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Naohisa Ogawa

Publications and source records attributed to Naohisa Ogawa.

18 recordsLinked to original sources
arXiv2023

Uncertainty Relation and Minimum Wave Packet on Circle

We discuss on the uncertainty relation (UR) for a closed one dimensional system (circle). In such a system, we cannot use the angle along the circle as a position variable. Otherwise we meet difficulties about the definition of the average position and the standard deviation (SD), and Hermitian property of angular momentum. From these reasons, we define the position variable as Cartesian variable $(X,Y)$ that have the periodic property for angle $ϕ$. In the same way we define a SD by using that variables. Then we obtain two URs. We also discuss the minimum wave packet (MWP) on the circle. MWPs are expressed by von Mises distribution functions. Next we construct total URs by combining two URs for $X$ and $Y$. Furthermore, we extend the variables to $(X_n, Y_n)$ \; with $n= 1,2,3,\cdots$ and we have infinite series of total URs. We consider the meaning of such extended URs.

quant-ph↗
arXiv2018

Geometric Flow appearing in Conservation Law in Classical and Quantum Mechanics

The appearance of a geometric flow in the conservation law of particle number in classical particle diffusion and in the conservation law of probability in quantum mechanics is discussed in the geometrical environment of a two-dimensional curved surface with thickness $ε$ embedded in $R_3$. In such a system with a small thickness $ε$, the usual two-dimensional conservation law does not hold and we find an anomaly. The anomalous term is obtained by the expansion of $ε$. We find that this term has a Gaussian and mean curvature dependence and can be written as the total divergence of some geometric flow. We then have a new conservation law by adding the geometric flow to the original one. This fact holds in both classical diffusion and quantum mechanics when we confine particles to a curved surface with a small thickness.

quant-ph↗
arXiv2017

Algebraic construction of spherical harmonics

The angular wave functions for a hydrogen atom are well known to be spherical harmonics, and are obtained as the solutions of a partial differential equation. However, the differential operator is given by the Casimir operator of the $SU(2)$ algebra and its eigenvalue $l(l+1) \hbar^2$, where $l$ is non-negative integer, is easily obtained by an algebraic method. Therefore the shape of the wave function may also be obtained by extending the algebraic method. In this paper, we describe the method and show that wave functions with different quantum numbers are connected by a rotational group in the cases of $l=0$, 1 and 2.

quant-ph↗
arXiv2013

Open End Correction for Flanged Circular Tube from the Diffusion Process

In the physics lessons on waves and resonance phenomena in high school and college, we usually consider sound waves in a tube with open or closed ends \cite{ResnikHalliday}. However, it is well known that we need a tube with open end correction $ΔL$. The correction for a flanged circular tube was first given by Rayleigh \cite{Rayleigh} and experimentally checked by several authors \cite{exp}. In this paper, we show the different methods of obtaining the end correction for a circular tube by a diffusion process.

physics.class-ph↗
arXiv2013

Diffusion in a Curved Tube

The diffusion of particles in confining walls forming a tube is discussed. Such a transport phenomenon is observed in biological cells and porous media. We consider the case in which the tube is winding with curvature and torsion, and the thickness of the tube is sufficiently small compared with its curvature radius. We discuss how geomerical quantities appear in a quasi-one-dimensional diffusion equation.

math-ph↗
arXiv2011

Simple model of photo acoustic system for greenhouse effect

The green house effect is caused by the gases which absorb infrared ray (IR) emitted by the earth. It is worthwhile if we can adjudicate on which gas causes the greenhouse effect in our class. For this purpose, one of our authors, Kaneko has designed an educational tool for testing greenhouse effect \cite{Kaneko}. This system (hereafter abbreviated PAS) is constructed based on photo acoustic effect. Without difficulty and high cost, we can build PAS and check the IR absorption of gas. In this paper we give the simple theoretical basis for this PAS. The amplitude of sound observed in PAS depends on the modulation frequency of IR pulse. Its dependence can be explained by this simple model. Further we show the sound amplitude does not depend on the thermal diffusion, which provides the accuracy of amplitude as the IR absorption rate of the gas. According to this model, sound signal is not the sinusoidal function and it has higher harmonics. The theory and experiment are compared in the third harmonics by spectrum analysis. From this apparatus and theory, students can study not only the greenhouse effect but also the basics of physics.

physics.pop-ph↗
arXiv2009

Curvature Dependent Diffusion Flow on Surface with Thickness

Particle diffusion in a two dimensional curved surface embedded in $R_3$ is considered. In addition to the usual diffusion flow, we find a new flow with an explicit curvature dependence. New diffusion equation is obtained in $ε$ (thickness of surface) expansion. As an example, the surface of elliptic cylinder is considered, and curvature dependent diffusion coefficient is calculated.

physics.bio-ph↗
arXiv2007

Dissipation Under the Magnetic Field on 2D Surface

It is well known that the convection of liquid solution or melt liquid is inhibited by the magnetic field experimentally, and so that we can make the larger and better crystals at the cost of slow growth rate. We shall show here another two effects due to the magnetic field. First, when the ionised molecule diffuses on the surface of crystal under the magnetic field applied normal to the surface,its diffusion constant decreases due to the magnetic effect. Second, even if the molecule has no electric charge, if it has electric dipole moment, the kinetic energy decreases by different mechanism.

