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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]

With the rapid development of microtechnology, the low-dimensional materials are fabricated with nontrivial topological structures, and then the action of geometric properties on the effective dynamics receives increasing attention. It is an effective theory that the quantum mechanics of low-dimensional curved systems can be given by using the thin-layer quantization approach, in which the geometric potential and the geometric momentum have been demonstrated experimentally. In the present paper, the thin-layer quantization formalism is first recalled, its fundamental calculation framework is first clarified, and the geometric quantum effects result from the diffeomorphism transformation and the rotation transformation connecting the local frames of different points. The results are helpful to understand the gravitational gauge and emerging gauge, and to image the geometries implied in the artificial gauge. In the particular quantum systems, the novel physical phenomena are briefly recalled that are induced by geometry, such as resonation tunneling, quantum block, quantum Hall effect, quantum Hall viscosity, quantum spin Hall effect, effective monopole magnetic field and so on. The results will shed light from a different angle on the relationships between the geometry and the novel physical phenomenon. [ABSTRACT FROM AUTHOR]

We consider the Dirac quantization in the first-class formalism to investigate the hypersphere soliton model (HSM) defined on the S 3 hypersphere. To do this, we construct the first-class Hamiltonian possessing the Weyl ordering correction. In the HSM, we evaluate the baryon physical quantities such as the baryon masses, magnetic moments, axial coupling constant and charge radii, most predicted values of which are in good agreement with the corresponding experimental data. Moreover, shuffling the baryon and transition magnetic moments, we find the model independent sum rules. In the HSM we also evaluate the baryon intrinsic frequencies such as ω N = 0.87 × 10 23 s − 1 and ω Δ = 1.74 × 10 23 s − 1 of the nucleon and delta baryon, respectively, to yield the identity ω Δ = 2 ω N . Next, making use of the Nambu-Goto string action and its extended rotating bosonic string theory, we formulate the stringy photon model to obtain the energy of the string configuration, which consists of the rotational and vibrational energies of the open string. Exploiting this total string energy, we evaluate the photon intrinsic frequency ω γ = 9.00 × 10 23 s − 1 , which is comparable to the corresponding baryon intrinsic frequencies. We also predict the photon size 〈 r 2 〉 1 / 2 (photon) = 0.17 fm , which is approximately 21% of the proton magnetic charge radius. [ABSTRACT FROM AUTHOR]

We develop the theory of transformation of intensive initial nonlinear wave pulses to trains of solitons emerging at asymptotically large time of evolution. Our approach is based on the theory of dispersive shock waves in which the number of nonlinear oscillations in the shock becomes the number of solitons at the asymptotic state. We show that this number of oscillations, which is proportional to the classical action of particles associated with the small-amplitude edges of shocks, is preserved by the dispersionless flow. Then, the Poincaré–Cartan integral invariant is also constant, and therefore, it reduces to the quantization rule similar to the Bohr–Sommerfeld quantization rule for a linear spectral problem associated with completely integrable equations. This rule yields a set of "eigenvalues," which are related to the asymptotic solitons' velocities and their characteristics. It is implied that the soliton equations under consideration give modulationally stable solutions; therefore, these "eigenvalues" are real. Our analytical results agree very well with the results of numerical solutions of the generalized defocusing nonlinear Schrödinger equation. [ABSTRACT FROM AUTHOR]

To the existing list of alternative formulations of quantum mechanics, a new version of the non-Hermitian interaction picture is added. What is new is that, in contrast to the more conventional non-Hermitian model-building recipes, the primary information about the observable phenomena is provided not only by the Hamiltonian but also by an additional operator with a real spectrum (say, R (t) ) representing another observable. In the language of physics, the information carried by R (t) ≠ R † (t) opens the possibility of reaching the exceptional-point degeneracy of the real eigenvalues, i.e., a specific quantum phase transition. In parallel, the unitarity of the system remains guaranteed, as usual, via a time-dependent inner-product metric Θ (t) . From the point of view of mathematics, the control of evolution is provided by a pair of conjugate Schrödiner equations. This opens the possibility od an innovative dyadic representation of pure states, by which the direct use of Θ (t) is made redundant. The implementation of the formalism is illustrated via a schematic cosmological toy model in which the canonical quantization leads to the necessity of working with two conjugate Wheeler-DeWitt equations. From the point of view of physics, the "kinematical input" operator R (t) may represent either the radius of a homogeneous and isotropic expanding empty Universe or, if you wish, its Hubble radius, or the scale factor a (t) emerging in the popular Lemaitre-Friedmann-Robertson-Walker classical solutions, with the exceptional-point singularity of the spectrum of R (t) mimicking the birth of the Universe ("Big Bang") at t = 0 . [ABSTRACT FROM AUTHOR]

