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Y. S. Kim

Publications and source records attributed to Y. S. Kim.

At least 37 records · Page 2Linked to original sources
arXiv2013

An alternative proof of the extended Saalschutz summation theorem for the r+3Fr+2(1) series with applications

A simple proof of a new summation formula for a terminating r+3Fr+2(1) hypergeometric series, representing an extension of Saalschutz's formula for a 3F2(1) series, is given for the case of r pairs of numeratorial and denominatorial parameters differing by positive integers. Two applications of this extended summation theorem are discussed. The first application extends two identities given by Ramanujan and the second, which also employs a similar extension of the Vandermonde-Chu summation theorem for the 2F1 series, extends certain reduction formulas for the Kamp?e de F?eriet function of two variables given by Exton and Cvijovi?c and Miller.

math.CV↗
arXiv2013

A note on a series containing the Laguerre polynomials

Expressions for the summation of a new series involving the Laguerre polynomials are obtained in terms of generalized hypergeometric functions. These results provide alternative, and in some cases simpler, expressions to those recently obtained in the literature.

math.CV↗
arXiv2013

On two Thomae-type transformations for hypergeometric series with integral parameter differences

We obtain two new Thomae-type transformations for hypergeometric series with r pairs of numeratorial and denominatorial parameters differing by positive integers. This is achieved by application of the so-called Beta integral method developed by Krattenthaler and Rao [Symposium on Symmetries in Science (ed. B. Gruber), Kluwer (2004)] to two recently obtained Euler-type transformations. Some special cases are given.

math.CV↗
arXiv2013

Historical Approach to Physics according to Kant, Einstein, and Hegel

It is known that Einstein's conceptual base for his theory of relativity was the philosophy formulated by Immanuel Kant. Things appear differently to observers in different frames. However, Kant's Ding-an-Sich leads to the existence of the absolute reference frame which is not acceptable in Einstein's theory. It is possible to avoid this conflict using the ancient Chinese philosophy of Taoism where two different views can co-exist in harmony. This is not enough to explain Einstein's discovery of the mass-energy relation. The energy-momentum relations for slow and ultra-fast particles take different forms. Einstein was able to synthesize these two formulas to create his energy-mass relation. Indeed, this is what Hegelianism is about in physics. Isaac Newton synthesized open orbits for comets and closed orbits for planets to create his second law of motion. Maxwell combined electricity and magnetism to create his four equations to the present-day wireless world. In order to synthesize wave and particle views of matter, Heisenberg formulated his uncertainty principle. Relativity and quantum mechanics are the two greatest theories formulated in the 20th Century. Efforts to synthesize these two theories are discussed in detail.

physics.hist-ph↗
arXiv2012

Quark-Parton Phase Transitions and the Entropy Problem in Quantum Mechanics

Since Feynman proposed his parton model in 1969, one of the most pressing problems in high-energy physics has been whether partons are quarks. It is shown that the quark model and the parton model are two different manifestations of one covariant entity. The nature of transition from the confined quarks to plasma-like partons is studied in terms of the entropy and temperature coming from the time-separation variable. According to Einstein, the time-separation variable exists wherever there is a spatial separation, but it is not observed in the present form of quantum mechanics. It belongs to Feynman's rest of the universe.

quant-ph↗
arXiv2012

Poincaré Sphere and Decoherence Problems

Henri Poincaré formulated the mathematics of the Lorentz transformations, known as the Poincaré group. He also formulated the Poincaré sphere for polarization optics. It is shown that these two mathematical instruments can be combined into one mathematical device which can address the internal space-time symmetries of elementary particles, decoherence problems in polarization optics, entropy problems, and Feynman's rest of the universe.

math-ph↗
arXiv2012

Lorentz Group in Ray and Polarization Optics

While the Lorentz group serves as the basic language for Einstein's special theory of relativity, it is turning out to be the basic mathematical instrument in optical sciences, particularly in ray optics and polarization optics. The beam transfer matrix, commonly called the $ABCD$ matrix, is shown to be a two-by-two representation of the Lorentz group applicable to the three-dimensional space-time consisting of two space and one time dimensions. The Jones matrix applicable to polarization states turns out to be the two-by-two representations of the Lorentz group applicable to the four-dimensional space-time consisting of three space and one time dimensions. The four-by-four Mueller matrix applicable to the Stokes parameters as well as the Poincaré sphere are both shown to be the representations of the Lorentz group.

