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Highlights • A very first real application of RS on vibration to evaluate its potential in machine monitoring. • A simulation study to evaluate the effect of RS parameters within its different modes. • An enhanced method for spectral analysis of RS signals based on zero insertion and Welch periodogram. Abstract Random sampling was first introduced in the 1960's (Beutler and Leneman, 1966 [1]), and was then reused in the Compressive Sensing theory (published in 2006 (Donoho, 2006 [2])) for having two important advantages: anti-aliasing property and low sampling rate. These advantages decrease the demand of high speed acquisition and big data storage. In this paper, a brief review of the principal random sampling modes is presented: Additive Random Sampling (ARS) and Jittered Random Sampling (JRS) that both use probability distributions: uniform or Gaussian (Wojtiuk, 2000; Ben Romdhane, 2009; Luo, 2012; Lo and Purvis, 1997 [3–6]). In fact, the stationarity of the random point process is the essential criterion to guarantee the anti-aliasing property (Bilinksis and Mikelson, 1992 [7]). Accordingly, these modes of sampling are studied and used in simulation and hardware implementation. In addition, a study of the time quantization effect is done to explore the different aspects of discrete random sampling (Ben Romdhane, 2009; Luo, 2012 [4,5]). The performance of this sampling is approved by simulation and practice, using respectively Matlab and Arduino microcontroller, respectively, for acquiring signals at a randomly spaced clock. A database was created in order to observe the impact of statistical parameters such as the mean and the standard deviation for Gaussian distribution, and the interval endpoints of uniform distribution. In conclusion, the ARS with uniform distribution has been proved to have less limitations (Ben Romdhane, 2009 [4]), whereas the spectrum of sampled signal is free of alias and the sampling frequency is reduced (a much smaller than Nyquist-Shannon sampling rate). In order to take advantage of this mode, it is applied on vibration signals to enhance remoted machine monitoring. [ABSTRACT FROM AUTHOR]

Abstract This paper deals with positive solutions of the fully parabolic system { u t = Δ u − χ ∇ ⋅ (u ∇ v) in Ω × (0 , ∞) , τ 1 v t = Δ v − v + w in Ω × (0 , ∞) , τ 2 w t = Δ w − w + u in Ω × (0 , ∞) under mixed boundary conditions (no-flux and Dirichlet conditions) in a smooth bounded convex domain Ω ⊂ R 4 with positive parameters τ 1 , τ 2 , χ > 0 and nonnegative smooth initial data (u 0 , v 0 , w 0). Global existence and boundedness of solutions were shown if ‖ u 0 ‖ L 1 (Ω) < (8 π) 2 / χ in Fujie–Senba (2017). In the present paper, it is shown that there exist blowup solutions satisfying ‖ u 0 ‖ L 1 (Ω) > (8 π) 2 / χ. This result suggests that the system can be regard as a generalization of the Keller–Segel system, which has 8 π / χ -dichotomy. The key ingredients are a Lyapunov functional and quantization properties of stationary solutions of the system in R 4. [ABSTRACT FROM AUTHOR]

Abstract A series of quantization identities are established for static vortex solutions governed by the Born–Infeld type actions. These identities are of a universal nature which are indifferent to the details of the models and provide refined descriptions of divergent energetic quantities. [ABSTRACT FROM AUTHOR]

Abstract The classical time of arrival in the interacting case is quantized by way of quantizing its expansion about the free time of arrival. The quantization is formulated in coordinate representation which represents ordering rules in terms of two variable polynomial functions. This leads to representations of the quantized time of arrival operators as integral operators whose kernels are determined by the chosen ordering rule. The formulation lends itself to generalization which allows construction of time of arrival operators that cannot be obtained by direct quantization using particular ordering rules. Weyl, symmetric and Born–Jordan quantizations are specifically studied. The dynamics of the eigenfunctions of the different time of arrival operators are investigated. The eigenfunctions exhibit unitary arrival at the intended arrival point at their respective eigenvalues. [ABSTRACT FROM AUTHOR]

The present work shows that the mathematical equivalence of the Jordan frame and its conformally transformed version, the Einstein frame, so as far as Brans–Dicke theory is concerned, survives a quantization of cosmological models, arising as solutions to the Brans–Dicke theory. We work with the Wheeler–deWitt quantization scheme and take up quite a few anisotropic cosmological models as examples. We effectively show that the transformation from the Jordan to the Einstein frame is a canonical one and hence two frames furnish equivalent description of same physical scenario. [ABSTRACT FROM AUTHOR]