Following our previous study of the Bohr–Sommerfeld (BS) quantization condition for one-dimensional case [J. C. del Valle and A. V. Turbiner, Int. J. Mod. Phys. A36, 2150221 (2021)], we extend it to d -dimensional power-like radial potentials. The BS quantization condition for S -states of the d -dimensional radial Schrödinger equation is proposed. Based on numerical results obtained for the spectra of power-like potentials, V (r) = r m with m ∈ [ − 1 , ∞) , the correctness of the proposed BS quantization condition is established for various dimensions d. It is demonstrated that by introducing the WKB correction γ into the right-hand side of the BS quantization condition leads to the so-called exact WKB quantization condition, which reproduces the exact energies, while γ remains always very small. For m = 2 (any integer d) and for m = − 1 (at d = 2) the WKB correction γ = 0 : for S states the BS spectra coincides with the exact ones. Concrete calculations for physically important cases of linear, cubic, quartic and sextic oscillators, as well as Coulomb and logarithmic potentials in dimensions d = 2 , 3 , 6 are presented. Radial quartic anharmonic oscillator is considered briefly. [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]

Using the thin-layer quantization, we formulate the problem of a Schrödinger particle constrained to move along a coordinate surface of the bi-spherical coordinate system. In three-dimensional space, the free Schrödinger equation is not separable in this coordinate system. However, when we consider the equation for a particle constrained to a given surface, there are only two degrees of freedom. One has to introduce a geometrical potential to attach the particle to the surface. This well-known potential has two contributions: one from Gauss' curvature and the other from the mean curvature. The Schrödinger equation leads to a general Heun equation. We solve it exactly and present the eigenfunctions and plots of the probability densities, and, as an application of this methodology, we study the problem of an electric charge propagating along these coordinate surfaces in the presence of a uniform magnetic field. [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]

A half-wavelength cavity, wherein the electromagnetic field is quantized as standing-wave photons, is a typical artificial quantum system that has widely been used to implement quantum information processing. In this paper, we propose an approach to confirm the quantization of the electromagnetic field in another type of cavity, namely, a quarter-wavelength transmission line resonator (TLR), by using traveling-photon scattering measurements. Furthermore, we show that the number of photons in a TLR can be destructively detected by using the usual IQ-mixed technique. We hope that quarter-wavelength TLRs may also serve as quantum devices to implement on-chip solid-state quantum information processing. [ABSTRACT FROM AUTHOR]

In this paper, we address the design of multi-user multiple-input single-output (MU-MISO) precoders for indoor visible light communication (VLC) systems. The goal is to minimize the transmitted optical power per light emitting diode (LED) under imperfect channel state information (CSI) at the transmitter side. Robust precoders for imperfect CSI available in the literature include noisy and outdated channel estimation cases. However, to the best of our knowledge, no work has considered adding robustness against channel quantization. In this paper, we fill this gap by addressing the case of imperfect CSI due to the quantization of VLC channels. We model the quantization errors in the CSI through polyhedric uncertainty regions. For polyhedric uncertainty regions and positive real channels, as is the case of VLC channels, we show that the robust precoder against channel quantization errors that minimizes the transmitted optical power while guaranteeing a target signal to noise plus interference ratio (SNIR) per user is the solution of a second order cone programming (SOCP) problem. Finally, we evaluate its performance under different quantization levels through numerical simulations. [ABSTRACT FROM AUTHOR]

In this article, mode‐reconfigurable orbit angular momentum (OAM) waves is developed by mechanically rotating a 2 bit phase quantization (0°, 90°, 180°, and 270°) transmitarray (TA) with size 6.2λ0 × 6.2λ0 × 0.98λ0 (λ0 wavelength in free space). The TA consists of three‐layer metasurfaces (MSs), which are in the top, middle, and bottom layers, respectively. The TA is excited by a horn. The top layer MS converts the spherical wave from the horn into plane wave. The middle and bottom layers are same, and they together convert the plane wave into OAM wave with mode l, and then reconfigurable mode can be achieved by rotating the bottom layer MS. To the knowledge of the authors, it is the first time to design mechanical OAM mode reconfigurability by phase quantization TA. As example, two TAs are designed for reconfigurable modes at 15.5 GHz: (1) Among l = 1, 0, −1. (2) Among l = 2, 0, −2. The TAs have the following advantages: high gain (15.1–21.5 dBi), high aperture efficiency (the highest up to 29.2%), high purity (92.67%–98.93%), and small size (6.2λ0 × 6.2λ0). The measured and simulated results agree well, and validate the design method. The developed OAM mode reconfigurable TAs have potential application for future high capacity communication. [ABSTRACT FROM AUTHOR]