math-ph↗
arXiv2011

The Language of Two-by-two Matrices spoken by Optical Devices

With its three independent parameters, the $ABCD$ matrix serves as the beam transfer matrix in optics. If it is transformed to an equi-diagonal form, the matrix has only two independent parameters determined by optical devices. It is shown that this two-parameter mathematical device contains enough information to describe the basic space-time symmetry of elementary particles. If its trace is smaller than two, this matrix can represent the internal space-time symmetry of massive particles. If equal to two, the matrix is of massless particles. If the trace is greater than two, this matrix describes imaginary-mass particles. This matrix speaks Einstein's language for space-time structure of elementary particles. As for the optical devices, the laser cavity and the multilayer system are discussed as illustrative physical examples.

math-ph↗
arXiv2011

Einstein's Hydrogen Atom

In 1905, Einstein formulated his special relativity for point particles. For those particles, his Lorentz covariance and energy-momentum relation are by now firmly established. How about the hydrogen atom? It is possible to perform Lorentz boosts on the proton assuming that it is a point particle. Then what happens to the electron orbit? The orbit could go through an elliptic deformation, but it is not possible to understand this problem without quantum mechanics, where the orbit is a standing wave leading to a localized probability distribution. Is this concept consistent with Einstein's Lorentz covariance? Dirac, Wigner, and Feynman contributed important building blocks for understanding this problem. The remaining problem is to assemble those blocks to construct a Lorentz-covariant picture of quantum bound states based on standing waves. It is shown possible to assemble those building blocks using harmonic oscillators.

quant-ph↗
arXiv2011

Sr flux stability against oxidation in oxide-MBE environment: flux, geometry, and pressure dependence

Maintaining stable fluxes for multiple source elements is a challenging task when the source materials have significantly different oxygen affinities in a complex-oxide molecular-beam-epitaxy (MBE) environment. Considering that Sr is one of the most easily oxidized and widely used element in various complex oxides, we took Sr as a probe to investigate the flux stability problem in a number of different conditions. Source oxidation was less for higher flux, extended port geometry, and un-melted source shape. The extended port geometry also eliminated the flux transient after opening a source shutter as observed in the standard port. We also found that the source oxidation occurred more easily on the crucible wall than on the surface of the source material. Atomic oxygen, in spite of its stronger oxidation effectiveness, did not make any difference in source oxidation as compared to molecular oxygen in this geometry. Our results may provide a guide for solutions to the source oxidation problem in oxide-MBE system.

cond-mat.mtrl-sci↗
arXiv2010

Time separation as a hidden variable to the Copenhagen school of quantum mechanics

The Bohr radius is a space-like separation between the proton and electron in the hydrogen atom. According to the Copenhagen school of quantum mechanics, the proton is sitting in the absolute Lorentz frame. If this hydrogen atom is observed from a different Lorentz frame, there is a time-like separation linearly mixed with the Bohr radius. Indeed, the time-separation is one of the essential variables in high-energy hadronic physics where the hadron is a bound state of the quarks, while thoroughly hidden in the present form of quantum mechanics. It will be concluded that this variable is hidden in Feynman's rest of the universe. It is noted first that Feynman's Lorentz-invariant differential equation for the bound-state quarks has a set of solutions which describe all essential features of hadronic physics. These solutions explicitly depend on the time separation between the quarks. This set also forms the mathematical basis for two-mode squeezed states in quantum optics, where both photons are observable, but one of them can be treated a variable hidden in the rest of the universe. The physics of this two-mode state can then be translated into the time-separation variable in the quark model. As in the case of the un-observed photon, the hidden time-separation variable manifests itself as an increase in entropy and uncertainty.

quant-ph↗
arXiv2010

Internal Space-time Symmetries of Particles derivable from Periodic Systems in Optics

While modern optics is largely a physics of harmonic oscillators and two-by-two matrices, it is possible to learn about some hidden properties of the two-by-two matrix from optical systems. Since two-by-two matrices can be divided into three conjugate classes depending on their traces, optical systems force us to establish continuity from one class to another. It is noted that those three classes are equivalent to three different branches of Wigner's little groups dictating the internal space-time symmetries massive, massless, and imaginary-mass particles. It is shown that the periodic systems in optics can also be described by have the same class-based matrix algebra. The optical system allow us to make continuous, but not analytic, transitions from massiv to massless, and massless to imaginary-mass cases.