This article is an introductory presentation of the quantization of the half-plane based on affine coherent states (ACS). The half-plane carries a natural affine symmetry, i.e. it is a homogeneous space for the 1d-affine group, and it is viewed as the phase space for the dynamics of a positive physical quantity evolving with time. Its affine symmetry is preserved due to the covariance of this type of quantization. We promote the interest of such a procedure for transforming a classical model into a quantum one, since the singularity at the origin is systematically removed, and the arbitrariness of boundary conditions for the Schrödinger operator can be easily overcome. We explain some important mathematical aspects of the method. Three elementary examples of applications are presented, the quantum breathing of a massive sphere, the quantum smooth bouncing of a charged sphere, and a smooth bouncing of “dust” sphere as a simple model of quantum Newtonian cosmology. [ABSTRACT FROM AUTHOR]

Room temperature quantized double layer charging was observed in 2 nm Cu 2 ZnSnS 4 (CZTS) quantum dots. In addition to this we observed a distinct non-linearity in the quantized double layer charging arising from UV light modulation of double layer. UV light irradiation resulted in a 26% increase in the integral capacitance at the semiconductor-dielectric (CZTS-oleylamine) interface of the quantum dot without any change in its core size suggesting that the cause be photocapacitive. The increasing charge separation at the semiconductor-dielectric interface due to highly stable and mobile photogenerated carriers cause larger electrostatic forces between the quantum dot and electrolyte leading to an enhanced double layer. This idea was supported by a decrease in the differential capacitance possible due to an enhanced double layer. Furthermore the UV illumination enhanced double layer gives us an AC excitation dependent differential double layer capacitance which confirms that the charging process is non-linear. This ultimately illustrates the utility of a colloidal quantum dot-electrolyte interface as a non-linear photocapacitor. [ABSTRACT FROM AUTHOR]

The use of the quantizer–dequantizer formalism to describe the evolution of a quantum system is reconsidered. We show that it is possible to embed a manifold in the space of quantum states of a given auxiliary system by means of an appropriate quantizer–dequantizer system. If this manifold of states is invariant with respect to some unitary evolution, the quantizer–dequantizer system provides a classical-like realization of such dynamics, which in general is non linear. Integrability properties are also discussed. Weyl systems and generalized coherent states are used as a simple illustration of these ideas. [ABSTRACT FROM AUTHOR]

Into a geometric setting, we import the physical interpretation of index theorems via semi-classical analysis in topological quantum field theory. We develop a direct relationship between Fedosov's deformation quantization of a symplectic manifold X and the Batalin–Vilkovisky (BV) quantization of a one-dimensional sigma model with target X . This model is a quantum field theory of AKSZ type and is quantized rigorously using Costello's homotopic theory of effective renormalization. We show that Fedosov's Abelian connections on the Weyl bundle produce solutions to the effective quantum master equation. Moreover, BV integration produces a natural trace map on the deformation quantized algebra. This formulation allows us to exploit a (rigorous) localization argument in quantum field theory to deduce the algebraic index theorem via semi-classical analysis, i.e., one-loop Feynman diagram computations. [ABSTRACT FROM AUTHOR]

The gauged model of Siegel type chiral boson is considered. It has been shown that the action of gauged model of Floreanini–Jackiw (FJ) type chiral boson is contained in it in an interesting manner. A BRST invariant action corresponding to the action of gauged FJ type chiral boson has been formulated using Batalin, Fradkin and Vilkovisky based improved Fujiwara, Igarishi and Kubo (FIK) formalism. An alternative quantization of the gauge symmetric action has been made with a Lorentz gauge and an attempt has been made to establish the equivalence between the gauge symmetric version of the extended phase space and original gauge non-invariant version of the usual phase space. [ABSTRACT FROM AUTHOR]

Dissipation in Quantum Mechanics took some time to become a robust field of investigation after the birth of the field. The main issue hindering developments in the field is that the Quantization process was always tightly connected to the Hamiltonian formulation of Classical Mechanics. In this paper we present a quantization process that does not depend upon the Hamiltonian formulation of Classical Mechanics (although still departs from Classical Mechanics) and thus overcome the problem of finding, from first principles, a completely general Schrödinger equation encompassing dissipation. This generalized process of quantization is shown to be nothing but an extension of a more restricted version that is shown to produce the Schrödinger equation for Hamiltonian systems from first principles (even for Hamiltonian velocity dependent potential). [ABSTRACT FROM AUTHOR]

We perform the gauge covariant quantization of the exponential model of nonlinear electrodynamics. Magnetically charged black holes, in the framework of our model are considered, and the regular black hole solution is obtained in general relativity. The asymptotic black hole solution at r → ∞ is found. We calculate the magnetic mass of the black hole and the metric function which are expressed via the parameter β of the model and the magnetic charge. The thermodynamic properties and thermal stability of regular black holes are analysed. We calculate the Hawking temperature of black holes and their heat capacity at the constant magnetic charge. We find a point where the temperature changes the sign that corresponds to the first-order phase transition. It is shown that at critical point, where the heat capacity diverges, there is a phase transition of the second-order. We obtain the parameters of the model when the black hole is stable. [ABSTRACT FROM AUTHOR]

