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We study irreducible spherical unitary representations of the Drinfeld double of the q-deformation of a connected simply connected compact Lie group, which can be considered as a quantum analogue of the complexification of the Lie group. In the case of SU q ⁢ (3) \mathrm{SU}_{q}(3) , we give a complete classification of such representations. As an application, we show the Drinfeld double of the quantum group SU q ⁢ (2 ⁢ n + 1) \mathrm{SU}_{q}(2n+1) has property (T), which also implies central property (T) of the dual of SU q ⁢ (2 ⁢ n + 1) \mathrm{SU}_{q}(2n+1). [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]

It is revealed that there is a link between the quantization approach employed and the dimension of the vector parameter which can be accurately estimated by a quantized estimation system. A critical quantity called inestimable dimension for quantized data (IDQD) is introduced, which does not depend on the quantization regions and the statistical models of the observations but instead depends only on the number of sensors and on the precision of the vector quantizers employed by the system. It is shown that the IDQD describes a quantization-induced fundamental limitation on the estimation capabilities of the system. To be specific, if the dimension of the desired vector parameter is larger than the IDQD of the quantized estimation system, then the Fisher information matrix for estimating the desired vector parameter is singular, and, moreover, there exist infinitely many nonidentifiable vector parameter points in the vector parameter space. Furthermore, it is shown that under some common assumptions on the statistical models of the observations and the quantization system, a smaller IDQD can be obtained, which can specify an even more limiting quantization induced fundamental limitation on the estimation capabilities of the system. [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]

Based on the pseudopotential method and the phenomenological model of coupling forces, electron scattering by short-wavelength phonons in the conduction band of superlattices ( GaAs ) m ( AlAs ) n with thin layers ( n , m  ≤ 10) is studied. Intervalley deformation potentials for transitions between the lower states of the Γ and M valleys of superlattices, which are analogs of the sphalerite transitions of Γ ̲ − X ̲ and X ̲ − X ̃ ̲ , are calculated. The intensity of the Γ −  M transitions is determined mainly by the longitudinal optical vibrations of the Al atoms and depends strongly on the mixing of the states Γ ̲ and X ̲ . The capture of phonons and electrons in AlAs layers leads to an increase in the deformation potentials of X ̲ − X ̃ ̲ transitions. [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]

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]

We evaluate the frame-independent gluon and charm parton-distribution functions (PDFs) of the deuteron utilizing light-front quantization and the impulse approximation. We use a nuclear wave function obtained from solving the nonrelativistic Schrödinger equation with the realistic Argonne v18 nuclear force, which we fold with the proton PDF. The predicted gluon distribution in the deuteron (per nucleon) is a few percent smaller than that of the proton in the domain x b j = Q 2 2 p N ⋅ q ∼ 0.4 , whereas it is strongly enhanced for x b j larger than 0.6. We discuss the applicability of our analysis and comment on how to extend it to the kinematic limit x b j → 2 . We also analyze the charm distribution of the deuteron within the same approach by considering both the perturbatively and non-perturbatively generated (intrinsic) charm contributions. In particular, we note that the intrinsic-charm content in the deuteron will be enhanced due to 6-quark “hidden-color” QCD configurations. [ABSTRACT FROM AUTHOR]

Lately, the yellow series of P-excitons in cuprous oxide could be resolved up to the principal quantum number n = 25. Adding a magnetic field, leads to additional confinement normal to the field. Thereby, the transition associated with the exciton n is transformed into the transition between the electron and hole Landau levels with quantum number n, once the associated magnetic length becomes smaller than the related exciton Bohr radius. The magnetic field of this transition scales roughly as n-3. As a consequence of the extended exciton series, we are able to observe Landau level transitions with unprecedented high quantum numbers of more than 75. [ABSTRACT FROM AUTHOR]

We define mixed states associated with submanifolds with probability densities in quantizable closed Kähler manifolds. Then, we address the problem of comparing two such states via their fidelity. First, we estimate the sub-fidelity and super-fidelity of two such states, giving lower and upper bounds for their fidelity, when the underlying submanifolds are two Lagrangian submanifolds intersecting transversally at a finite number of points, in the semiclassical limit. Second, we investigate a family of examples on the sphere, for which we manage to obtain a better upper bound for the fidelity. We conclude by stating a conjecture regarding the fidelity in the general case. [ABSTRACT FROM AUTHOR]

