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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]

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]

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]

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]

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]

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]

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]

We study Markovian stochastic motion on a graph with finite number of nodes and adiabatically periodically driven transition rates. We show that, under general conditions, the quantized currents that appear at low temperatures are a manifestation of topological invariants in the counting statistics of currents. This observation provides an approach for classification of topological properties of the counting statistics, as well as for extensions of the phenomenon of the robust quantization of currents at low temperatures to the properties of the counting statistics which persist to finite temperatures. [ABSTRACT FROM AUTHOR]

This article studies Markovian stochastic motion of a particle on a graph with finite number of nodes and periodically time-dependent transition rates that satisfy the detailed balance condition at any time. We show that under general conditions, the currents in the system on average become quantized or fractionally quantized for adiabatic driving at sufficiently low temperature. We develop the quantitative theory of this quantization and interpret it in terms of topological invariants. By implementing the celebrated Kirchhoff theorem we derive a general and explicit formula for the average generated current that plays a role of an efficient tool for treating the current quantization effects. [ABSTRACT FROM AUTHOR]

Shot noise, which accompanies the emergence of the quantization nature (discreteness) of electrons, indicates dynamic fluctuations in electrical current and further reveals underlying operations in mesoscopic applications. This work presents a multichannel junction device with which to study the shot noise of coupled-channel transports as in normal nanocircuits, and it describes the theoretical algorithms. The numerical results show that, in contrast to the indistinguishable results of average current on direct-current measurements, the shot noise related to a dynamic current definitely exhibits significant differences among devices with diverse multichannel set-ups and presents super-Poissonian behaviors associated with the splitting of tunneling states. [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]

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]

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]

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]

The well-known trigonometric Scarf potential is generalized by adding a sinusoidal term and then treated using the Asymptotic Iteration Method (AIM) and the Tridiagonal Representation Approach (TRA). The energy spectrum of the associated bound states is computed. For the AIM, we have improved convergence of the quantization condition that terminates the iterations asymptotically. This is accomplished by looking for the range of initial values of the space variable in the terminating condition that produces stable results (plateau of convergence). We have shown that with increasing iteration, this plateau of convergence grows up rapidly to an optimal iteration number and then shrinks slowly to a point. The value of this point (or points) may depend on the physical parameters. The numerical results have been compared favorably with those resulting from the TRA. [ABSTRACT FROM AUTHOR]

In addition to stable pulse generation, passively mode-locked fiber lasers can easily run into an unstable regime of multipulse mode-locking. The birth and dynamic behaviors of multipulse mode-locking so far have rarely been experimentally explored, particularly in the spectral domain. In this letter, several kinds of multipulse spectral-temporal dynamics of a passively mode-locked fiber laser are observed in a single-shot manner, e.g., energy quantization, self-phase modulation spectral broadening, wavelength shifting, spectral interfering, and ultraweak pulse interaction. This study is enabled by the high temporal resolution of spectral-temporal technology, i.e., 50 ps in the time domain and tens of nanoseconds in the spectral domain. Moreover, a wide observing time span of our spectral-temporal analyzing system, i.e., >6 ms—equivalent to 100 000 round trips, enables evolutionary characterization of individual pulses. The results will have a significant impact on optimizing the performance of mode-locked fiber lasers and understanding the nonlinear physics in a dissipative system. [ABSTRACT FROM AUTHOR]

We analyze the dynamics of the AdSN+1 particle realized on the coset SO(2,N)/SO (1,N). Hamiltonian reduction provides the physical phase space in terms of the coadjoint orbit obtained by boosting a timelike element of so(2,N). We show equivalence of this approach to geometric quantization and to the SO(N) covariant oscillator description, for which the boost generators entail a complicated operator ordering. As an alternative scheme, we introduce dual oscillator variables and derive their algebra at the classical and the quantum levels. This simplifies the calculations of the commutators for the boost generators and leads to unitary irreducible representations of so(2,N) for all admissible values of the mass parameter. We furthermore discuss an SO(N) covariant supersymmetric extension of the oscillator quantization, with its realization for superparticles in AdS2 and AdS3 given by recent works. [ABSTRACT FROM AUTHOR]