This paper proposes an approach of the unified consideration of classical and quantum mechanics from the standpoint of the complex analysis effects. It turns out that quantization can be interpreted in terms of the Riemann surface corresponding to the multivalent L n Ψ function. A visual interpretation of “trajectories” of the quantum system and of the Feynman’s path integral is presented. A magnetic dipole having a magnetic charge that satisfies the Dirac quantization rule was obtained. [ABSTRACT FROM AUTHOR]

We address the issue of the infinite ambiguity that affects the construction of a Fock quantization of a Dirac field propagating in a cosmological spacetime with flat compact sections. In particular, we discuss a physical criterion that restricts to a unique possibility (up to unitary equivalence) the infinite set of available vacua. We prove that this desired uniqueness is guaranteed, for any possible choice of spin structure on the spatial sections, if we impose two conditions. The first one is that the symmetries of the classical system must be implemented quantum mechanically, so that the vacuum is invariant under the symmetry transformations. The second and more important condition is that the constructed theory must have a quantum dynamics that is implementable as a (non-trivial) unitary operator in Fock space. Actually, this unitarity of the quantum dynamics leads us to identify as explicitly time dependent some very specific contributions of the Dirac field. In doing that, we essentially characterize the part of the dynamics governed by the Dirac equation that is unitarily implementable. The uniqueness of the Fock vacuum is attained then once a physically motivated convention for the concepts of particles and antiparticles is fixed. [ABSTRACT FROM AUTHOR]

We examine mathematical questions around angle (or phase) operator associated with a number operator through a short list of basic requirements. We implement three methods of construction of quantum angle. The first one is based on operator theory and parallels the definition of angle for the upper half-circle through its cosine and completed by a sign inversion. The two other methods are integral quantization generalizing in a certain sense the Berezin–Klauder approaches. One method pertains to Weyl–Heisenberg integral quantization of the plane viewed as the phase space of the motion on the line. It depends on a family of “weight” functions on the plane. The third method rests upon coherent state quantization of the cylinder viewed as the phase space of the motion on the circle. The construction of these coherent states depends on a family of probability distributions on the line. [ABSTRACT FROM AUTHOR]

Kinematics and dynamics of a particle moving on a torus knot poses an interesting problem as a constrained system. In the first part of the paper we have derived the modified symplectic structure or Dirac brackets of the above model in Dirac’s Hamiltonian framework, both in toroidal and Cartesian coordinate systems. This algebra has been used to study the dynamics, in particular small fluctuations in motion around a specific torus. The spatial symmetries of the system have also been studied. In the second part of the paper we have considered the quantum theory of a charge moving in a torus knot in the presence of a uniform magnetic field along the axis of the torus in a semiclassical quantization framework. We exploit the Einstein–Brillouin–Keller (EBK) scheme of quantization that is appropriate for multidimensional systems. Embedding of the knot on a specific torus is inherently two dimensional that gives rise to two quantization conditions. This shows that although the system, after imposing the knot condition reduces to a one dimensional system, even then it has manifested non-planar features which shows up again in the study of fractional angular momentum. Finally we compare the results obtained from EBK (multi-dimensional) and Bohr–Sommerfeld (single dimensional) schemes. The energy levels and fractional spin depend on the torus knot parameters that specifies its non-planar features. Interestingly, we show that there can be non-planar corrections to the planar anyon-like fractional spin. [ABSTRACT FROM AUTHOR]

The symplectic analysis of a four dimensional B F theory in the context of the Faddeev–Jackiw symplectic approach is performed. It is shown that this method is more economical than Dirac’s formalism. In particular, the complete set of Faddeev–Jackiw constraints and the generalized Faddeev–Jackiw brackets are reported. In addition, we show that the generalized Faddeev–Jackiw brackets and the Dirac ones coincide to each other. Finally, the similarities and advantages between Faddeev–Jackiw method and Dirac’s formalism are briefly discussed. [ABSTRACT FROM AUTHOR]

We investigate the quantisation in the Heisenberg representation of a relativistically covariant version of the Hopfield model for dielectric media, which entails the interaction of the quantum electromagnetic field with the matter dipole fields, represented by a mesoscopic polarisation field. A full quantisation of the model is provided in a covariant gauge, with the aim of maintaining explicit relativistic covariance. Breaking of the Lorentz invariance due to the intrinsic presence in the model of a preferred reference frame is also taken into account. Relativistic covariance forces us to deal with the unphysical (scalar and longitudinal) components of the fields, furthermore it introduces, in a more tricky form, the well-known dipole ghost of standard QED in a covariant gauge. In order to correctly dispose of this contribution, we implement a generalised Lautrup trick. Furthermore, causality and the relation of the model with the Wightman axioms are also discussed. [ABSTRACT FROM AUTHOR]

