in the form of a matrix connecting the Fourier components of the electric field at the boundaries of neighboring layers. Based on the calculated reflection and transmission vectors for all polarizations and Fourier components, the scattering matrix for the entire structure is formed and quantization is carried out by equating the eigenvalues of the scattering matrix to unity. The developed method makes it possible to obtain the spatial profiles of eigenmodes without solving a system of nonlinear integro-differential equations and significantly reduces the computational resources required for calculating the probability of spontaneous emission in three-dimensional systems. [ABSTRACT FROM AUTHOR]

We study the edge transport properties of 2d interacting Hall systems, displaying single-mode chiral edge currents. For this class of many-body lattice models, including for instance the interacting Haldane model, we prove the quantization of the edge charge conductance and the bulk-edge correspondence. Instead, the edge Drude weight and the edge susceptibility are interaction-dependent; nevertheless, they satisfy exact universal scaling relations, in agreement with the chiral Luttinger liquid theory. Moreover, charge and spin excitations differ in their velocities, giving rise to the spin-charge separation phenomenon. The analysis is based on exact renormalization group methods, and on a combination of lattice and emergent Ward identities. The invariance of the emergent chiral anomaly under the renormalization group flow plays a crucial role in the proof. [ABSTRACT FROM AUTHOR]

This manuscript presents a significant frame selection (SFS) and quantization of coefficient difference based robust video watermarking scheme in the lifting wavelet transform domain (LWT). In this scheme, a new procedure based on the mathematical relationship between a number of original video frames, coefficient block size and embedding capacity for significant frame selection is proposed. Third level frequency sub-bands of selected frames are obtained using LWT and lower frequency sub-band (i.e. LH3 sub-band) is considered for watermark embedding. Watermark bits are embedded using the quantization of coefficient difference of two maximum frequency components of significant frame blocks. To improve the security against an external intruder, secret key based randomization of video frames, blocks of coefficients and watermark bits is incorporated. Various geometric and image processing operations are tested and the proposed scheme successfully proves its robustness without compromising the quality of watermarked image. Comparing with other existing schemes, a remarkable improvement in terms of robustness is observed however in some cases the imperceptibility is compromised. [ABSTRACT FROM AUTHOR]

In order to improve the JPEG compression resistant performance of the current steganogrpahy algorithms resisting statistic detection, an adaptive steganography algorithm resisting JPEG compression and detection based on dither modulation is proposed. Utilizing the adaptive dither modulation algorithm based on the quantization tables, the embedding domains resisting JPEG compression for spatial images and JPEG images are determined separately. Then the embedding cost function is constructed by the embedding costs calculation algorithm based on side information. Finally, the RS coding is combined with the STCs to realize the minimum costs messages embedding while improving the correct rates of the extracted messages after JPEG compression. The experimental results demonstrate that the algorithm can be applied to both spatial images and JPEG images. Compared with the current S-UNIWARD steganography, the message extraction error rates of the proposed algorithm after JPEG compression decrease from about 50 % to nearly 0; compared with the current JPEG compression and detection resistant steganography algorithms, the proposed algorithm not only possesses the comparable JPEG compression resistant ability, but also has a stronger detection resistant performance and a higher operation efficiency. [ABSTRACT FROM AUTHOR]

A second-quantization treatment of the solution of the equation of classical mechanics is carried out. It is shown that all of the information about the multiparticle process of creation of a pair of scalar particles by a nonstationary potential barrier is contained in the solutions of Newton’s one-particle equation. The corresponding solution does not depend on Planck’s constant. It is shown that for any spatial quantum problem there exists a temporal classical analog. The obtained results can be used in quantum geometrodynamics. [ABSTRACT FROM AUTHOR]

The paper considers absorption of linearly polarized radiation in a semiconductor size-quantized well related to optical transitions both between the branches of light and heavy holes and between the size-quantized subbands. Main features of the light absorption in an infinitely deep symmetric well are elucidated. These features are characterized by intraband absorption of light and associated with the direct optical transitions of holes between the subbands of the semiconductor valence band formed due to the size quantization. [ABSTRACT FROM AUTHOR]

We show that a notion of one-particle state and the corresponding vacuum state exists in general curved backgrounds for spin 12 fields. A curved spacetime can be equipped with a coordinate system in which the metric component g--=0. We separate the component of the left-handed massless Dirac field which is annihilated by the null vector ∂- and compute the corresponding Feynman propagator. We find that the propagating modes are localized on two dimensional subspaces and the Feynman propagator is similar to the Feynman propagator of chiral fermions in two dimensional Minkowski spacetime. Therefore, it can be interpreted in terms of one-particle states and the corresponding vacuum state similarly to the second quantization in Minkowski spacetime. [ABSTRACT FROM AUTHOR]