In this article, I discuss the criticisms raised against Thomas Kuhn's Black-Body Theory. These criticisms concern two issues: how to understand Planck's position with regards to the quantization of energy in 1901, and how to understand the book's relation to The Structure of Scientific Revolutions. Both criticisms, I argue, concern the notion of a paradigm: the first concerns how Boltzmann acted as an exemplar for Planck, and the second whether the book provides a paradigm change. I will then argue that both criticisms presume a conceptualization of paradigms that does not align well with Kuhn's conceptualization of it in both Structure and later work: they assume, more specifically, that sharing a paradigm presupposes sharing an interpretation of it, and that paradigm changes are essentially identical to gestalt switches. On the basis of this, I will then argue that the criticisms are misguided, that Kuhn's position regarding Planck's work is in fact quite close to the indetermination-view developed by some of his critics, and that the book fits Structure quite well. In conclusion, I will then reflect on how the narrative provided in Black-Body Theory connects with Kuhn's views on the relation between history and philosophy of science. [ABSTRACT FROM AUTHOR]

In 1970, Edwards and Freed presented an elegant representation of interacting branched polymers that resembles the coherent states (CS) formulation of second-quantized field theory. This CS polymer field theory has been largely overlooked during the intervening period in favor of more conventional “auxiliary field” (AF) interacting polymer representations that form the basis of modern self-consistent field theory (SCFT) and field-theoretic simulation approaches. Here we argue that the CS representation provides a simpler and computationally more efficient framework than the AF approach for broad classes of reversibly bonding polymers encountered in supramolecular polymer science. The CS formalism is reviewed, initially for a simple homopolymer solution, and then extended to supramolecular polymers capable of forming reversible linkages and networks. In the context of the Edwards model of a non-reacting homopolymer solution and one and two-component models of telechelic reacting polymers, we discuss the structure of CS mean-field theory, including the equivalence to SCFT, and show how weak-amplitude expansions (random phase approximations) can be readily developed without explicit enumeration of all reaction products in a mixture. We further illustrate how to analyze CS field theories beyond SCFT at the level of Gaussian field fluctuations and provide a perspective on direct numerical simulations using a recently developed complex Langevin technique. [ABSTRACT FROM AUTHOR]

On the basis of revising the quantum concept and reinterpreting Bohr's hydrogen atom structure model in classical physics, this paper deduces the elliptical orbital energy level formula of electrons in hydrogen like atoms in detail. When the electron transition time is taken as unit time (1 s), the energy level formula is completely consistent with Bohr Sommerfeld's atomic structure Theory. [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]

An approach of the proper quantization rule to find exact solution of radial Schrödinger equation for non-polynomial potentials, which are quasi exactly solvable, is developed in this work. Using this rule, the determination of the energy spectrum En for non-pollynomialy potentials is somewhat impossible and limited, which provides their energy at ground state only. To overcome this difficulty, we devised in this approach the potential into two potentials: an exact potential Ve(r) and a non-linear extension Va(r), the potential will be expressed as:V (r) = Ve(r)+Va(r), then calculate the energy level εn and the ground state ε0 energy for exactly solvable potential Ve(r) using the proper quantization rule, from which an analytical expression of energie En for non-polynomial potential V (r) related with the ground level energy E0 is found easily. We conclude that the study of non-exactly potential remain to the study of the first exactly solvable potential. [ABSTRACT FROM AUTHOR]

Quantization provides a very natural way to preserve the convex order when approximating two ordered probability measures by two finitely supported ones. Indeed, when the convex order dominating original probability measure is compactly supported, it is smaller than any of its dual quantizations while the dominated original measure is greater than any of its stationary (and therefore any of its quadratic optimal) primal quantization. Moreover, the quantization errors then correspond to martingale couplings between each original probability measure and its quantization. This permits to prove that any martingale coupling between the original probability measures can be approximated by a martingale coupling between their quantizations in Wassertein distance with a rate given by the quantization errors but also in the much finer adapted Wassertein distance. As a consequence, while the stability of (Weak) Martingale Optimal Transport problems with respect to the marginal distributions has only been established in dimension 1 so far, their value function computed numerically for the quantized marginals converges in any dimension to the value for the original probability measures as the numbers of quantization points go to ∞. [ABSTRACT FROM AUTHOR]