In this article we prove that many Hamiltonian systems that cannot be separably quantized in the classical approach of Robertson and Eisenhart can be separably quantized if we extend the class of admissible quantizations through a suitable choice of Riemann space adapted to the Poisson geometry of the system. Actually, in this article we prove that for every quadratic in momenta Stäckel system (defined on 2 n dimensional Poisson manifold) for which Stäckel matrix consists of monomials in position coordinates there exist infinitely many quantizations–parametrized by n arbitrary functions–that turn this system into a quantum separable Stäckel system. [ABSTRACT FROM AUTHOR]

In this paper, we analyse the Wheeler–DeWitt equation in the third quantized formalism. We will demonstrate that for certain operator ordering, the early stages of the universe are dominated by quantum fluctuations, and the universe becomes classical at later stages during the cosmic expansion. This is physically expected, if the universe is formed from quantum fluctuations in the third quantized formalism. So, we will argue that this physical requirement can be used to constrain the form of the operator ordering chosen. We will explicitly demonstrate this to be the case for two different cosmological models. [ABSTRACT FROM AUTHOR]

We study the mean field equation derived by Neri in the context of the statistical mechanics description of 2D-turbulence, under a “stochastic” assumption on the vortex circulations. The corresponding mathematical problem is a nonlocal semilinear elliptic equation with exponential type nonlinearity, containing a probability measure P ∈ M ( [ − 1 , 1 ] ) which describes the distribution of the vortex circulations. Unlike the more investigated “deterministic” version, we prove that Neri's equation may be viewed as a perturbation of the widely analyzed standard mean field equation, obtained by taking P = δ 1 . In particular, in the physically relevant case where P is non-negatively supported and P ( { 1 } ) > 0 , we prove the mass quantization for blow-up sequences. We apply this result to construct minimax type solutions on bounded domains in R 2 and on compact 2-manifolds without boundary. [ABSTRACT FROM AUTHOR]

We clearly refine the fundamental framework of the thin-layer quantization procedure, and further develop the procedure by taking the proper terms of degree one in q 3 ( q 3 denotes the curvilinear coordinate variable perpendicular to curved surface) back into the surface quantum equation. The well-known geometric potential and kinetic term are modified by the surface thickness. Applying the developed formalism to a toroidal system obtains the modification for the kinetic term and the modified geometric potential including the influence of the surface thickness. [ABSTRACT FROM AUTHOR]

The standard time-of-arrival distribution cannot reproduce both the temporal and the spatial profile of the modulus squared of the time-evolved wave function for an arbitrary initial state. In particular, the time-of-arrival distribution gives a non-vanishing probability even if the wave function is zero at a given point for all values of time. This poses a problem in the standard formulation of quantum mechanics where one quantizes a classical observable and uses its spectral resolution to calculate the corresponding distribution. In this work, we show that the modulus squared of the time-evolved wave function is in fact contained in one of the degenerate eigenfunctions of the quantized time-of-arrival operator. This generalizes our understanding of quantum arrival phenomenon where particle detection is not a necessary requirement, thereby providing a direct link between time-of-arrival quantization and the outcomes of the two-slit experiment. [ABSTRACT FROM AUTHOR]

We propose a new image representation for texture categorization and facial analysis, relying on the use of higher-order local differential statistics as features. It has been recently shown that small local pixel pattern distributions can be highly discriminative while being extremely efficient to compute, which is in contrast to the models based on the global structure of images. Motivated by such works, we propose to use higher-order statistics of local non-binarized pixel patterns for the image description. The proposed model does not require either (i) user specified quantization of the space (of pixel patterns) or (ii) any heuristics for discarding low occupancy volumes of the space. We propose to use a data driven soft quantization of the space, with parametric mixture models, combined with higher-order statistics, based on Fisher scores. We demonstrate that this leads to a more expressive representation which, when combined with discriminatively learned classifiers and metrics, achieves state-of-the-art performance on challenging texture and facial analysis datasets, in low complexity setup. Further, it is complementary to higher complexity features and when combined with them improves performance. [ABSTRACT FROM AUTHOR]

