Quantum Dispersion Research Articles

Effective description of a quantum particle constrained to a catenoid

We describe a quantum particle constrained on a catenoid, employing an effective description of quantum mechanics based on expected values of observables and quantum dispersions. We obtain semiclassical trajectories for particles, displaying general features of the quantum behavior; most interestingly, particles present tunneling through the throat of the catenoid, a characteristic having important physical applications.

Photon statistics and quantum phase distribution for coherent optical links in the presence of phase noise from both the laser source and the RF oscillator, and dispersion

A model of photon statistics and quantum phase distribution is analyzed for coherent optical communication links in the presence of quantum phase noise, dispersion and phase noise of the radio-frequency (RF) oscillator using an in-line optical amplifier. The quantum analysis of a dual drive Mach–Zehnder modulator and the quantum transfer function for an optical field mode across an in-line amplifier is performed by taking into account both the quantum and the classical phase noises. The resulting photon statistics are compared with the semiclassical model. We analyze the quantum phase distribution by considering the Wigner quasiprobability distribution for a coherent optical link. Here, we investigate the broadening of the quantum phase distribution due to quantum phase noise of the laser, the dispersive optical fiber, the phase noise of the RF oscillator and the inevitable noise coefficient of the optical amplifier for arbitrary amplified spontaneous emission (ASE) field modes. We analytically investigate the quantum analog to the bit error rate (BER) as a function of the laser’s linewidth, the linewidth of the RF oscillator and chromatic dispersion. The results of quantum models are compared with the semiclassical model. Quantum treatment of both the BER and variance is found to agree with prior results for a single-mode ASE field in the absence of phase noise but deviate when the effect of phase noise is considered. Including phase noise effects in the amplitude in the semiclassical treatment of the BER yields a new semiclassical expression that agrees with quantum expressions of machine precision for single-mode ASE fields.

Anisotropic motion of an electric dipole in a photon gas near a flat conducting boundary

The quantum Brownian motion of a single neutral particle with nonzero electric dipole moment placed in a photon gas at fixed temperature and close to a conducting wall is here examined. The interaction of the particle with the photon field leads to quantum dispersions of its linear and angular momenta, whose magnitudes depend on the temperature, distance to the wall, and also on the dipole moment characteristics. It is shown that for typical experimental parameters the amount of energy held by the dipole rotation is expressively larger than the one related to the center of mass translation. Furthermore, the particle kinetic energy in presence of a thermal bath can decrease if the wall is added to the system, representing a novel quantum cooling effect where the work done by the quantum vacuum extracts energy from the particle. Finally, possible observable consequences are discussed.

Effect of Quantum Dots Dispersion on the Structural, Optical, and Thermal Properties of Liquid Crystal System

Liquid crystal-quantum dot (LC-QD) composites are promising new materials for a number of applications in displays, energy harvesting, and photonics. In the present work, quantum dispersion in the mixture of LCs of cholesteric and nematic phases is reported. The combination of two LCs, namely Cholesteryl Palmitate (cholesteric 97%) and 4′-Pentyl-4-biphenylcarbonitrile (nematic, 98%), were used in equal proportion while CdS quantum dots were added in this mixture. The thermal, optical, and structural properties of this new LC-QD composite system were analyzed using differential scanning calorimetry (DSC), ultra-violet visible (UV-VIS) spectroscopy, Fabry-Perot scattering studies (FPSS), and Fourier transform infrared (FTIR) spectroscopy. Structural studies indicate that the QDs are uniformly dispersed inside the LC matrix rather than on the surface area. It was observed that quantum dot dispersion increases the strength of the LC mixture. It also changes the phase behavior of the LC mixture affecting the overall performance of LC-QD composite systems. The present findings would be very helpful for the design of the display and photonic devices with an improved optical response.

Tomography in loop quantum cosmology

We analyze the tomographic representation for the Friedmann–Robertson–Walker (FRW) model within the Loop Quantum Cosmology framework. We focus on the Wigner quasi-probability distributions associated with Gaussian and Schrödinger cat states, and then, by applying a Radon integral transform for those Wigner functions, we are able to obtain the symplectic tomograms which define measurable probability distributions that fully characterize the quantum model of our interest. By appropriately introducing the quantum dispersion for a rotated and squeezed quadrature operator in terms of the position and momentum, we efficiently interpret the properties of such tomograms, being consequent with Heisenberg’s uncertainty principle. We also obtain, by means of the dual tomographic symbols, the expectation value for the volume operator, which coincides with the values reported in the literature. We expect that our findings result interesting as the introduced tomographic representation may be further benefited from the well-developed measure techniques in the areas of Quantum optics and Quantum information theory.