The hybrid beamforming can significantly improve the spectral and energy efficiencies of the millimeter‐wave (mmWave) massive multiple input multiple output (MIMO) systems without obvious performance loss. However, the fundamental limitation of existing hybrid beamforming is that they include high‐resolution analog‐to‐digital converters (ADCs) which consume high power. To overcome this fundamental limitation, in this paper, spectrum and energy efficient mmWave massive MIMO transmission scheme is proposed that jointly optimizes the hybrid combiner and the number of ADC bits. Particularly, the hybrid combiner is presented as a combination of three parts: the analog combiner matrix, the quantization matrix, and the digital baseband matrix which is based on the Kalman filter. Unlike most existing works that rely on sumrate optimization to design the hybrid combiner, in this work, the mean square error (MSE) is chosen as the main performance metric to describe the reliability of the system. Simulations results confirm that the proposed Kalman based hybrid combiner exhibits the best performance in terms of spectral and energy efficiencies compared to minimum mean square error (MMSE) and zero forcing (ZF) receivers. [ABSTRACT FROM AUTHOR]

Efficient quantizer design is vital in high‐speed optical receivers. In this paper, the authors propose a three‐level (1.5‐bit) reliability‐based quantizer for low‐complexity soft decoding of low‐density parity‐check (LDPC) codes, and show that it outperforms a conventional quantizer employing eight levels (3 bits). Different approaches for obtaining the quantization thresholds are discussed, and it is shown that the achievable channel capacity with the proposed quantizer is within 0.4 dB of the Shannon limit of the unquantized channel. Rate‐compatible LDPC codes are also designed tailored to the asymmetric optical channel terminated with the proposed reliability‐based quantizer, and it is shown that the resulting quantizer‐aware LDPC codes significantly outperform other existing codes of similar rates. [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]

Higher-spin diffeomorphisms are to higher-order differential operators what diffeomorphisms are to vector fields. Their rigorous definition is a challenging mathematical problem which might predate a better understanding of higher-spin symmetries and interactions. Several yes-go and no-go results on higher-spin diffeomorphisms are collected from the mathematical literature in order to propose a generalisation of the algebra of differential operators on which higher-spin diffeomorphisms are well-defined. This work is dedicated to the memory of Christiane Schomblond, who taught several generations of Belgian physicists the formative rigor and delicate beauty of theoretical physics. [ABSTRACT FROM AUTHOR]

We reviewed the canonical quantisation of the geometry of the spacetime in the cases of a simply and a non-simply connected manifold. In the former, we analysed the information contained in the solutions of the Wheeler--DeWitt equation and showed their interpretation in terms of the customary boundary conditions that are typically imposed on the semiclassical wave functions. In particular, we reviewed three different paradigms for the quantum creation of a homogeneous and isotropic universe. For the quantisation of a non-simply connected manifold, the best framework is the third quantisation formalism, in which the wave function of the universe is seen as a field that propagates in the space of Riemannian 3-geometries, which turns out to be isomorphic to a (part of a) 1 + 5 Minkowski spacetime. Thus, the quantisation of the wave function follows the customary formalism of a quantum field theory. A general review of the formalism is given, and the creation of the universes is analysed, including their initial expansion and the appearance of matter after inflation. These features are presented in more detail in the case of a homogeneous and isotropic universe. The main conclusion in both cases is that the most natural way in which the universes should be created is in entangled universe--antiuniverse pairs. [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]

Using quantum transport simulations, the impact of electron-phonon scattering on the transfer characteristic of a gate-all-around nanowire (GaAs) field effect transistor (NWFET) has been thoroughly investigated. The Non-Equilibrium Green's Function formalism in the effective mass approximation using a decoupled mode decomposition has been deployed. NWFETs of different dimensions have been considered, and scattering mechanisms including acoustic, optical and polar optical phonons have been included. The effective masses were extracted from tight binding simulations. High and low drain bias have been considered. We found substantial source to drain tunnelling current and significant impact of phonon scattering on the performance of the NWFET. At low drain bias, for a 2.2×2.2 nm² cross-section transistor, scattering caused a 72%, 77%, and 81% decrease in the on-current for a 6 nm, 10nm, and 20nm channel length, respectively. This reduction in the current due to scattering is influenced by the increase in the tunnelling current. We include the percentage tunnelling for each valley at low and high drain bias. It was also found that the strong quantisation caused the relative position of the valleys to vary with the cross-section. This had a large effect on the overall tunnelling current. The phonon-limited mobility was also calculated, finding a mobility of 950 cm²/V s at an inversion charge density of 1012cm-2 for a 4.2×4.2 nm² cross-section device. [ABSTRACT FROM AUTHOR]