The arising of geometric quantum phases in the wave function of a moving particle possessing a magnetic quadrupole moment is investigated. It is shown that an Aharonov–Anandan quantum phase (Aharonov and Anandan, 1987) can be obtained in the quantum dynamics of a moving particle with a magnetic quadrupole moment. In particular, it is obtained as an analogue of the scalar Aharonov–Bohm effect for a neutral particle (Anandan, 1989). Besides, by confining the quantum particle to a hard-wall confining potential, the dependence of the energy levels on the geometric quantum phase is discussed and, as a consequence, persistent currents can arise from this dependence. Finally, an analogue of the Landau quantization is discussed. [ABSTRACT FROM AUTHOR]

We present a theoretical description of the process of therahertz emission in biased semiconductor superlattices that follows an ultra-fast interband excitation. The results show that the average current performs Bloch oscillations whose amplitude depends on the intrinsic characteristic of the superlattice as well as on the light pulse parameters. In these calculations we use a fully three-dimensional picture and include the excitonic effects. We also studied the terahertz intensity when the sample is subjected to a magnetic field parallel to its axis. We considered in detail the high magnetic field regime, where the in-plane motion is frozen in Landau orbits spectrally well separated. In this regime, a set of quasi one-dimensional Bloch oscillators can be ideally generated (oscillators with decoupled vertical and lateral electron motions), making the terahertz emission more intense and more coherent. [ABSTRACT FROM AUTHOR]

The idea about a new type of THz modulator, based on the dependence of separation between space quantized energy levels in a quantum well (QW) on the degree of ionization of shallow impurity delta doped layer situated within the QW is supported with theoretical calculations of absorption coefficients for intersubband optical transitions of n-type Si 0.8 Ge 0.2 /Si/Si 0.8 Ge 0.2 QW structure. Both center and edge doping of two QWs widths of – 10 and 20 nm – were considered at lattice temperatures 4 and 77 K for low and high degrees of impurity ionization. The obtained results are explained and they point to out the ranges of THz tuning of the structures under study. It is also emphasized that besides the electric field the changing temperature can control the efficiency of THz modulation. [ABSTRACT FROM AUTHOR]

With the increase of complexity and coherence of superconducting systems made using the principles of circuit quantum electrodynamics, more accurate methods are needed for the characterization, analysis and optimization of these quantum processors. Here we introduce a new method of modeling that can be applied to superconducting structures involving multiple Josephson junctions, high- Q superconducting cavities, external ports, and voltage sources. Our technique, an extension of our previous work on single-port structures (Solgun, 2014), permits the derivation of system Hamiltonians that are capable of representing every feature of the physical system over a wide frequency band and the computation of T 1 times for qubits. We begin with a “black box” model of the linear and passive part of the system. Its response is given by its multiport impedance function Z s i m ( ω ) , which can be obtained using a finite-element electromagnetics simulator. The ports of this black box are defined by the terminal pairs of Josephson junctions, voltage sources, and 50 Ω connectors to high-frequency lines. We fit Z s i m ( ω ) to a positive-real (PR) multiport impedance matrix Z ( s ) , a function of the complex Laplace variable s . We then use state-space techniques to synthesize a finite electric circuit admitting exactly the same impedance Z ( s ) across its ports; the PR property ensures the existence of this finite physical circuit. We compare the performance of state-space algorithms to classical frequency domain methods, justifying their superiority in numerical stability. The Hamiltonian of the multiport model circuit is obtained by using existing lumped element circuit quantization formalisms (Burkard et al., 2004; Burkard, 2005). Due to the presence of ideal transformers in the model circuit, these quantization methods must be extended, requiring the introduction of an extension of the Kirchhoff voltage and current laws. [ABSTRACT FROM AUTHOR]

A detailed Faddeev–Jackiw quantization of an Abelian and non-Abelian exotic action for gravity in three dimensions is performed. We obtain for the theories under study the constraints, the gauge transformations, the generalized Faddeev–Jackiw brackets and we perform the counting of physical degrees of freedom. In addition, we compare our results with those found in the literature where the canonical analysis is developed, in particular, we show that both the generalized Faddeev–Jackiw brackets and Dirac’s brackets coincide to each other. Finally we discuss some remarks and prospects. [ABSTRACT FROM AUTHOR]

This article is an essay that discusses the concepts underlying the application of modern transition state theory to reactions in enzymes. Issues covered include the potential of mean force, the quantization of vibrations, the free energy of activation, and transmission coefficients to account for nonequilibrium effect, recrossing, and tunneling. [ABSTRACT FROM AUTHOR]

This paper presents a singular-value-based semi-fragile watermarking scheme for image content authentication. The proposed scheme generates secure watermark by performing a logical operation on content-dependent watermark generated by a singular-value-based sequence and content-independent watermark generated by a private-key-based sequence. It next employs the adaptive quantization method to embed secure watermark in approximation subband of each 4 × 4 block to generate the watermarked image. The watermark extraction process then extracts watermark using the parity of quantization results from the probe image. The authentication process starts with regenerating secure watermark following the same process. It then constructs error maps to compute five authentication measures and performs a three-level process to authenticate image content and localize tampered areas. Extensive experimental results show that the proposed scheme outperforms five peer schemes and its two variant systems and is capable of identifying intentional tampering, incidental modification, and localizing tampered regions under mild to severe content-preserving modifications. [ABSTRACT FROM AUTHOR]