In this work, a suitable Hamiltonian that describes the damped harmonic oscillator is constructed. Besides, the Hamilton-Jacobi equation for this dissipative system is written and the action function is obtained. Then, the system is quantized using two methods: the WKB approximation and the canonical quantization. In addition, evolution of the probability density is plotted at different times, and it is observed that the width of these densities decreases with time. The average energy of the system is also calculated and found to decrease with time. [ABSTRACT FROM AUTHOR]

Light-front (LF) quantization of massless fields in two spacetime dimensions is a long-standing and much debated problem. Even though the classical wave-equation is well-documented for almost two centuries, either as problems with initial values in spacetime variables or with initial data on characteristics in light-cone variables, the way to a consistent quantization in both types of frames is still a puzzle in many respects. This is in contrast to the most successful Conformal Field Theoretic (CFT) approach in terms of complex variables z , z ̄ pioneered by Belavin, Polyakov and Zamolodchikov in the ’80s. It is shown here that the 2D-massless canonical quantization in both reference frames is completely consistent provided that quantum fields are treated as Operator-Valued Distributions (OPVD) with Partition of Unity (PU) test functions. We recall first that classical fields have to be considered as distributions (e.g. generalized functions in the Russian literature). Then, a necessary condition on the PU test function follows from the required matching of the classical solutions of the massless differential equations in both types of reference frame. Next we use a mathematical formulation for OPVD, developed in the recent past. Specifically, smooth 𝒞 ∞ fields are introduced through the convolution operation in the distributional context. Due to the specific behavior of the Fourier-transform of the initial test function, this convolution transform has a well-defined integral in the dual space, whatever the initial choice of the reference frame. The relation to the conformal fields method follows immediately from the transition to Euclidean time and leads directly to explicit calculations of a few correlation functions of the scalar field and its energy–momentum tensor. The LF derivation of the Virasoro algebra is then obtained from the z and z ̄ expansions of the canonical fields as distributional Laplace-transform in these variables. Finally, the popular and problematic Discretized Light Cone Quantization (DLCQ) method is scrutinized with respect to its zero mode and ultraviolet content as encompassed in the continuum OPVD formulation. [ABSTRACT FROM AUTHOR]

In this paper we study the quantization of a massless scalar field in a rotating frame. In particular, we obtain the Casimir energy in a space–time with one extra compactified dimension for a rotating observer. We consider a uniformly rotating system on the circle S1 and present an equation for spin-0 bosons where noninertial effects can be taken into account. It is shown that the spectrum of the scalar field depends on the angular velocity of the rotating system and in this way, positive and negative modes can be defined through an appropriate choice of the angular velocity. We show that noninertial effects restrict the physical region of the space–time where particles can be placed, and furthermore that the Casimir energy in the space–time with one extra compactified dimension is shifted by these effects. In addition, we pointed out that rotating effects modify the length of the extra dimension for a co-rotating observer in this kind of space–time. [ABSTRACT FROM AUTHOR]

In this letter, we have discussed the implications of nonlocal-in-time kinetic energy approach recently introduced by Suykens on the dynamics of charge particles spin in a magnetic field with spin. It was observed that both the Landau quantization of the energy and their levels positions are modified. Besides, massive photons are generated in magnetic materials similar to the one encountered in massive quantum electrodynamics. These massive photons depend on the electron mass and on the nonlocal relaxation time. For solid copper, we found M ≈ 3.4 × 10 - 20 α - 2 eV / c 2 where α is a real free parameter. [ABSTRACT FROM AUTHOR]

It is often said that quantum and classical randomness are of different nature, the former being ontological and the latter epistemological. However, so far the question of 'What is quantum in quantum randomness?', i.e. what is the impact of quantization and discreteness on the nature of randomness, remains to be answered. In a first part, we make explicit the differences between quantum and classical randomness within a recently proposed ontology for quantum mechanics based on contextual objectivity. In this view, quantum randomness is the result of contextuality and quantization. We show that this approach strongly impacts the purposes of quantum theory as well as its areas of application. In particular, it challenges current programmes inspired by classical reductionism, aiming at the emergence of the classical world from a large number of quantum systems. In a second part, we analyse quantum physics and thermodynamics as theories of randomness, unveiling their mutual influences. We finally consider new technological applications of quantum randomness that have opened up in the emerging field of quantum thermodynamics. This article is part of a discussion meeting issue 'Foundations of quantum mechanics and their impact on contemporary society'. [ABSTRACT FROM AUTHOR]