In the present work, we have investigated the effect of trapping as a microscopic phenomenon on the formation of solitary structures in the presence of a quantizing magnetic field in an electronpositron-ion (e-p-i) plasma having degenerate electrons and positrons, whereas ions are taken to be classical and cold. We have found that positron concentration, quantizing magnetic field, and finite electron temperature effects not only affect the linear dispersion characteristics of the electrostatic waves under consideration but also have a significant bearing on the propagation of solitary structures in the nonlinear regime. Importantly, the system under consideration has been found to allow the formation of compressive solitary structures only. The work presented here may be beneficial to understand the propagation of nonlinear electrostatic structures in dense astrophysical environments and in intense-laser plasma interactions. [ABSTRACT FROM AUTHOR]

The quantization of a pair of commuting differential operators is a pair of noncommuting differential operators. Both at the classical and quantum levels, the flows of the Kadomtsev-Petviashvili (KP) hierarchy are defined and further one can consider switching, up to a sign, the ordering of the operators. We discuss the interaction of these operations with the quantization. [ABSTRACT FROM AUTHOR]

We introduce exactly solvable quantum parametric oscillators, which are generalizations of the quantum problems related with the classical orthogonal polynomials of Hermite, Laguerre, and Jacobi type, introduced in the work of Büyüka, sık et al. [J. Math. Phys. 50, 072102 (2009)]. Quantization of these models with specific damping, frequency, and external forces is obtained using the Wei-Norman Lie algebraic approach. This determines the evolution operator exactly in terms of two linearly independent homogeneous solutions and a particular solution of the corresponding classical equation of motion. Then, time-evolution of wave functions and coherent states are found explicitly. Probability densities, expectation values, and uncertainty relations are evaluated and their properties are investigated under the influence of the external terms. [ABSTRACT FROM AUTHOR]

In this article, the third of three, we analyse how the Weyl quantisation for compact Lie groups presented in the second article of this series fits with the projective-phase space structure of loop quantum gravity-type models. Thus, the proposedWeyl quantisation may serve as the main mathematical tool to implement the program of space adiabatic perturbation theory in such models. As we already argued in our first article, space adiabatic perturbation theory offers an ideal framework to overcome the obstacles that hinder the direct implementation of the conventional Born-Oppenheimer approach in the canonical formulation of loop quantum gravity. [ABSTRACT FROM AUTHOR]

We revisit the subject of perturbatively quantizing the nonlinear sigma model in two dimensions from a rigorous, mathematical point of view. Our main contribution is to make precise the cohomological problem of eliminating potential anomalies that may arise when trying to preserve symmetries under quantization. The symmetries we consider are twofold: (i) diffeomorphism covariance for a general target manifold; (ii) a transitive group of isometries when the target manifold is a homogeneous space. We show that there are no anomalies in case (i) and that (ii) is also anomaly-free under additional assumptions on the target homogeneous space, in agreement with the work of Friedan. We carry out some explicit computations for the O(N)-model. Finally, we show how a suitable notion of the renormalization group establishes the Ricci flow as the one loop renormalization group flow of the nonlinear sigma model. [ABSTRACT FROM AUTHOR]

The Weyl quantization of classical observables on the torus (as phase space) without regularity assumptions is explicitly computed. The equivalence class of symbols yielding the same Weyl operator is characterized. The Heisenberg equation for the dynamics of general quantum observables is written through the Moyal brackets on the torus and the support of theWigner transform is characterized. Finally, a dequantization procedure is introduced that applies, for instance, to the Pauli matrices. As a result we obtain the corresponding classical symbols. [ABSTRACT FROM AUTHOR]