We propose a new world-line Lagrangian model of the D=4 massless relativistic particle with continuous spin and develop its twistorial formulation. The description uses two Penrose twistors subjected to four first class constraints. After the first quantization of the world-line twistorial model, the wave function is defined by an unconstrained function on the two-dimensional complex affine plane. We find the twistor transform that determines the space-time field of the continuous spin particle through the corresponding twistor one, which plays the role of a prepotential. It is shown that this space-time field is an exact solution of the space-time constraints defining the irreducible massless representation of the Poincaré group with continuous spin. [ABSTRACT FROM AUTHOR]

Given two sets S1, S2 and unital C*-algebras A1, A2 of functions thereon, we show that a map σ:S1⟶S2 can be lifted to a continuous map σ¯:specA1⟶specA2 iff σ*A2:={σ*f|f∈A2}⊆A1. Moreover, σ¯ is unique if existing, and injective iff σ*A2 is dense. Then, we apply these results to loop quantum gravity and loop quantum cosmology. For all usual technical conventions, we decide whether the cosmological quantum configuration space is embedded into the gravitational one; indeed, both are spectra of some C*-algebras, say, Acosm and Agrav, respectively. Typically, there is no embedding, but one can always get an embedding by the defining Acosm:=C*(σ*Agrav), where σ denotes the embedding between the classical configuration spaces. Finally, we explicitly determine C*(σ*Agrav) in the homogeneous isotropic case for Agrav generated by the matrix functions of parallel transports along analytic paths. The cosmological quantum configuration space so equals the disjoint union of R and the Bohr compactification of R, appropriately glued together. [ABSTRACT FROM AUTHOR]

In this work we consider the instant-form and light-front quantization of some field theories. As an example, we consider a class of gauged non-linear sigmamodels with different regularizations. In particular, we present the path integral quantization of the gauged non-linear sigma model in the Faddeevian regularization. We also make a comparision of the possible differences in the instant-form and light-front quantization at appropriate places. [ABSTRACT FROM AUTHOR]

Superconductivity is a macroscopic coherent state exhibiting various quantum phenomena such as magnetic flux quantization. When a superconducting ring is placed in a magnetic field, a current flows to expel the field from the ring and to ensure that the enclosed flux is an integer multiple of h/(2|e|). Although the quantization of magnetic flux in ring structures is extensively studied in literature, the applied magnetic field is typically assumed to be homogeneous, implicitly implying an interplay between field expulsion and flux quantization. Here, we propose to decouple these two effects by employing an Aharonov-Bohm-like structure where the superconducting ring is threaded by a magnetic core (to which the applied field is confined). Although the magnetic field vanishes inside the ring, the formation of vortices takes place, corresponding to a change in the flux state of the ring. The time evolution of the density of superconducting electrons is studied using the time-dependent Ginzburg-Landau equations. [ABSTRACT FROM AUTHOR]

We discuss a link between symplectic displacement energy, a fundamental notion of symplectic topology, and the quantum speed limit, a universal constraint on the speed of quantum-mechanical processes. The link is provided by the quantum-classical correspondence formalized within the framework of the Berezin-Toeplitz quantization. [ABSTRACT FROM AUTHOR]

We study Tamm plasmon structure based on GaAs/Al0.95GaAs distributed Bragg reflector covered by thin silver layer, with active area formed by InAs quantum dots. We have measured the spectral and angular characteristics of photoluminescence and performed theoretical calculation of the spontaneous emission rate (modal Purcell factor) in the structure by using S-quantization formalism. We show that for Tamm plasmon mode the spontaneous emission can be enhanced by more than an order of magnitude, despite absorption in metallic layer. [ABSTRACT FROM AUTHOR]

We study the quantization of Hitchin systems in terms of β-deformations of generalized matrix models related to conformal blocks of Liouville theory on punctured Riemann surfaces. We show that in a suitable limit, corresponding to the Nekrasov-Shatashvili one, the loop equations of the matrix model reproduce the Hamiltonians of the quantum Hitchin system on the sphere and the torus with marked points. The eigenvalues of these Hamiltonians are shown to be the ϵ1-deformation of the chiral observables of the corresponding N=2 four dimensional gauge theory. Moreover, we find the exact wave-functions in terms of the matrix model representation of the conformal blocks with degenerate field insertions. [ABSTRACT FROM AUTHOR]

