Entropic Corrections to Coulomb’s Law

Two well-known quantum corrections to the area law have been introduced in the literatures, namely, logarithmic and power-law corrections. Logarithmic corrections, arises from loop quantum gravity due to thermal equilibrium fluctuations and quantum fluctuations, while, power-law correction appears in dealing with the entanglement of quantum fields in and out the horizon. Inspired by Verlinde’s argument on the entropic force, and assuming the quantum corrected relation for the entropy, we propose the entropic origin for the Coulomb’s law in this note. Also we investigate the Uehling potential as a radiative correction to Coulomb potential in 1-loop order and show that for some value of distance the entropic corrections of the Coulomb’s law is compatible with the vacuum-polarization correction in QED. So, we derive modified Coulomb’s law as well as the entropy corrected Poisson’s equation which governing the evolution of the scalar potential ϕ. Our study further supports the unification of gravity and electromagnetic interactions based on the holographic principle.     

Three Slit Experiments and the Structure of Quantum Theory

In spite of the interference manifested in the double-slit experiment, quantum theory predicts that a measure of interference defined by Sorkin and involving various outcome probabilities from an experiment with three slits, is identically zero. We adapt Sorkin’s measure into a general operational probabilistic framework for physical theories, and then study its relationship to the structure of quantum theory. In particular, we characterize the class of probabilistic theories for which the interference measure is zero as ones in which it is possible to fully determine the state of a system via specific sets of ‘two-slit’ experiments.     

Complementarity controversy in wave-particle duality revisited

On the face of some recent experiments claiming the simultaneous presence of both ‘sharp interference’ and ‘highly reliable which way information’ and some others casting light on the origin of complementarity in quantum interferometric experiments, the whole issue is reviewed on the basis of our earlier precise formulation of Bohr’s complementarity principle. It is pointed out that contradicting the principle (in this specific formulation) is impossible without contradicting quantum mechanics and a lack of general consensus regarding the origin of the mutual exclusiveness is at the root of the controversy and confusions.      

Algebraic Structure and Poisson’s Integral Theory of f(R) Cosmology

In this paper, the algebraic structure and the Poisson’s integral theory of f(R) cosmology are presented. Firstly, the Hamilton canonical equations are derived for the system. Secondly, the contravariant algebraic forms of f(R) cosmology are obtained. Thirdly, the Lie algebraic structure admitted and Poisson’s integral methods are investigated for f(R) cosmology. Further, the first integrals and solution of f(R) cosmology are given. Finally, an example is given to illustrate the results.     

Wave packet splitting and zitterbewegung in two-dimensional semiconductor structures with spin-orbit coupling

Dynamics of electron wave packets in an asymmetric quantum well in the presence of Rashba spinorbit coupling was analytically and numerically studied. Electron Green’s functions were introduced and the evolution of 1D and 2D wave packets was studied. The effect of packet splitting caused by the presence of two branches with different chiralities in the Rashba Hamiltonian spectrum and zitterbewegung, i.e., packet center’s jitter, was studied. Spatial components of the spin density were calculated. It was shown that the component of the spin density S _y in split parts of the wave packet has opposite signs, and two other spin density components oscillate in space between scattering packets.     

Theory of Atom Optics: Feynman''s Path Integral Approach

The present theory of atom optics is established mainly on the Schr?dinger equations or the matrix mechanics equation. The authors present a new theoretical formulation of atom optics: Feynman’s path integral theory. Its advantage is that one can describe the diffraction and interference of atoms passing through slits (or grating), apertures, and standing wave laser field in Earth’s gravitational field by using a type of wave function and calculation is simple. For this reason, we derive the wave functions of particles in the following configurations: single slit (and slit with the van der Waals interaction), double slit, N slit, rectangular aperture, circular aperture, the Mach-Zehnder-type interferometer, the interferometer with the Raman beams, the Sagnac effect, the Aharonov-Casher effect, the Kapitza-Dirac diffraction effect, and the Aharonov-Bohm effect. The authors give a wave function of the state of particles on the screen in abovementioned configurations. Our formulas show good agreement with present experimental measurements.     

What is Erased in the Quantum Erasure?

In this paper, we re-examine a series of gedanken welcher Weg (WW) experiments introduced by Scully, Englert and Walther that contain the essential ideas underlying the quantum eraser. For this purpose we use the Bohm model which gives a sharp picture of the behaviour of the atoms involved in these experiments. This model supports the thesis that interference disappears in such WW experiments, even though the centre of mass wave function remains coherent throughout the experiment. It also shows exactly what it means to say ‘that the interference can be restored by manipulating the WW detectors long after the atoms have passed’. It does not support Wheeler’s notion that ‘the past is undefined and undefinable without the observation (in the present)’.     