THE DYNAMICS OF A PARTICLE IN A TIGHT-BINDING LATTICE UNDER A COULOMB POTENTIAL

We study the tight-binding dynamics of a charged particle by the hopping mechanism in a one - dimensional lattice under the action of a Coulomb potential due to another fixed particle (impurity). The quantum dynamics is studied using the pseudo-spectral method applied to a tight-binding Hamiltonian with nearest neighbors interactions. The resulting expected values for position and velocity are then compared with those deduced by the semi-classical method invoking the effective potential in the lattice. These results are notably similar when the particle is located far from the impurity position since the Coulomb field is approximately uniform, while when near to the impurity the results are different due to the quantum dispersion of the particle’s wavepacket under a highly inhomogeneous field. Interestingly, however, the quantum and semiclassical results coincide in the continuous regime (parabolic dispersion relation) due to the transmission of the particle’s wavepacket through the impurity.

The calculation for quantized valence subband structure of zinc-blende GaN heterojunction quantum well based on k·p method

A quantized valence subband model is proposed to study the energy dispersion of zinc-blende GaN P-channel heterojunction quantum well under arbitrary stress. Anisotropic band structures of bulk GaN and GaN in quantum well under field confinement effect are computed using a six-band stress-dependent k·p Hamiltonian and self-consistently Poisson–Schrödinger equation. A comprehensive study of microscopic relationship between stress and hole effective mass in GaN quantum well has been performed according to the stress effects on quantized valence subband. Simulation results show that uniaxial compression can be considered as the most effective stress in the hole effective mass reduction of zinc-blende GaN heterojunction.

Interfacial electron-phonon coupling and quantum confinement in ultrathin Yb films on graphite

Interfacial electron-phonon coupling in ultrathin films has attracted much interest recently. Here, by combining angle-resolved photoemission spectroscopy and scanning tunneling microscopy, we report quantized electronic states and strong interfacial electron-phonon coupling in ultrathin Yb films on graphite. We observed clear kinks in the energy-momentum dispersion of quantum well states, and the kink positions agree well with the energies of optical phonons of graphite. The extracted coupling strength $\ensuremath{\lambda}$ is largest for the thinnest film with a preferred (``magic'') thickness of four monolayers and exhibits a strong band dependence, which can be qualitatively accounted for by a simple model. The interfacial electron-phonon coupling also gives rise to characteristic steplike structures in the $dI/dV$ spectra, implying dominant coupling with the phonons with zero in-plane momentum. A Lifshitz transition occurs at higher coverage, where quantum well states derived mainly from $5d$ electrons dominate near the Fermi level and possess large effective mass (up to $\ensuremath{\sim}19\phantom{\rule{0.28em}{0ex}}{m}_{e}$). Our results highlight the potentially important role of interfacial electron-phonon interaction for ultrathin films and provide spectroscopic insight to understand this cross-interface fermion-boson interaction.

Dynamics of primordial fields in quantum cosmological spacetimes

Quantum cosmological models are commonly described by means of semiclassical approximations in which a smooth evolution of the expectation values of elementary geometry operators replaces the classical and singular dynamics. The advantage of such descriptions is that they are relatively simple and display the classical behavior for large universes. However, they may smooth out an important inner structure and to include it a more detailed treatment is needed. The purpose of the present work is to investigate quantum uncertainty in the basic background variables and its influence on primordial gravitational waves. To this end we quantize a model of the Friedmann-Lemaitre-Robertson-Walker universe filled with a linear barotropic cosmological fluid and with gravitational waves. We carefully derive the dynamical equations for the perturbations in quantum spacetime. The quantization yields an equation of motion for the Fourier modes of gravitational radiation, which is a quantum extension to the usual parametric oscillator equation for gravitational waves propagating in an expanding universe. The two quantum effects from the cosmological background that enter the enhanced equation of motion are (i) a repulsive potential resolving the big bang singularity and replacing it with a big bounce and (ii) uncertainties in the numerical values for the background spacetime dynamical variables. First we study the former effect and its consequences for the primordial amplitude spectrum and carefully discuss the relation between the bounce scale and the physical predictions of the model. Next we investigate the latter effect, in particular the extent to which it may affect the primordial amplitude of gravitational waves. Making use of the WKB approximation we find an analytical formula for the amplitude spectrum as a function of the quantum dispersion of the background spacetime.

Effective quantum tunneling from a semiclassical momentous approach

In this work, we study the quantum tunnel effect through a potential barrier within a semiclassical formulation of quantum mechanics based on expectation values of configuration variables and quantum dispersions as dynamical variables. The evolution of the system is given in terms of a dynamical system for which we are able to determine numerical effective trajectories for individual particles, similar to the Bohmian description of quantum mechanics. We obtain a complete description of the possible trajectories of the system, finding semiclassical reflected, tunneled and confined paths due to the appearance of an effective time-dependent potential.