The helical edge states of two-dimensional topological insulators (TIs) experience appreciable quantum mechanical scattering in narrow channels when the width changes abruptly. The interference of the geometry scattering in narrow-wide-narrow waveguide structures is shown to give rise to the strong suppression of transmission when the incident energy is barely above the propagation threshold. Periodic resonant transmission takes place in this high reflection regime while the length of the wide section is varied. The resonance condition is governed by the transverse confinement in the wide section, where the form of quantization is manifested to differ for the two orthogonal directions. The confined energy levels in TI quantum dots are derived based on this observation. In addition, the off-diagonal spin-orbit term is found to produce an anomalous resonance state, which merges with the bottom ordinary resonance state to annihilate. [ABSTRACT FROM AUTHOR]

We present a semiclassical quantization condition, i.e., quantum-classical correspondence, for steady states of nonadiabatic systems consisting of fast and slow degrees of freedom (DOFs) by extending Gutzwiller's trace formula to a nonadiabatic form. The quantum-classical correspondence indicates that a set of primitive hopping periodic orbits, which are invariant under time evolution in the phase space of the slow DOF, should be quantized. The semiclassical quantization is then applied to a simple nonadiabatic model and accurately reproduces exact quantum energy levels. In addition to the semiclassical quantization condition, we also discuss chaotic dynamics involved in the classical limit of nonadiabatic dynamics. [ABSTRACT FROM AUTHOR]

The interaction of a number of impurities (H2, Ag, Cu, Ag2, Cu2, Li, He3+, He* (³S), He2* (³Σu), and e-) with quantized rectilinear vortex lines in superfluid 4He is calculated by using the Orsay-Trento density functional theory (DFT) method at 0 K. The Donnelly-Parks (DP) potential function binding ions to the vortex is combined with DFT data, yielding the impurity radius as well as the vortex line core parameter. The vortex core parameter at 0 K (0.74 Å) obtained either directly from the vortex line geometry or through the DP potential fitting is smaller than previously suggested but is compatible with the value obtained from re-analysis of the Rayfield-Reif experiment. All of the impurities have significantly higher binding energies to vortex lines below 1 K than the available thermal energy, where the thermally assisted escape process becomes exponentially negligible. Even at higher temperatures 1.5-2.0 K, the trapping times for larger metal clusters are sufficiently long that the previously observed metal nanowire assembly in superfluid helium can take place at vortex lines. The binding energy of the electron bubble is predicted to decrease as a function of both temperature and pressure, which allows adjusting the trap depth for either permanent trapping or to allow thermally assisted escape. Finally, a new scheme for determining the trapping of impurities on vortex lines by optical absorption spectroscopy is outlined and demonstrated for He*. [ABSTRACT FROM AUTHOR]

In this study, we address the electronic properties of conducting films constituted of an array of randomly distributed few layer graphene patches and investigate on their most salient galvanometric features in the moderate and extreme disordered limit. We demonstrate that, in annealed devices, the ambipolar behaviour and the onset of Landau level quantization in high magnetic field constitute robust hallmarks of few-layer graphene films. In the strong disorder limit, however, the magnetotransport properties are best described by a variable-range hopping behaviour. A large negative magneto-conductance is observed at the charge neutrality point, in consistency with localized transport regime. [ABSTRACT FROM AUTHOR]

We experimentally demonstrated 16384-ary quadrature amplitude modulation (16384QAM) mobile fronthaul based on 3-amplitude quantization high-pass Delta-sigma Modulation (DSM) in the O band intensity-modulated direct detection (IM/DD) system. By using 3-amplitude quantized high-pass DSM, we successfully quantize the analog waveform of intermediate frequency (IF) Orthogonal Frequency Division Multiplexing (OFDM) signal into 3-Level Pulse Amplitude Modulation (PAM3) signal, and 1 GHz bandwidth 16384-QAM and 1024QAM are successful transmission in 20Gb/s IM/DD link. 0.63% Error Vector Magnitude (EVM) of 16384QAM and 0.7% EVM of 2048QAM are achieved after 25km SSMF and 50km SSMF transmission, respectively. The signal-to-noise ratio (SNR) of the retrieved OFDM signal is 43 dB, which shows that the proposed scheme can support 16384QAM mobile fronthaul network. [ABSTRACT FROM AUTHOR]

How can discrete pitches and chords emerge from the continuum of sound? Using a quantum cognition model of tonal music, we prove that the associated Schrödinger equation in Fourier space is invariant under continuous pitch transpositions. However, this symmetry is broken in the case of transpositions of chords, entailing a discrete cyclic group as transposition symmetry. Our research relates quantum mechanics with music and is consistent with music theory and seminal insights by Hermann von Helmholtz. [ABSTRACT FROM AUTHOR]