Pressure dependent mechanical and thermodynamical properties of Hg<Subscript>0.91</Subscript>Mn<Subscript>0.09</Subscript>Te semiconductor

The mechanical, thermodynamical and elastic properties of Hg_0.91Mn_0.09Te compound are calculated by formulating an effective interionic interaction potential. This potential consists of the long-range Coulomb, three body force parameter, the Hafemeister and Flygare type short-range overlap repulsion extended upto the second neighbor ions and the van der Waals (vdW) interaction. The estimated values of phase transition pressure have revealed reasonably good agreement with the available experimental data on the phase transition pressure P _t = 11.5 GPa and the vast volume discontinuity in pressure-volume (PV) phase diagram indicate the structural phase transition from zincblende (B3) to rock salt (B1) structure. Later on, the Poisson’s ratio ν, the ratio R _S/B of S (Voigt averaged shear modulus) over B (bulk modulus), elastic anisotropy parameter, elastic wave velocity, average wave velocity and Debye temperature as functions of pressure is calculated. From Poisson’s ratio and the ratio R _S/B it is inferred that Hg_0.91Mn_0.09Te is brittle in nature in both B3 phase and B1 phase. To our knowledge this is the first quantitative theoretical prediction of the pressure dependence of ductile (brittle) nature of Hg_0.91Mn_0.09Te compounds and still awaits experimental confirmations.     

A Random Surface Wave Equation for Bosonic QCD(<Emphasis Type="Italic">SU</Emphasis>(∞))

We propose a quantum surface wave functional describing the interaction between a colored SU(N _c ) membrane and a quantized Yang-Mills field. Additionally, we deduce its associated wave equation in the t’Hooft N _c →∞ limit. We show that its reproduces the Yang-Mills Field Theory at a large rigid random surface scale.     

Acoustic meta-materials in MEMS BAW resonators

This paper presents a meta-material-based design method for bulk acoustic wave (BAW) resonators with enhanced characteristics compared to those obtained with the typical bulk material implementation. We demonstrate the novel use of empty inclusions (i.e., ‘holes’) in bulk materials for engineering their acoustic (mechanical) properties (e.g. Young’s modulus E, Poisson’s ratio ν and mass density ρ) to tune and achieve optimal acoustical performance/characteristics. Inclusions have been demonstrated before to produce phononic band gaps for wave trapping. We focus on the propagation characteristics of the meta-materials brought into being by these inclusions. We implement patterns of holes with different sizes and distributions, to effectively scatter acoustic waves in bar-type BAW resonators and to devise the desired resonator properties, e.g., the resonant frequency. While the available bulk material is homogeneous and isotropic, the bar consists of an equivalent non-homogeneous material that can for example be distributed by design in order to shrink the overall resonator size, enhance electromechanical transduction coefficients or reject spurious modes. Our paper compares two extraction methods for the equivalent material properties of a periodically hole-punched material: the steady-state mechanical simulation of a unit cell and its ‘phase delay’ counterpart. We discuss their validity and practical use for the design of bar resonators.     

Concentration dependences of the elastic constants of the two-dimensional graphene-silicene system

The concentration dependences of the elastic constants of the two-dimensional Si _x C_{1 − x} system have been investigated with the use of the Harrison bonding-orbital method and the Keating model. The central and non-central force constants and the Grüneisen parameter have been considered by means of the bonding-orbital method. All quantities under consideration have been shown to exhibit a nonlinear behavior during the transition from graphene to silicene. A nontrivial role of the short-range repulsion has been discussed. The second-order and third-order elastic constants, the pressure dependences of the second-order elastic constants, as well as the Poisson’s ratio and Young’s modulus have been investigated in the Keating model. It has been found that the elastic constants and Young’s modulus change almost linearly upon the transition from graphene to silicene, whereas the other quantities under consideration exhibit nonlinearity.     

Interference, Reduced Action, and Trajectories

Instead of investigating the interference between two stationary, rectilinear wave functions in a trajectory representation by examining the trajectories of the two rectilinear wave functions individually, we examine a dichromatic wave function that is synthesized from the two interfering wave functions. The physics of interference is contained in the reduced action for the dichromatic wave function. As this reduced action is a generator of the motion for the dichromatic wave function, it determines the dichromatic wave function’s trajectory. The quantum effective mass renders insight into the behavior of the trajectory. The trajectory in turn renders insight into quantum nonlocality.     