We present simple solutions of IKKT-type matrix models describing a quantized homogeneous and isotropic cosmology with k = − 1 , finite density of microstates and a resolved Big Bang. At late times, a linear coasting cosmology a ( t ) ∝ t is obtained, which is remarkably close to observation. The solution consists of two sheets with opposite intrinsic chiralities, which are connected in a Euclidean pre-big bang era. [ABSTRACT FROM AUTHOR]

In this paper, the problem of adaptive neural network asymptotical tracking is investigated for a class of nonlinear system with unknown function, external disturbances and input quantisation. Based on neural network technique, an adaptive asymptotical tracking controller is provided for an uncertain nonlinear system via backstepping method. In order to reduce complexity of the control algorithm in the backstepping design process, a sliding mode differentiator is employed to estimate the virtual control law and only two parameters need to be estimated via adaptive control technique. The stability of the closed-loop system is analysed by using Lyapunov function method and zero-tracking error performance is obtained in the presence of unknown nonlinear function, external disturbances and input quantisation. Finally, an application example is employed to demonstrate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

This paper analyzes the limitations of a reduced-order model for modular multilevel converters (MMCs) by elucidating the relation between its accuracy, operating frequency, and converter parameters. A reduced-order simplifies the analysis of the MMC and thereby may provide additional information about the converter behavior. However, the accuracy of such model depends on several factors. In this paper, the effect of approximating the converter as a continuous system by neglecting quantization issues associated with having a finite number of modules is studied in detail. The analysis is done based on Fourier-series approximations with which it is possible to elucidate the relationship between the resonant frequencies of the MMC and the error of the reduced-order model. With the Fourier approximation, it is also possible to characterize resonant frequencies of the converter, both numerically and analytically, in terms of the converter parameters. The results can serve as a tool to identify situations when the reduced-order model produces good and also less accurate approximations especially when a low number of modules is available. [ABSTRACT FROM PUBLISHER]

In this paper, we consider the problem of sensor fusion over networks with asymmetric links, where the common goal is linear parameter estimation. For the scenario of bandwidth-constrained networks, existing literature shows that nonvanishing errors always occur, which depend on the quantization scheme. To tackle this challenging issue, we introduce the notion of virtual measurements and propose a distributed solution LS-DSFS, which is a combination of a quantized consensus algorithm and the least squares approach. We provide detailed analysis of the LS-DSFS on its performance in terms of unbiasedness and mean square property. Analytical results show that the LS-DSFS is effective in smearing out the quantization errors, and achieving the minimum mean square error (MSE) among the existing centralized and distributed algorithms. Moreover, we characterize its rate of convergence in the mean square sense and that of the mean sequence. More importantly, we find that the LS-DSFS outperforms the centralized approaches within a moderate number of iterations in terms of MSE, and will always consume less energy and achieve more balanced energy expenditure as the number of nodes in the network grows. Simulation results are presented to validate theoretical findings and highlight the improvements over existing algorithms. [ABSTRACT FROM AUTHOR]

The theory of electron energy quantization in an N atom long chain affected by a homogeneous electric field E e is extended to the 2D case of N atom long and N atom wide conductor with the lattice constant a. The conductor is modeled by the standard one‐parameter tight‐binding Hamiltonian (hopping integral t) of an atomic rectangular square lattice, where the change of electron site energy from atom to atom across the conductor equals (in | t | units) to electric field parameter a e E e / | t | (efp). Each field‐provoked level E μ (transverse μ‐mode energy) is shown giving rise to the μth subband of field‐independent levels of extended states due to the electron resonant transfer in the longitudinal direction perpendicular to the electric field. The level spacing and, hence, the width of μ subbands, is dictated by the conductor width and hopping integral t. The spectra of arbitrary‐size atomic square lattices are classified in terms of subband center spacing (SBCS) within the transverse‐mode bands of extended states, edge‐localized states, and Wannier–Stark states. We identified special cases of integer and fractional SBCS quantization in efp‐portions and found the exact and/or highly accurate explicit approximate expressions for the weighted number of states within these bands. The presented novel results clarify and correct their analogs reported previously. [ABSTRACT FROM AUTHOR]