Dark energy as a large scale quantum gravitational phenomenon

In our recently proposed quantum theory of gravity, the universe is made of ‘atoms‘” of space-time-matter (STM). Planck scale foam is composed of STM atoms with Planck length as their associated Compton wave-length. The quantum dispersion and accompanying spontaneous localization of these STM atoms amounts to a cancellation of the enormous curvature on the Planck length scale. However, an effective dark energy term arises in Einstein equations, of the order required by current observations on cosmological scales. This happens if we propose an extremely light particle having a mass of about [Formula: see text], forty-two orders of magnitude lighter than the proton. The holographic principle suggests there are about [Formula: see text] such particles in the observed universe. Their net effect on space-time geometry is equivalent to dark energy, this being a low energy quantum gravitational phenomenon. In this sense, the observed dark energy constitutes evidence for quantum gravity. We then invoke Dirac’s large number hypothesis to also propose a dark matter candidate having a mass halfway (on the logarithmic scale) between the proton and the dark energy particle, i.e. about [Formula: see text].

Classical and Quantum Dispersion Relations

It is showed that, in general, classical and quantum dispersion relations are different due to the presence of the Bohm potential. There are exact particular solutions of the quantum (wave) theory which obey the classical dispersion relation, but they differ in the general case. The dispersion relations may also coincide when additional assumptions are made, such as WKB or eikonal approximations, for instance. This general result also holds for non–quantum wave equations derived from classical counterparts, such as in ray and wave optics, for instance. Explicit examples are given for covariant scalar, vectorial and tensorial fields in flat and curved spacetimes.

Dark energy effects in the Schrödinger-Newton approach

The Schr\"odinger-Newton equation is a proposed model to explain the localization of macroscopic particles by suppressing quantum dispersion with the particle's own gravitational attraction. On cosmic scales, however, dark energy also acts repulsively, as witnessed by the accelerating rate of universal expansion. Here, we introduce the effects of dark energy in the form of a cosmological constant $\Lambda$, that drives the late-time acceleration of the Universe, into the Schr\"odinger-Newton approach. We then ask in which regime dark energy dominates both canonical quantum diffusion and gravitational self-attraction. It turns out that this happens for sufficiently delocalized objects with an arbitrary mass and that there exists a minimal delocalization width of about $67$ m. While extremely macroscopic from a quantum perspective, the value is in principle accessible to laboratories on Earth. Hence, we analyze, numerically, how the dynamics of an initially spherical Gaussian wave packet is modified in the presence of $\Lambda > 0$. A notable feature is the gravitational collapse of part of the wave packet, in the core region close to the center of mass, accompanied by the accelerated expansion of the more distant shell surrounding it. The order of magnitude of the distance separating collapse from expansion matches analytical estimates of the classical turnaround radius for a spherically symmetric body in the presence of dark energy. However, the time required to observe these modifications is astronomical. They can potentially be measured only in physical systems simulating a high effective cosmological constant, or, possibly, via their effects on the inflationary universe.

Structural localization in the classical and quantum Fermi-Pasta-Ulam model.

We study the statistics and short-time dynamics of the classical and the quantum Fermi-Pasta-Ulam chain in the thermal equilibrium. We analyze the distributions of single-particle configurations by integrating out the rest of the system. At low temperatures, we observe a systematic increase in the mobility of the chain when transitioning from classical to quantum mechanics due to zero-point energy effects. We analyze the consequences of quantum dispersion on the dynamics at short times of configurational correlation functions.

Quark-flavor dependence of the shear viscosity in a quasiparticle model

We study the temperature dependence of the shear viscosity to entropy density ratio in pure Yang-Mills theory and in QCD with light and strange quarks within kinetic theory in the relaxation time approximation. As effective degrees of freedom in a deconfined phase we consider quasiparticle excitations with quark and gluon quantum numbers and dispersion relations that depend explicitly on the temperature. The quasiparticle relaxation times are obtained by computing the microscopic two-body scattering amplitudes for the elementary scatterings among the quasiparticles. For pure Yang-Mills theory, we show that the shear viscosity to entropy density ratio exhibits a characteristic nonmonotonicity with a minimum at the first-order phase transition. In the presence of dynamical quarks, the ratio smoothens while still exhibiting a minimum near confinement. Furthermore, there is a significant increase of the shear viscosity to entropy density ratio in QCD resulting from the quark contributions. This observation differs from previously reported estimates based on functional methods but is in line with perturbative QCD expectations at higher temperatures.