In this paper, we will incorporate the generalized uncertainty principle into field theories with Lifshitz scaling. We will first construct both bosonic and fermionic theories with Lifshitz scaling based on generalized uncertainty principle. After that we will incorporate the generalized uncertainty principle into a non-abelian gauge theory with Lifshitz scaling. We will observe that even though the action for this theory is non-local, it is invariant under local gauge transformations. We will also perform the stochastic quantization of this Lifshitz fermionic theory based generalized uncertainty principle. [ABSTRACT FROM AUTHOR]

Open strings on a D p -brane in the pp-wave spacetime, accompanied by a linear dilaton background, will be studied. Various properties of this system such as solvability of equations of motion and quantization will be investigated. [ABSTRACT FROM AUTHOR]

The inverse of the Faddeev–Popov operator plays a pivotal role within the Gribov–Zwanziger approach to the quantization of Euclidean Yang–Mills theories in Landau gauge. Following a recent proposal (Capri et al., 2014), we show that the inverse of the Faddeev–Popov operator can be consistently coupled to quark fields. Such a coupling gives rise to a local action while reproducing the behaviour of the quark propagator observed in lattice numerical simulations in the non-perturbative infrared region. By using the algebraic renormalization framework, we prove that the aforementioned local action is multiplicatively renormalizable to all orders. [ABSTRACT FROM AUTHOR]

We perform and extend real-time numerical simulation of a low-dimensional scalar field theory or a quantum mechanical system using stochastic quantization. After a brief review of the quantization method and the complex Langevin dynamics, we calculate the propagator and make a comparison with analytical results. This is a first step toward general applications, and we focus only on the vacuum properties of the theory; this enables us to handle the boundary condition with the i ϵ prescription in frequency space. While we can control stability of the numerical simulation for any coupling strength, our results turn out to flow into an unphysical fixed-point, which is qualitatively understood from the corresponding Fokker–Planck equation. We propose a simple truncation scheme, “restricted phase-space approximation”, to avoid the unphysical fixed-point. With this method, we obtain stable results at reasonably good accuracy. Finally we give a short discussion on the closed-time path formalism and demonstrate the direct computation of the vacuum expectation value not with the i ϵ prescription but from an explicit construction of the Feynman kernel. [ABSTRACT FROM AUTHOR]

Let X be a smooth algebraic variety over a field K containing the real numbers. We introduce the notion of twisted associative (resp. Poisson) deformation of the structure sheaf O X . These are stack-like versions of usual deformations. We prove that there is a twisted quantization operation from twisted Poisson deformations to twisted associative deformations, which is canonical and bijective on gauge equivalence classes. This result extends work of Kontsevich, and our own earlier work, on deformation quantization of algebraic varieties. [ABSTRACT FROM AUTHOR]

In this paper we quantize the N -dimensional classical Hamiltonian system H = | q | 2 ( η + | q | ) p 2 − k η + | q | , that can be regarded as a deformation of the Coulomb problem with coupling constant k , that it is smoothly recovered in the limit η → 0 . Moreover, the kinetic energy term in H is just the one corresponding to an N -dimensional Taub–NUT space, a fact that makes this system relevant from a geometric viewpoint. Since the Hamiltonian H is known to be maximally superintegrable, we propose a quantization prescription that preserves such superintegrability in the quantum mechanical setting. We show that, to this end, one must choose as the kinetic part of the Hamiltonian the conformal Laplacian of the underlying Riemannian manifold, which combines the usual Laplace–Beltrami operator on the Taub–NUT manifold and a multiple of its scalar curvature. As a consequence, we obtain a novel exactly solvable deformation of the quantum Coulomb problem, whose spectrum is computed in closed form for positive values of η and k , and showing that the well-known maximal degeneracy of the flat system is preserved in the deformed case. Several interesting algebraic and physical features of this new exactly solvable quantum system are analyzed, and the quantization problem for negative values of η and/or k is also sketched. [ABSTRACT FROM AUTHOR]

A generalized Weyl quantization formalism for a particle on the circle is shown to supply an effective method for defining the number–phase Wigner function in quantum optics. A Wigner function for the state ϱ ˆ and the kernel K for a particle on the circle is defined and its properties are analysed. Then it is shown how this Wigner function can be easily modified to give the number–phase Wigner function in quantum optics. Some examples of such number–phase Wigner functions are considered. [ABSTRACT FROM AUTHOR]