Bateman’s dual system (BDS) is a linear time-reversal invariant system that consists of damping and amplifying coordinate variables subjected to a harmonic oscillator potential. It is known that canonical quantization of the BDS in the underdamping region suffers from pathologies such as the non-stationary vacuum and the breakdown of Heisenberg’s uncertainty principle. In this paper, following a previous study that targeted the pathology-free massless BDS, the massive BDS is quantized by decomposing it into two independent effectively massless subsystems with reduced degrees of freedom. In each subsystem, the amplifying variable is the conjugate momentum of a damping variable that obeys a non-canonical quantization condition. By virtue of general scaling invariance including U(1), the variables in BDS are treated as non-self-adjoint without changing the total degrees of freedom. The physical states are constructed with time-reversal normalization and are shown to satisfy the time-independent uncertainty relation. The original massive BDS that fulfills the canonical quantization condition is reconstructed by superposing the two subsystems. The same method is also applied to the underdamped BDS to obtain the time-independent uncertainty relations. The expectation values of the coordinate operators represent the complex representation of the solution of the classical equation of motion. The scaling invariance may be broken by coupling with the environment. [ABSTRACT FROM AUTHOR]

In this paper, we outline the construction of semiclassical eigenfunctions of integrable models in terms of the semiclassical path integral for the Poisson sigma model with the target space being the phase space of the integrable system. The semiclassical path integral is defined as a formal power series with coefficients being Feynman diagrams. We also argue that in a similar way one can obtain irreducible semiclassical representations of Kontsevich’s star product. Dedicated to the memory of L. D. Faddeev [ABSTRACT FROM AUTHOR]

About 30 years ago, in a joint work with L. Faddeev we introduced a geometric action on coadjoint orbits. This action, in particular, gives rise to a path integral formula for characters of the corresponding group G. In this paper, we revisit this topic and observe that the geometric action is a 1-cocycle for the loop group LG. In the case of G being a central extension, we construct Wess–Zumino (WZ) type terms and show that the cocycle property of the geometric action gives rise to a Polyakov–Wiegmann (PW) formula with boundary term given by the 2-cocycle which defines the central extension. In particular, we obtain a PW type formula for Polyakov’s gravitational WZ action. After quantization, this formula leads to an interesting bulk-boundary decoupling phenomenon previously observed in the WZW model. We explain that this decoupling is a general feature of the Wess–Zumino terms obtained from geometric actions, and that in this case, the path integral is expressed in terms of the 2-cocycle which defines the central extension. In memory of our teacher Ludwig Faddeev [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]

A set of six-degree-of-freedom robotic welding automatic tracking platform was designed in this study to realize the real-time tracking of weld seams. Moreover, the feature point tracking method and the adaptive fuzzy control algorithm in the welding process were studied and analyzed. A laser vision sensor and its measuring principle were designed and studied, respectively. Before welding, the initial coordinate values of the feature points were obtained using morphological methods. After welding, the target tracking method based on Gaussian kernel was used to extract the real-time feature points of the weld. An adaptive fuzzy controller was designed to input the deviation value of the feature points and the change rate of the deviation into the controller. The quantization factors, scale factor, and weight function were adjusted in real time. The input and output domains, fuzzy rules, and membership functions were constantly updated to generate a series of smooth bias robot voltage. Three groups of experiments were conducted on different types of curve welds in a strong arc and splash noise environment using the welding current of 120 A short-circuit Metal Active Gas (MAG) Arc Welding. The tracking error was less than 0.32 mm and the sensor’s metrical frequency can be up to 20 Hz. The end of the torch run smooth during welding. Weld trajectory can be tracked accurately, thereby satisfying the requirements of welding applications. [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]