The quantum transmission characteristic of one-dimensional photonic crystals

In this paper, we have given the quantum transfer matrix, quantum dispersion relation, quantum transmissivity and reflectivity of one-dimensional photonic crystals with the quantum theory of photon. We have studied the quantum transmission characteristic of different structure one-dimensional photonic crystals, which include mirror and nonmirror structures, with and without defect, and the defects are active and inactive media. On that basis, we compared the dispersion relation, transmissivity and reflectivity of quantum with classical for one-dimensional photonic crystals, and found they are identical, which indicate the quantum theory approach of photonic crystals is true, it can further study the quantum topological property of photonic crystals, such as quantum Zak phase, Chern number and quantum edge state and so on.

Research on one-dimensional photonic crystals with quantum theory approach

In this paper, we have proposed the spinor wave equation of free and non-free photon, and given the quantum transfer matrix, dispersion relation, quantum transmissivity and quantum reflectivity of one-dimensional photonic crystals with the quantum theory of photon. On that basis, we have studied the effect of different incident angle, refractive index and thickness of medium on quantum and classical dispersion relation, transmissivity and reflectivity. We have found the results of quantum and classical are identical, which indicate the quantum theory approach for photonic crystals is reasonable and true, it will be studied the quantum edge state, quantum Zak phase and Chern number of the quantum topological property for photonic crystals.

Quantum Cosmology in the Light of Quantum Mechanics

There is a formal analogy between the evolution of the universe, when it is seen as a trajectory in the minisuperspace, and the worldline followed by a test particle in a curved spacetime. The analogy can be extended to the quantum realm, where the trajectories are transformed into wave packets that give us the probability of finding the universe or the particle in a given point of their respective spaces: the spacetime in the case of the particle and the minisuperspace in the case of the universe. The wave function of the spacetime and the matter fields, all together, can then be seen as a super-field that propagates in the minisuperspace and the so-called third quantisation procedure can be applied in a parallel way as the second quantisation procedure is performed with a matter field that propagates in the spacetime. The super-field can thus be interpreted as made up of universes propagating, i.e., evolving, in the minisuperspace. The analogy can also be used in the opposite direction. The way in which the semiclassical state of the universe is obtained in quantum cosmology allows us to obtain, from the quantum state of a field that propagates in the spacetime, the geodesics of the underlying spacetime as well as their quantum uncertainties or dispersions. This might settle a new starting point for a different quantisation of the spacetime.

Solitons in normal Fermi liquid

To be based on the new quantum kinetic equation of Fermi particles, which recently was derived by N.L. Tsintsadze and L.N. Tsintsadze, a general quantum dispersion equation for almost ideal Fermi gas is derived and studied for some interesting cases. Here we consider only pair interactions between particles and we used energy expression derived by V.M. Galitski in the ordinary perturbation theory, which involves only the scattering amplitude. New effect that we have shown is that novel quantum term (Madelung term) in the kinetic equation leads to the formation of rarefaction solitary waves in neutral Fermi liquid. Furthermore, attraction and repulsion between particles have tendency to change rarefaction solitary wave speed and shape: Attraction between particles increases rarefaction soliton speed and amplitude, repulsion decreases soliton speed and amplitude.

Quantum effects on dislocation motion from ring-polymer molecular dynamics

Quantum motion of atoms known as zero-point vibration was recently proposed to explain a long-standing discrepancy between theoretically computed and experimentally measured low-temperature plastic strength of iron and possibly other metals with high atomic masses. This finding challenges the traditional notion that quantum motion of atoms is relatively unimportant in solids comprised of heavy atoms. Here we report quantum dynamic simulations of quantum effects on dislocation motion within the exact formalism of Ring-Polymer Molecular Dynamics (RPMD). To extend the reach of quantum atomistic simulations to length and time scales relevant for extended defects in materials, we implemented RPMD in the open-source code LAMMPS thus making the RPMD method widely available to the community. We use our RPMD/LAMMPS approach for direct calculations of dislocation mobility and its effects on the yield strength of α-iron. Our simulation results establish that quantum effects are noticeable at temperatures below 50 K but account for only a modest (≈13% at T = 0 K) overall reduction in the Peierls barrier, at variance with the factor of two reduction predicted earlier based on the more approximate framework of harmonic transition state theory. Our results confirm that zero-point vibrations provide ample additional agitation for atomic motion that increases with decreasing temperature, however its enhancing effect on dislocation mobility is largely offset by an increase in the effective atom size, an effect known as quantum dispersion that has not been accounted for in the previous calculations.