The most momentous requirement a quantum theory of gravity must satisfy is Background Independence, necessitating in particular an ab initio derivation of the arena all non-gravitational physics takes place in, namely spacetime. Using the background field technique, this requirement translates into the condition of an unbroken split-symmetry connecting the (quantized) metric fluctuations to the (classical) background metric. If the regularization scheme used violates split-symmetry during the quantization process it is mandatory to restore it in the end at the level of observable physics. In this paper we present a detailed investigation of split-symmetry breaking and restoration within the Effective Average Action (EAA) approach to Quantum Einstein Gravity (QEG) with a special emphasis on the Asymptotic Safety conjecture. In particular we demonstrate for the first time in a non-trivial setting that the two key requirements of Background Independence and Asymptotic Safety can be satisfied simultaneously. Carefully disentangling fluctuation and background fields, we employ a ‘bi-metric’ ansatz for the EAA and project the flow generated by its functional renormalization group equation on a truncated theory space spanned by two separate Einstein–Hilbert actions for the dynamical and the background metric, respectively. A new powerful method is used to derive the corresponding renormalization group (RG) equations for the Newton- and cosmological constant, both in the dynamical and the background sector. We classify and analyze their solutions in detail, determine their fixed point structure, and identify an attractor mechanism which turns out instrumental in the split-symmetry restoration. We show that there exists a subset of RG trajectories which are both asymptotically safe and split-symmetry restoring: In the ultraviolet they emanate from a non-Gaussian fixed point, and in the infrared they loose all symmetry violating contributions inflicted on them by the non-invariant functional RG equation. As an application, we compute the scale dependent spectral dimension which governs the fractal properties of the effective QEG spacetimes at the bi-metric level. Earlier tests of the Asymptotic Safety conjecture almost exclusively employed ‘single-metric truncations’ which are blind towards the difference between quantum and background fields. We explore in detail under which conditions they can be reliable, and we discuss how the single-metric based picture of Asymptotic Safety needs to be revised in the light of the new results. We shall conclude that the next generation of truncations for quantitatively precise predictions (of critical exponents, for instance) is bound to be of the bi-metric type. [ABSTRACT FROM AUTHOR]

Under the generic designation of unimodular theory, two theoretical models of gravity are considered: the unimodular gravity and the TDiff theory. Our approach is primarily pedagogical. We aim to describe these models both from a geometric and a field-theoretical point of view. In addition, we explore connections with the cosmological-constant problem and outline some applications. We do not discuss the application of this theory to the quantization of gravity. [ABSTRACT FROM AUTHOR]

In this paper we use Dirac function to construct a fractional operator called fractional corresponding operator, which is the general form of momentum corresponding operator. Then we give a judging theorem for this operator and with this judging theorem we prove that R–L, G–L, Caputo, Riesz fractional derivative operator and fractional derivative operator based on generalized functions, which are the most popular ones, coincide with the fractional corresponding operator. As a typical application, we use the fractional corresponding operator to construct a new fractional quantization scheme and then derive a uniform fractional Schrödinger equation in form. Additionally, we find that the five forms of fractional Schrödinger equation belong to the particular cases. As another main result of this paper, we use fractional corresponding operator to generalize fractional quantization scheme by using Lévy path integral and use it to derive the corresponding general form of fractional Schrödinger equation, which consequently proves that these two quantization schemes are equivalent. Meanwhile, relations between the theory in fractional quantum mechanics and that in classic quantum mechanics are also discussed. As a physical example, we consider a particle in an infinite potential well. We give its wave functions and energy spectrums in two ways and find that both results are the same. [ABSTRACT FROM AUTHOR]

We analyze the quantum phenomenon arising from the interaction of a spinless charged particle with a rotating cosmic string, under the action of a static and uniform magnetic field parallel to the string. We calculate the energy levels of the particle in the non-relativistic approach, showing how these energies depend on the parameters involved in the problem. In order to do this, we solve the time independent Schrödinger equation in the geometry of the spinning cosmic string, taking into account that the coupling between the rotation of the spacetime and the angular momentum of the particle is very weak, such that makes sense to apply the Schrödinger equation in a curved background whose metric has an off diagonal term which involves time and space. It is also assumed that the particle orbits sufficiently far from the boundary of the region of closed timelike curves which exist around this topological defect. Finally, we find the Landau levels of the particle in the presence of a spinning cosmic string endowed with internal structure, i.e. , having a finite width and uniformly filled with both material and vacuum energies. [ABSTRACT FROM AUTHOR]