In this paper, a new high-performance lossy compression technique based on DCT is proposed. The image is partitioned into blocks of a size of NxN (where N is multiple of 2), each block is categorized whether it is high frequency (uncorrelated block) or low frequency (correlated block) according to its spatial details, this done by calculating the energy of block by taking the absolute sum of differential pulse code modulation (DPCM) differences between pixels to determine the level of correlation by using a specified threshold value. The image blocks will be scanned and converted into 1D vectors using horizontal scan order. Then, 1D-DCT is applied for each vector to produce transform coefficients. The transformed coefficients will be quantized with different quantization values according to the energy of the block. Finally, an enhanced entropy encoder technique is applied to store the quantized coefficients. To test the level of compression, the quantitative measures of the peak signal-to-noise ratio (PSNR) and compression ratio (CR) is used to ensure the effectiveness of the suggested system. The PSNR values of the reconstructed images are taken between the intermediate range from 28dB to 40dB, the best attained compression gain on standard Lena image has been increased to be around (96.60 %). Also, the results were compared to those of the standard JPEG system utilized in the “ACDSee Ultimate 2020” software to evaluate the performance of the proposed system. [ABSTRACT FROM AUTHOR]

Graphene and carbon nanotubes are materials with large potentials for applications in flexible electronics. Such devices require a high level of sustainable strain and an understanding of the materials electrical properties under strain. Using supercell theory in conjunction with a comprehensive molecular mechanics model, the full band phonon dispersion of carbon nanotubes under uniaxial strain is studied. The results suggest an overall phonon softening and open up the possibility of phonon quantization tuning with uniaxial strain. The change in phonon quantization and the resulting increase in electron-phonon and phonon-phonon scattering rates offer further explanation and theoretical basis to the experimental observation of electrical properties degradation for carbon nanotubes under uniaxial strain. [ABSTRACT FROM AUTHOR]

We present mixed quantum classical calculations of the proton transfer (PT) reaction rates represented by a double well system coupled to a dissipative bath. The rate constants are calculated within the so called nontraditional view of the PT reaction, where the proton motion is quantized and the solvent polarization is used as the reaction coordinate. Quantization of the proton degree of freedom results in a problem of non-adiabatic dynamics. By employing the reactive flux formulation of the rate constant, the initial sampling starts from the transition state defined using the collective reaction coordinate. Dynamics of the collective reaction coordinate is treated classically as over damped diffusive motion, for which the equation of motion can be derived using the path integral, or the mixed quantum classical Liouville equation methods. The calculated mixed quantum classical rate constants agree well with the results from the numerically exact hierarchical equation of motion approach for a broad range of model parameters. Moreover, we are able to obtain contributions from each vibrational state to the total reaction rate, which helps to understand the reaction mechanism from the deep tunneling to over the barrier regimes. The numerical results are also compared with those from existing approximate theories based on calculations of the non-adiabatic transmission coefficients. It is found that the two-surface Landau-Zener formula works well in calculating the transmission coefficients in the deep tunneling regime, where the crossing point between the two lowest vibrational states dominates the total reaction rate. When multiple vibrational levels are involved, including additional crossing points on the free energy surfaces is important to obtain the correct reaction rate using the Landau-Zener formula. [ABSTRACT FROM AUTHOR]

In this paper, we extend the previously introduced Post-Quantization Constraints (PQC) procedure [G. Guillon, T. Zeng, and P.-N. Roy, J. Chem. Phys. 138, 184101 (2013)] to construct approximate propagators and energy estimators for different rigid body systems, namely, the spherical, symmetric, and asymmetric tops. These propagators are for use in Path Integral simulations. A thorough discussion of the underlying geometrical concepts is given. Furthermore, a detailed analysis of the convergence properties of the density as well as the energy estimators towards their exact counterparts is presented along with illustrative numerical examples. The Post-Quantization Constraints approach can yield converged results and is a practical alternative to so-called sum over states techniques, where one has to expand the propagator as a sum over a complete set of rotational stationary states [as in E. G. Noya, C. Vega, and C. McBride, J. Chem. Phys. 134, 054117 (2011)] because of its modest memory requirements. [ABSTRACT FROM AUTHOR]