We survey the theory of Poisson traces (or zeroth Poisson homology) developed by the authors in a series of recent papers. The goal is to understand this subtle invariant of (singular) Poisson varieties, conditions for it to be finite-dimensional, its relationship to the geometry and topology of symplectic resolutions, and its applications to quantizations. The main technique is the study of a canonical D-module on the variety. In the case the variety has finitely many symplectic leaves (such as for symplectic singularities and Hamiltonian reductions of symplectic vector spaces by reductive groups), the D-module is holonomic, and hence, the space of Poisson traces is finite-dimensional. As an application, there are finitely many irreducible finite-dimensional representations of every quantization of the variety. Conjecturally, the D-module is the pushforward of the canonical D-module under every symplectic resolution of singularities, which implies that the space of Poisson traces is dual to the top cohomology of the resolution. We explain many examples where the conjecture is proved, such as symmetric powers of du Val singularities and symplectic surfaces and Slodowy slices in the nilpotent cone of a semisimple Lie algebra. We compute the D-module in the case of surfaces with isolated singularities and show it is not always semisimple. We also explain generalizations to arbitrary Lie algebras of vector fields, connections to the Bernstein–Sato polynomial, relations to two-variable special polynomials such as Kostka polynomials and Tutte polynomials, and a conjectural relationship with deformations of symplectic resolutions. In the appendix we give a brief recollection of the theory of D-modules on singular varieties that we require. [ABSTRACT FROM AUTHOR]

These notes are an expanded version of a mini-course given at the Poisson 2016 conference in Geneva. Starting from classical integrable systems in the sense of Liouville, we explore the notion of non-degenerate singularities and expose recent research in connection with semi-toric systems. The quantum and semiclassical counterparts are also presented, in the viewpoint of the inverse question: from the quantum mechanical spectrum, can one recover the classical system? [ABSTRACT FROM AUTHOR]

We provide a short proof of the quantization of the Hall conductance for gapped interacting quantum lattice systems on the twodimensional torus. This is not new and should be seen as an adaptation of the proof of Hastings and Michalakis (Commun Math Phys 334:433-471, 2015), simplified by making the stronger assumption that the Hamiltonian remains gapped when threading the torus with fluxes. We argue why this assumption is very plausible. The conductance is given by Berry's curvature and our key auxiliary result is that the curvature is asymptotically constant across the torus of fluxes. [ABSTRACT FROM AUTHOR]

This study attempts to spell out more explicitly than has been done previously the connection between two types of formal correspondence that arise in the study of quantum-classical relations: one the one hand, deformation quantization and the associated continuity between quantum and classical algebras of observables in the limit ħ→0, and, on the other, a certain generalization of Ehrenfest’s Theorem and the result that expectation values of position and momentum evolve approximately classically for narrow wave packet states. While deformation quantization establishes a direct continuity between the abstract algebras of quantum and classical observables, the latter result makes in-eliminable reference to the quantum and classical state spaces on which these structures act—specifically, via restriction to narrow wave packet states. Here, we describe a certain geometrical re-formulation and extension of the result that expectation values evolve approximately classically for narrow wave packet states, which relies essentially on the postulates of deformation quantization, but describes a relationship between the actions of quantum and classical algebras and groups over their respective state spaces that is non-trivially distinct from deformation quantization. The goals of the discussion are partly pedagogical in that it aims to provide a clear, explicit synthesis of known results; however, the particular synthesis offered aspires to some novelty in its emphasis on a certain general type of mathematical and physical relationship between the state spaces of different models that represent the same physical system, and in the explicitness with which it details the above-mentioned connection between quantum and classical models. [ABSTRACT FROM AUTHOR]

Quantum states have been calculated analytically; the dynamics of a wave packet in a magnetic field has been investigated, and the optical absorption coefficient has been calculated for surface states in 3D topological insulators of the Bi2Te3 family. We have detected a qualitative effect of the hexagonal warping of the spectrum on the structure of wavefunctions at the Landau levels, its manifestation in the features of the wave packet dynamics in a quantizing magnetic field, as well as in the frequency dependence of the optical absorption coefficient, in which new peaks that are absent in the isotropic model of the spectrum appear depending on the polarization of the incident wave. The effects considered here can be manifested in the optical and transport experiments with topological insulators, which makes it possible to determine the parameters of their band structure. [ABSTRACT FROM AUTHOR]