A Digital-to-Time Converter based (DTC-based) fractional- N digital phase-locked loop (DPLL) using probability-density-shaping (PDS) spur immunity and quantization phase (Q-noise) reduction techniques is presented. PDS-DSM is used to generate a loop spur immunity control code for DTC. A diff type dither is proposed to further suppress the fractional spur. The loop nonlinearity will not cause fractional spurs if certain conditions are obeyed. Moreover, to reduce the quantization noise, a configurable Phase Interpolator (PI) with 0.125/0.25/0.5/1.0 division step is integrated with a multi-module divider (MMDIV), leading to an 18-dB Q-noise suppression. A reference doubler with duty-cycle correction is adopted to further reduce phase noise. The fractional spurs are greatly mitigated by combining the PDS-DSM and phase interpolator. A DPLL prototype using the aforementioned techniques was designed in a 40-nm standard CMOS process, occupying a 0.99 mm2 silicon area. At a near-integer- N frequency, i.e., near 2.23 GHz, with PDS turned on and off, the post-layout simulated fractional spur is −59 dBc and −20 dBc, respectively. The RMS jitter of the whole chip is 4.218 ps, corresponding to a figure of merit (FOM) of −220.5 dB. [ABSTRACT FROM AUTHOR]

Quantum transport is studied for the nonequilibrium Anderson impurity model at zero temperature employing the multilayer multiconfiguration time-dependent Hartree theory within the second quantization representation (ML-MCTDH-SQR) of Fock space. To address both linear and nonlinear conductance in the Kondo regime, two new techniques of the ML-MCTDH-SQR simulation methodology are introduced: (i) the use of correlated initial states, which is achieved by imaginary time propagation of the overall Hamiltonian at zero voltage and (ii) the adoption of the logarithmic discretization of the electronic continuum. Employing the improved methodology, the signature of the Kondo effect is analyzed. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of quantized H∞ filtering for multi-output discrete-time systems over independent identically distributed (i.i.d.) fading channels and Markov fading channels, respectively. The measurement outputs are quantized by a logarithmic quantizer, and then transmitted to the filter over fading channels. For the i.i.d. fading channels, the stochastic multiplicative noise form is used to model the unreliable communication environment. For the Markov fading channels, a set of Markov channel state processes is introduced to model time-varying fading channels, which characterizes various configurations of the physical communication environment and/or different channel fading amplitudes. The sufficient condition for stochastic stability with a prescribed H∞ performance is obtained by using a Lyapunov method and matrix decoupling technique. The corresponding filter design casts into a convex optimization problem. Finally, simulation results are provided to illustrate the effectiveness of our results. [ABSTRACT FROM AUTHOR]

We present a generally covariant approach to quantum mechanics in which generalized positions, momenta and time variables are treated as coordinates on a fundamental “phase-spacetime”. We show that this covariant starting point makes quantization into a purely geometric flatness condition. This makes quantum mechanics purely geometric, and possibly even topological. Our approach is especially useful for time-dependent problems and systems subject to ambiguities in choices of clock or observer. As a byproduct, we give a derivation and generalization of the Wigner functions of standard quantum mechanics. [ABSTRACT FROM AUTHOR]

A way to encode acceleration directly into fields has recently being proposed, thus establishing a new kind of fields, the accelerated fields. The definition of accelerated fields points to the quantization of space and time, analogously to the way quantities like energy and momentum are quantized in usual quantum field theories. Unruh effect has been studied in connection with quantum field theory in curved spacetime and it is described by recruiting a uniformly accelerated observer. In this work, as a first attempt to demonstrate the utility of accelerated fields, we present an alternative way to derive Unruh effect. We show, by studying quantum field theory on quantum spacetime, that Unruh effect can be obtained without changing the reference frame. Thus, in the framework of accelerated fields, the observational confirmation of Unruh effect could be assigned to the existence of quantum properties of spacetime. [ABSTRACT FROM AUTHOR]

We found that quantization of the scanning tunneling microscope (STM) current becomes apparent as the size of a quantum corral (QC) decreases and the corral thickness increases. It is shown that STM current images provide the position dependence of the conduction channels and local density of states (LDOS) images provide the spatial distribution of differential conductance channels. We clarified for the first time that there exist fractal structures in the QC size dependence of the - characteristic and in that of the LDOS. LDOS images also exhibit a fractal structure as a function of bias voltage. These results demonstrate fractal structures in energy space and real space. For an extremely large QC, we found that the - curve becomes Ohmic and the LDOS converges to a constant corresponding to the bulk two-dimensional density of states. [ABSTRACT FROM AUTHOR]