In bosonic cascades of excitons or exciton-polaritons the absorption of electromagnetic radiation resonant to the energy spacing between neighboring quantization levels may be stimulated by the initial state occupation number. This opens way to realization of ultrasensitive detectors of infrared or terahertz radiation. The stimulated absorption of light by bosonic condensates has also a high potentiality for photovoltaic applications. [ABSTRACT FROM AUTHOR]

A theoretical investigation of the hole - polar optical phonon scattering processes in thin GaAs/AlxGa1-xAs quantum wellsxGa1-xAs quantum wells is carried out at room temperature for both the confined and interface phonon modes within the dielectric continuum model framework. For high accuracy, the model for the hole dispersion uses the 6×6 Luttinger-Kohn Hamiltonian. Detailed and extensive calculations based on this model show that the rates for intra-subband scattering processes differ significantly from those of bulk GaAs because of quantization and reduced dimensionality. Moreover, the study of scattering as a function of hole energy shows that the trend of the scattering rates is governed mostly by (i) overlap integrals and (ii) the density of the final states to which the hole scatters. The influence of warping, in the hole energy dispersion, on the phonon scattering rates is also explored and found to be important when the initial hole energy is high. Our calculations show evidence of strong anisotropy in the scattering rates especially for processes involving the heavy hole subband, which anisotropy is in fact quite important and far from being negligible. [ABSTRACT FROM AUTHOR]

Abstract: The parametrized Dirac wave equation represents position and time as operators, and can be formulated for many particles. It thus provides, unlike field-theoretic Quantum Electrodynamics (QED), an elementary and unrestricted representation of electrons entangled in space or time. The parametrized formalism leads directly and without further conjecture to the Bethe–Salpeter equation for bound states. The formalism also yields the Uehling shift of the hydrogenic spectrum, the anomalous magnetic moment of the electron to leading order in the fine structure constant, the Lamb shift and the axial anomaly of QED. [Copyright &y& Elsevier]

Abstract: The paper concerns integral quantization, a procedure based on operator-valued measure and resolution of the identity. We insist on covariance properties in the important case where group representation theory is involved. We also insist on the inherent probabilistic aspects of this classical–quantum map. The approach includes and generalizes coherent state quantization. Two applications based on group representation are carried out. The first one concerns the Weyl–Heisenberg group and the euclidean plane viewed as the corresponding phase space. We show that a world of quantizations exist, which yield the canonical commutation rule and the usual quantum spectrum of the harmonic oscillator. The second one concerns the affine group of the real line and gives rise to an interesting regularization of the dilation origin in the half-plane viewed as the corresponding phase space. [Copyright &y& Elsevier]

Abstract: In this work we apply the affine group formalism for four dimensional gravity of Lorentzian signature, which is based on Klauder’s affine algebraic program, to the formulation of the Hamiltonian constraint of the interaction of matter and all forces, including gravity with non-vanishing cosmological constant , as an affine Lie algebra. We use the hermitian action of fermions coupled to gravitation and Yang–Mills theory to find the density weight one fermionic super-Hamiltonian constraint. This term, combined with the Yang–Mills and Higgs energy densities, are composed with York’s integrated time functional. The result, when combined with the imaginary part of the Chern–Simons functional , forms the affine commutation relation with the volume element . Affine algebraic quantization of gravitation and matter on equal footing implies a fundamental uncertainty relation which is predicated upon a non-vanishing cosmological constant. [Copyright &y& Elsevier]

Abstract: Quantization theory gives rise to transverse phonons for the traditional Coulomb gauge condition and to scalar and longitudinal photons for the Lorentz gauge condition. We describe a new approach to quantize the general singular QED system by decomposing a general gauge potential into two orthogonal components in general field theory, which preserves scalar and longitudinal photons. Using these two orthogonal components, we obtain an expansion of the gauge-invariant Lagrangian density, from which we deduce the two orthogonal canonical momenta conjugate to the two components of the gauge potential. We then obtain the canonical Hamiltonian in the phase space and deduce the inherent constraints. In terms of the naturally deduced gauge condition, the quantization results are exactly consistent with those in the traditional Coulomb gauge condition and superior to those in the Lorentz gauge condition. Moreover, we find that all the nonvanishing quantum commutators are permanently gauge-invariant. A system can only be measured in physical experiments when it is gauge-invariant. The vanishing longitudinal vector potential means that the gauge invariance of the general QED system cannot be retained. This is similar to the nucleon spin crisis dilemma, which is an example of a physical quantity that cannot be exactly measured experimentally. However, the theory here solves this dilemma by keeping the gauge invariance of the general QED system. [Copyright &y& Elsevier]

Abstract: We construct a version of the complex Heisenberg algebra based on the idea of endless analytic continuation. The algebra would be large enough to capture quantum effects that escape ordinary formal deformation quantisation. [Copyright &y& Elsevier]