It is standardly claimed in loop quantum gravity (LQG) that spacetime both disappears, fundamentally, and emerges from spin-networks in the low energy regime. In this paper, I critically explore these claims and develop a variety of substantival and relational interpretations of LQG for which these claims are false. According to most of the interpretations I consider, including the "received interpretation", it is in fact false that spacetime emerges from spin-networks. In the process of supporting these claims, I also explain why spacetime is thought to be missing from the theory's fundamental ontology and demonstrate how this conclusion depends on our interpretation of the theory. In fact, I will argue that for a variety of interpretations spacetime survives quantization just as the electromagnetic field survives quantization. The upshot of the following analysis is a much needed clarification of the ontology of LQG and how it relates, or fails to relate, to the spacetime of general relativity. • Explicate the formal structure of LQG with an eye towards its ontology. • Explain why spacetime is thought to go missing from the theory's fundamental ontology. • Dispel common misconceptions about the status of the manifold in LQG. • Provide a series of novel and ontologically consistent interpretations of LQG. • Spacetime fails to emerge either because spacetime does not disappear or because there are no spin-networks. [ABSTRACT FROM AUTHOR]

We study the stochastic cubic nonlinear Schrödinger equation (SNLS) with an additive noise on the one-dimensional torus. In particular, we prove local well-posedness of the (renormalized) SNLS when the noise is almost space–time white noise. We also discuss a notion of criticality in this stochastic context, comparing the situation with the stochastic cubic heat equation (also known as the stochastic quantization equation). [ABSTRACT FROM AUTHOR]

The problem of time in the quantization of gravity arises from the fact that time in Schrödinger's equation is a parameter. This sets time apart from the spatial coordinates, represented by operators in quantum mechanics (QM). Thus "time" in QM and "time" in general relativity (GR) are seen as mutually incompatible notions. The introduction of a dynamical time operator in relativistic quantum mechanics (RQM), that follows from the canonical quantization of special relativity and that in the Heisenberg picture is also a function of the parameter t (identified as the laboratory time), prompts to examine whether it can help to solve the disfunction referred to above. In particular, its application to the conditional interpretation of time in the canonical quantization approach to quantum gravity is developed. [ABSTRACT FROM AUTHOR]

With the advent of massive MIMO and mmWave, Antenna selection is the new frontier in hybrid beamforming employed in 5G base stations. Tele-operators are reworking on the components while upgrading to 5G where the antenna is a last-mile device. The burden on the physical layer not only demands smart and adaptive antennas but also an intelligent antenna selection mechanism to reduce power consumption and improve system capacity while degrading the hardware cost and complexity. This work focuses on reducing the power consumption and finding the optimal number of RF chains for a given millimeter wave massive MIMO system. At first, we investigate the power scaling method for both perfect Channel State Information (CSI) and imperfect CSI where the power is reduced by 1/Nr and 1/√Nr respectively. We further propose to reduce the power consumption by emphasizing on the subdued resolution of Analog-to-Digital Converters (ADCs) with quantization awareness. The proposed algorithm selects the optimal number of antenna elements based on the resolution of ADCs without compromising on the quality of reception. The performance of the proposed algorithm shows significant improvement when compared with conventional and random antenna selection methods. [ABSTRACT FROM AUTHOR]

Kohn and Luttinger [Phys. Rev. 118, 41 (1960)] showed that the conventional finite-temperature extension of the second-order many-body perturbation theory had the incorrect zero-temperature limit in metals and, on this basis, argued that the theory was incorrect. We show that this inconsistency arises from the noninclusion of the temperature effect in the energies of the zeroth-order eigenstates of the perturbation theory, which causes not only the Kohn-Luttinger conundrum but also another inconsistency with the zero-temperature many-body perturbation theory, namely, the different rates of divergence of the correlation energy in a homogeneous electron gas (HEG). We propose a renormalized many-body perturbation theory derivable from the finite-temperature extension of the normal-ordered second quantization applied to the denominators of the energy expression, which involves the energies of the zeroth-order states, as well as to the numerators. The renormalized theory is shown to have the correct zero-temperature limit and the same rate of divergence in a HEG as the zero-temperature counterpart, and is, therefore, the correct finite-temperature many-body perturbation theory. [ABSTRACT FROM AUTHOR]

We present a formulation of quantized Hamiltonian dynamics (QHD) using variables that arise naturally from the Heisenberg equation of motion. The QHD equations are obtained and solved either directly in terms of these generalized variables, or by employing a wavefunction ansatz. The approach avoids a Taylor expansion and other approximations to the potential, leading to more stable dynamics and a higher precision of the calculated quantities. The proposed formulation is also amenable to for analytic and numerical implementations, thus facilitating its use in molecular dynamics simulation. [ABSTRACT FROM AUTHOR]