Examples of many-body Hamiltonians are identified which yield time-evolutions, having the property that the projection of an arbitrary orbit in phase space onto configuration space is periodic with a period independent of initial data (“isochrony”), while the evolution in phase space is not periodic. These include a variation on the harmonic oscillator as well as a Hamiltonian yielding the “goldfish” equations of motion. We then investigate a one-body version in the complex plane of this goldfish Hamiltonian. Its quantization is studied, and it is shown that the spectrum is continuous and infinitely degenerate; the general solution of the time-dependent Schrödinger equation in the position representation is not time-periodic, but its square modulus does evolve isochronously. [ABSTRACT FROM AUTHOR]

We consider the problem of recovering a high-dimensional structured signal from independent Gaussian linear measurements each of which is quantized to $b$ bits. The focus is on a specific method of signal recovery that extends a procedure originally proposed by Plan and Vershynin for one-bit quantization to a multi-bit setting. At the heart of this paper is a characterization of the optimal trade-off between the number of measurements m$ and the bit depth per measurement b$ given a total budget of B = m \cdot b -error in estimating the signal. It turns out that the choice b = 1$ is optimal for estimating the unit vector (direction) corresponding to the signal for any level of additive Gaussian noise before quantization as well as for a specific model of adversarial noise, whereas in a noiseless setting the choice b = 2$ is optimal for estimating the direction and the norm (scale) of the signal. Moreover, Lloyd–Max quantization is shown to be an optimal quantization scheme with respect to -estimation error. Our analysis is corroborated by the numerical experiments showing nearly perfect agreement with our theoretical predictions. This paper is complemented by an empirical comparison to alternative methods of signal recovery. The results of that comparison point to a regime change depending on the noise level: in a low-noise setting, the approach under study falls short of more sophisticated competitors while being competitive in moderate- and high-noise settings. [ABSTRACT FROM PUBLISHER]

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]

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]

A fully canonical quantization of electromagnetic field in the presence of a bi-anisotropic absorbing magneto-dielectric slab is demonstrated. The electric and the magnetic polarization densities of the magneto-dielectric slab are defined in terms of the dynamical variables modeling the slab and the coupling tensors that couple the electromagnetic field to the slab. The four susceptibility tensors of the bi-anisotropic magneto-dielectric slab are expressed in terms of the coupling tensors that couple an electromagnetic field to the slab. It is shown that the four susceptibility tensors of the bi-anisotropic magneto-dielectric slab satisfy Kramers-Kronig relations. The Maxwell's equations are exactly solved in the presence of the bi-anisotropic magneto-dielectric slab. The tangential and the normal components of the Casimir forces exerted on the bi-anisotropic magnet-dielectric slab exactly are calculated in the vacuum state and thermal state of the total system. It is shown that the tangential components of the Casimir forces vanish when the bi-anisotropic slab is converted to an isotropic slab. [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]

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]

We prove a criterion for a "magnetic" Weyl operator to be trace-class by extending a method developed by Cordes, Kato and Arsu. Using the Calderon-Vaillancourt type Theorem for magnetic Weyl operators and an interpolation argument we also give a criterion for a "magnetic" Weyl operator to be in a Schatten-von Neumann class with 1 < p < ∞. [ABSTRACT FROM AUTHOR]

Abstract: A fundamental problem regarding the Dirac quantization of a free particle on an N − 1 ( N ≥ 2) curved hypersurface embedded in N flat space is the impossibility to give the same form of the curvature‐induced quantum potential, the geometric potential as commonly called, as that given by the Schrödinger equation method where the particle moves in a region confined by a thin‐layer sandwiching the surface. This problem is resolved by means of a previously proposed scheme that hypothesizes a simultaneous quantization of positions, momenta, and Hamiltonian, among which the operator‐ordering‐free section is identified and is then found sufficient to lead to the expected form of geometric potential. [ABSTRACT FROM AUTHOR]