cond-mat.other↗
arXiv2004

Theoretical calculation of the surface energy of water

The estimation of the surface tension of water is theoretically dealt on the basis of the dipole molecular model. It is known that the experimentally determined surface tension of freshly exposed surface has a higher value than the nominal value of 73 [mN/m]. We calculated the value corresponding to the fresh surface where the reorientation of the molecules has not occurred.

physics.chem-ph↗
arXiv2003

From Fermat Principle to Wave equation

The Fermat principle indicates that light chooses the temporally shortest path. The action for this "motion" is the observed time, and it has no Lorentz invariance. In this paper we show how this action can be obtained from relativistic action, and how the classical wave equation of light can be obtained from this action.

quant-ph↗
arXiv2002

Surface Instability of Icicles

Quantitatively-unexplained stationary waves or ridges often encircle icicles. Such waves form when roughly 0.1 mm-thick layers of water flow down the icicle. These waves typically have a wavelength of 1cm approximately independent of external temperature, icicle thickness, and the volumetric rate of water flow. In this paper we show that these waves can not be obtained by naive Mullins-Sekerka instability, but are caused by a quite new surface instability related to the thermal diffusion and hydrodynamic effect of thin water flow.

cond-mat.mtrl-sci↗
arXiv2001

Waves on Icicles

Icicles with wave patterns on their surfaces can sometimes be seen hanging from roofs of buildings. Surprisingly, most of these wave patterns are at intervals of about 1 cm. The reason for this uniformity of interval has not been clarified. Here we show a formula to explain this remarkable phenomenon by introducing a new instability theory. This theory is given by thermal diffusion in thin water layer streams flowing along the icicles. The streams change the temperature distribution and control waves of short wavelengths. The specific wavelength (about 1 cm) can be determined by Laplace instability of the heat field in the atmosphere and by the thermal diffusion effect in thin-layer streams.

cond-mat.mtrl-sci↗
arXiv2000

A Note on Classical Solution of Chaplygin-gas as D-brane

The classical solution of bosonic d-brane in (d+1,1) space-time is studied. We work with light-cone gauge and reduce the problem into Chaplygin gas problem. The static equation is equivalent to vanishing of extrinsic mean curvature, which is similar to Einstein equation in vacuum. We show that the d-brane problem in this gauge is closely related to Plateau problem, and we give some non-trivial solutions from minimal surfaces. The solutions of d-1,d,d+1 spatial dimensions are obtained from d-dimensional minimal surfaces as solutions of Plateau problem. In addition we discuss on the relation to Hamiltonian-BRST formalism for d-branes.

hep-th↗
arXiv1998

A Note on the scale symmetry and Noether current

Usually we consider the symmetry of action as the symmetry of the theory, however, in the Keplar problem the scaling symmetry existing in equa tion of motion is not the ones for action. It changes the multiplicative c onstant of action and the time boundary. In such a case that the scale tran sformation does not leave the action invariant but keeping the equation inva riant, the following statement is proved. The time integration of Lagrangian is explicitly performed and the action ca n be expressed by the difference of formal (non-conserved) Noether charges a t time boundaries. In field theory the action can be expressed by the bound ary integration of the formal Noether current.

hep-th↗
arXiv1998

A Note on Gauge Principle and Spontaneous Symmetry Breaking in Classical Particle Mechanics

The U(1) gauge field is usually induced from the gauge principle, that is, the extension of global U(1) phase transformation for matter field. However the phase itself is realized only for quantum theory. In this paper we introduce the U(1) gauge field and gauge coupling from the gauge principle classically. The gauge symmetry is spontaneously broken from the out set. The Higgs mechanism occurs and we obtain the London equation. The Hydrodynamical interpretation of classical field we utilized is given, and the relation to super conductivity is discussed.

hep-th↗
arXiv1997

Embedding of Relativistic Particles and Spinor Natural-Frame

Embedding of Klein-Gordon and Dirac particle onto Riemannian submanifold in higher dimensional Minkowski space is given by using Hamiltonian BRST formalism. Up to the ordering and quantum potential term induced by embedding, obtained K-G equation is the usual one in Riemannian space, instead, the obtained Dirac equation is essentially different from the usual well known form using vierbein. The requirement of equivalence between two Dirac equations gives the property of natural-frame for spinor.

hep-th↗
arXiv1997

Pedagogical Introduction to Hamiltonian BRST formalism

Hamiltonian BRST formalism (FV formalism) includes many auxiliary fields without explanation. Its path-integration has a simple form by using BRST charge, but its construction is quite mechanically and hard to understand physical meaning. In this paper we perform the phase space path-integral with requiring BRST invariance for action and measure, and show that the resultant form is equivalent to the Hamiltonian BRST (FV) formalism in gravitational theory. This explains why so many auxiliary fields are necessary to be introduced. We also find the gauge fixing is automatically done by requiring the BRST invariance of the path-integral measure. This is a pedagogical introduction to Hamiltonian BRST formalism.

hep-th↗