math-ph↗
arXiv2010

Internal Space-time Symmetries according to Einstein, Wigner, Dirac, and Feynman

When Einstein formulated his special relativity in 1905, he established the law of Lorentz transformations for point particles. It is now known that particles have internal space-time structures. Particles, such as photons and electrons, have spin variables. Protons and other hadrons are regarded as bound states of more fundamental particles called quarks which have their internal variables. It is still one of the most outstanding problems whether these internal space-time variables are transformed according to Einstein's law of Lorentz transformations. It is noted that Wigner, Dirac, and Feynman made important contributions to this problem. By integrating their efforts, it is then shown possible to construct a picture of the internal space-time symmetry consistent with Einstein's Lorentz covariance.

math-ph↗
arXiv2010

The Fourth Element: Characteristics, Modelling, and Electromagnetic Theory of the Memristor

In 2008, researchers at HP Labs published a paper in {\it Nature} reporting the realisation of a new basic circuit element that completes the missing link between charge and flux-linkage, which was postulated by Leon Chua in 1971. The HP memristor is based on a nanometer scale TiO$_2$ thin-film, containing a doped region and an undoped region. Further to proposed applications of memristors in artificial biological systems and nonvolatile RAM (NVRAM), they also enable reconfigurable nanoelectronics. Moreover, memristors provide new paradigms in application specific integrated circuits (ASICs) and field programmable gate arrays (FPGAs). A significant reduction in area with an unprecedented memory capacity and device density are the potential advantages of memristors for Integrated Circuits (ICs). This work reviews the memristor and provides mathematical and SPICE models for memristors. Insight into the memristor device is given via recalling the quasi-static expansion of Maxwell's equations. We also review Chua's arguments based on electromagnetic theory.

cond-mat.mes-hall↗
arXiv2009

Feynman and Squeezed States

In 1971, Feynman et al. published a paper on hadronic mass spectra and transition rates based on the quark model. Their starting point was a Lorentz-invariant differential equation. This equation can be separated into a Klein-Gordon equation for the free-moving hadron and a harmonic oscillator equation for the quarks inside the hadron. However, their solution of the oscillator equation is not consistent with the existing rules of quantum mechanics and special relativity. On the other hand, their partial differential equation has many other solutions depending on boundary conditions. It is noted that there is a Lorentz-covariant set of solutions totally consistent with quantum mechanics and special relativity. This set constitutes a representation of the Poincaré group which dictates the fundamental space-time symmetry of particles in the Lorentz-covariant world. It is then shown that the same set of solutions can be used as the mathematical basis for two-photon coherent states or squeezed states in quantum optics. It is thus possible to transmit the physics of squeezed states into the hadronic world. While the time-like separation is the most puzzling problem in the covariant oscillator regime, this variable can be interpreted like the unobserved photon in the two-mode squeezed state which leads to an entropy increase.

quant-ph↗
arXiv2009

QCD's Partner needed for Mass Spectra and Parton Structure Functions

As in the case of the hydrogen atom, bound-state wave functions are needed to generate hadronic spectra. For this purpose, in 1971, Feynman and his students wrote down a Lorentz-invariant harmonic oscillator equation. This differential equation has one set of solutions satisfying the Lorentz-covariant boundary condition. This covariant set generates Lorentz-invariant mass spectra with their degeneracies. Furthermore, the Lorentz-covariant wave functions allow us to calculate the valence parton distribution by Lorentz-boosting the quark-model wave function from the hadronic rest frame. However, this boosted wave function does not give an accurate parton distribution. The wave function needs QCD corrections to make a contact with the real world. Likewise QCD needs the wave function as a starting point for calculating the parton structure function.

hep-ph↗
arXiv2009

Fundamental thickness limit of itinerant ferromagnetic SrRuO$_3$ thin films

We report on a fundamental thickness limit of the itinerant ferromagnetic oxide SrRuO$_3$ that might arise from the orbital-selective quantum confinement effects. Experimentally, SrRuO$_3$ films remain metallic even for a thickness of 2 unit cells (uc), but the Curie temperature, T$_C$, starts to decrease at 4 uc and becomes zero at 2 uc. Using the Stoner model, we attributed the T$_C$ decrease to a decrease in the density of states (N$_o$). Namely, in the thin film geometry, the hybridized Ru-d$_yz,zx$ orbitals are terminated by top and bottom interfaces, resulting in quantum confinement and reduction of N$_o$.

cond-mat.str-el↗