A new classical model for the general second-quantized many-electron Hamiltonian in Cartesian coordinates and momenta is presented; this makes semiclassical (SC) calculations using an initial value representation (IVR) more useful than the classical Hamiltonian in action-angle variables given earlier by Miller and White [J. Chem. Phys. 84, 5059-5066 (1986)]. If only 1-electron terms are included in this Hamiltonian, the classical equations of motion for the Cartesian variables are linear, and the SC-IVR gives exact results for the propagator (and thus for transition probabilities, the energy spectrum, etc.), as confirmed by analytic proof and numerical calculations. Though this new Hamiltonian is not exact when 2-electron interactions are included, we observe good results for the SC-IVR transition probabilities for times that are not too long. Test calculations, for example, show that the SC-IVR is accurate for times long enough to obtain good result for the eigenvalue spectrum (i.e., the energy levels of the electronic system). [ABSTRACT FROM AUTHOR]

Si and Ge nanocrystals (nc-Si and nc-Ge) with average sizes in the range of 6 and 6.3 nm, embedded in SiO2/GeO2 matrix, were fabricated and their acoustic-phonon vibrational properties were investigated using two different approaches by considering the elastic continuum model and fixed boundary condition. The breathing and quadrupolar modes are found in the spectra. The presence of medium significantly affects the phonon peaks and results into the broadening of the modes which is more in the case of elastically similar materials. The phonon line width is found to depend inversely on the size, similar to that reported experimentally. Using first and second-order optical modes, the electron-phonon coupling strengths have been estimated. The result shows that e-p coupling strength is more in the case of elastically dissimilar materials. [ABSTRACT FROM AUTHOR]

We demonstrate theoretically that it may be possible to encode states of a multi-qubit system into the progression of quantized motional/vibrational levels of an ion trapped in a weakly anharmonic potential. Control over such register of quantum information is achieved by applying oscillatory radio-frequency fields shaped optimally for excitation of the desired state-to-state transitions. Anharmonicity of the vibrational spectrum plays a key role in this approach to the control and quantum computation, since it allows resolving different state-to-state transitions and addressing them selectively. Optimal control theory is used to derive pulses for implementing the four-qubit version of Shor's algorithm in a single step. Accuracy of the qubit-state transformations, reached in the numerical simulations, is around 0.999. Very detailed insight is obtained by analysis of the time-evolution of state populations and by spectral analysis of the optimized pulse. [ABSTRACT FROM AUTHOR]

This paper discusses about the scatter of the intensity of vibration signals of paper prints and analyses their mechanical parameters applying the theory of covariance functions. It is an important practical problem, before starting printing process of colour prints, expecting the correct position of fixed raster points, to adjust the paper sheet tension between printing machine sections. The results of measuring the intensity of vibration signals at the fixed points were presented on a time scale in the form of arrays (matrices). The estimates of cross-covariance functions between digital arrays result in measuring the intensity of vibrations, and the estimates of auto-covariance functions of single arrays were calculated upon changing the quantization interval on the time scale. Application of normed auto-covariance and crosscovariance functions enables reduction of preprinting experimental measurements, which saves time (what is actual for industry). Tension force depends on the mechanical properties of the paper sheet and print. These characteristics depend on paper type, layers of printing colors and positioning of the coverage. In the calculation, the software Matlab 7 in batch statement environment was applied.

The propagation characteristics of solitary wave in a degenerate plasma in the presence of Landau-quantised magnetic field and heavy negative ion are studied. The nature of solitary wave in such plasma under the influence of magnetic quantisation and the concentration of both electrons and negative ions, as well as in the presence of degenerate temperature, are studied with the help of a time-independent analytical scheme of the solution of Zakharov–Kuznetsov equation. The electron density, as well as the magnetic quantisation parameter, has an outstanding effect on the features of solitary wave proliferation in such plasma. Interestingly, for any fixed electron density, the magnetic quantisation parameter has an equal control on the maximum height and dispersive properties of the solitary wave. Toward higher temperatures and higher magnetic fields, the width of the solitary wave decreases. For a lower magnetic field, the maximum amplitude of the solitary wave decreases rapidly at higher values of degenerate temperature and negative ion concentration; however, at a lower value of degenerate temperature, the maximum amplitude increases with increasing negative ion concentration. [ABSTRACT FROM AUTHOR]

We give a brief overview how to couple general relativity to the Standard Model of elementary particles, within the higher gauge theory framework, suitable for the spinfoam quantization procedure. We begin by providing a short review of all relevant mathematical concepts, most notably the idea of a categorical ladder, 3-groups and generalized parallel transport. Then, we give an explicit construction of the algebraic structure which describes the full Standard Model coupled to Einstein-Cartan gravity, along with the classical action, written in the form suitable for the spinfoam quantization procedure. We emphasize the usefulness of the 3-group concept as a superior tool to describe gauge symmetry, compared to an ordinary Lie group, as well as the possibility to employ this new structure to classify matter fields and study their spectrum, including the origin of fermion families. [ABSTRACT FROM AUTHOR]