Ultrasonic measurement of the elastic properties of benzoyl glycine single crystals

Certain organic crystals are found to possess high non-linear optical coefficients, often one to two orders of magnitude higher than those of the well-known inorganic non-linear optical materials. Benzoyl glycine is one such crystal whose optical second-harmonic generation efficiency is much higher than that of potassium dihydrogen phosphate. Single crystals of benzoyl glycine are grown by solvent evaporation technique usingN, N-dimethyl formamide as the solvent. All the nine second-order elastic stiffness constants of this orthorhombic crystal are determined from ultrasonic wave velocity measurements employing the pulse echo overlap technique. The anisotropy of elastic wave propagation in this crystal is demonstrated by plotting the phase velocity, slowness, Young’s modulus and linear compressibility surfaces along symmetry planes. The volume compressibility, bulk modulus and relevant Poisson’s ratios are also determined. Variation of the diagonal elastic stiffness constants with temperature over a limited range are measured and reported.     

Riesz Fractional Derivatives and Fractional Dimensional Space

The Fourier transform method is used to solve fractional Poisson’s equation with Riesz fractional derivative of order α. It is shown that the solution is given in terms of the fractional dimensional space D. Gauss law for the electrostatic problem is given and the total electric flux is obtained in terms of α and D.     

Ab initio calculation of the electronic structure,Fermi surface,and elastic properties of the new 7.5-K superconductor Nb<Subscript>2</Subscript>InC

Ab initio calculations were performed to investigate electronic and elastic properties of the newly discovered 7.5 K superconductor: layered Nb₂InC. As a result, electronic bands, total and site-projected l—decomposed density of states at the Fermi level, shape of the Fermi surface for Nb₂InC were obtained for the first time. Besides, independent elastic constants, bulk modulus, compressibility, shear modulus, Young’s modulus, Poisson’s ratio together with the elastic anisotropy parameters and indicator of brittle/ductile behavior of Nb₂InC were evaluated and analyzed in comparison with the available data.     

Propagation and interaction of ion-acoustic solitary waves in a quantum electron-positron-ion plasma

This paper discusses the existence of ion-acoustic solitary waves and their interaction in a dense quantum electron-positron-ion plasma by using the quantum hydrodynamic equations.The extended Poincar’e-Lighthill-Kuo perturbation method is used to derive the Korteweg-de Vries equations for quantum ion-acoustic solitary waves in this plasma.The effects of the ratio of positrons to ions unperturbation number density p and the quantum diffraction parameter H e (H p) on the newly formed wave during interaction,and the phase shift of the colliding solitary waves are studied.It is found that the interaction between two solitary waves fits linear superposition principle and these plasma parameters have significantly influence on the newly formed wave and phase shift of the colliding solitary waves.The investigations should be useful for understanding the propagation and interaction of ion-acoustic solitary waves in dense astrophysical plasmas (such as white dwarfs) as well as in intense laser-solid matter interaction experiments.     

Relation between the parameters of the elasticity theory and averaged bulk modulus of solids

A relation between the elastic moduli and Poisson’s ratio of crystalline and vitreous solids is considered. The feasibility of introducing the averaged bulk modulus, which has the same attributes as other elastic moduli, is substantiated. A relationship between the Grüneisen parameter and Poisson’s ratio is discussed.     

Double-Delta Potentials: One Dimensional Scattering The Casimir Effect and Kink Fluctuations

The path is explored between one-dimensional scattering through Dirac-δ walls and one-dimensional quantum field theories defined on a finite length interval with Dirichlet boundary conditions. It is found that two δ’s are related to the Casimir effect whereas two δ’s plus the first transparent P?sch-Teller well arise in the context of the sine-Gordon kink fluctuations, both phenomena subjected to Dirichlet boundary conditions. One or two delta wells will be also explored in order to describe absorbent plates, even though the wells lead to non unitary Quantum Field Theories.     

Formulation and picture of quantum phase

Based on the concept of classical phase, we formulate a new explanation for the quantum phase from the quantum mechanical point of view. The quantum phase is the canonically conjugate variable of an angular momentum operator, which corresponds to the angular position φ in an actual physical space with a classical reference frame, but it takes a complex exponential form e ^iφ≡cosφ+i sinφ in the abstract Hilbert space of a quantum reference frame. This formulation is simply the famous Euler formula in a complex number field. In particular, when φ = π/2, the correlative quantum phase is a unitary pure imaginary number e ^iπ/2≡cos(π/2)+i sin(π/2) ≡ i. By using a photon state-vector function that is the general solution of photon Schr?dinger equation and can completely describe a photon’s behavior, we discuss the relationship between the angular momentum of a photon and the phase of the photon; we also analyze the intrinsic relationship between the macroscopic light wave phase and the microscopic photon phase.