하이젠베르크의 노벨상 강연의 수사학적 상황 분석 - 비처의 개념을 중심으로 -

구자현 성균관대학교 인문학연구원 2022 人文科學 Vol.- No.87

This paper analyzes the rhetorical situations of Heisenberg's Nobel Lecture with reference to Lloyd Bitzer's concepts. Bitzer regards discourses as being formed for solving specific rhetorical situations each of which consists of exigence, audience, and constraints. Carrying out the lecture on the development of quantum mechanics in 1933, Heisenberg presents in what circumstances quantum mechanics is situated and in which direction it proceeds. Toward physicists as the audience, he maintains that quantum mechanics receives as its foundation Bohr's quantum model of atoms, the correspondence principle, and the complimentary principle. Toward the scientific community as the audience, he maintains that quantum mechanics gives up the visualization of systems in time and space to regard the world as in a statistical transition between its states. Saying that quantum mechanics constructs a new physics with the aid of Schrödinger's wave mechanics, he attempts to liberate physicists from the constraint of the belief in the centrality of wave mechanics. Besides, predicting the advent of an extended quantum mechanics, he attempts to put to rest the worries of scientists over the future of quantum mechanics. 이 논문은 하이젠베르크의 노벨상 강연에 대하여 비처의 개념을 따라 수사학적 상황 분석을 수행한다. 비처는 담론이 특수한 수사학적 상황, 즉 사태, 청중, 제약을 요소로 하는 상황을 수사학적으로 해결하기 위하여 형성되는 것으로 본다. 하이젠베르크는 강연을 수행하면서 물리학계와 관련 과학계에 양자역학이 어떤 상황에 있으며 어떤 방향으로 나아가고 있는지를 제시한다. 그는 양자역학이 보어의 양자론적 원자 모형, 대응 원리, 상보성 원리를 그 토대로 삼고 있음을 물리학자들을 청중으로 삼아 주장하고, 과학계를 청중으로 삼아 양자역학이 시공간에서 계의 시각화를 포기하고 세계를 상태 간의 전이가 확률적으로 이루어지는 곳으로 보게 되었음을 주장한다. 그는 양자역학이 슈뢰딩거의 파동역학으로부터 도움을 받아 새로운 물리학을 구축하고 있다고 말하여 파동역학을 양자역학의 중심으로 믿는 ‘제약’에서 물리학자들을 벗어나게 하려고 시도한다. 또한 그는 확장된 양자역학의 출현이 가능할 것임을 전망하여 양자역학의 미래에 대한 우려라는 ‘사태’를 종식시키기를 꾀한다.

Thickness dependence of antiferromagnetic phase transition in Heisenberg-type MnPS3

임수연,김강원,이성민,박재근,정현식 한국물리학회 2021 Current Applied Physics Vol.21 No.-

The behavior of 2-dimensional (2D) van der Waals (vdW) layered magnetic materials in the 2D limit of the fewlayer thickness is an important fundamental issue for the understanding of the magnetic ordering in lower dimensions. The antiferromagnetic transition temperature TN of the Heisenberg-type 2D magnetic vdW material MnPS3 was estimated as a function of the number of layers. The antiferromagnetic transition was identified by temperature-dependent Raman spectroscopy, from the broadening of a phonon peak at 155 cm 1, accompanied by an abrupt redshift and an increase of its spectral weight. TN is found to decrease only slightly from ~78 K for bulk to ~66 K for 3L. The small reduction of TN in thin MnPS3 approaching the 2D limit implies that the interlayer vdW interaction is playing an important role in stabilizing magnetic ordering in layered magnetic materials.

APPLICATIONS ON THE BESSEL-STRUVE-TYPE FOCK SPACE

Soltani, Fethi Korean Mathematical Society 2017 대한수학회논문집 Vol.32 No.4

In this work, we establish Heisenberg-type uncertainty principle for the Bessel-Struve Fock space ${\mathbb{F}}_{\nu}$ associated to the Airy operator $L_{\nu}$. Next, we give an application of the theory of extremal function and reproducing kernel of Hilbert space, to establish the extremal function associated to a bounded linear operator $T:{\mathbb{F}}_{\nu}{\rightarrow}H$, where H be a Hilbert space. Furthermore, we come up with some results regarding the extremal functions, when T are difference operators.

TIME-FREQUENCY ANALYSIS ASSOCIATED WITH K-HANKEL-WIGNER TRANSFORMS

Boubatra, Mohamed Amine Korean Mathematical Society 2022 대한수학회논문집 Vol.37 No.2

In this paper, we introduce the k-Hankel-Wigner transform on R in some problems of time-frequency analysis. As a first point, we present some harmonic analysis results such as Plancherel's, Parseval's and an inversion formulas for this transform. Next, we prove a Heisenberg's uncertainty principle and a Calderón's reproducing formula for this transform. We conclude this paper by studying an extremal function for this transform.

QUALITATIVE UNCERTAINTY PRINCIPLES FOR THE INVERSE OF THE HYPERGEOMETRIC FOURIER TRANSFORM

Mejjaoli, Hatem The Kangwon-Kyungki Mathematical Society 2015 한국수학논문집 Vol.23 No.1

In this paper, we prove an $L^p$ version of Donoho-Stark's uncertainty principle for the inverse of the hypergeometric Fourier transform on $\mathbb{R}^d$. Next, using the ultracontractive properties of the semigroups generated by the Heckman-Opdam Laplacian operator, we obtain an $L^p$ Heisenberg-Pauli-Weyl uncertainty principle for the inverse of the hypergeometric Fourier transform on $\mathbb{R}^d$.

ROTA-BAXTER OPERATORS OF 3-DIMENSIONAL HEISENBERG LIE ALGEBRA

Ji, Guangzhi,Hua, Xiuying The Kangwon-Kyungki Mathematical Society 2018 한국수학논문집 Vol.26 No.1

In this paper, we consider the question of the Rota-Baxter operators of 3-dimensional Heisenberg Lie algebra on ${\mathbb{F}}$, where ${\mathbb{F}}$ is an algebraic closed field. By using the Lie product of the basis elements of Heisenberg Lie algebras, all Rota-Baxter operators of 3-dimensional Heisenberg Lie algebras are calculated and left symmetric algebras of 3-dimensional Heisenberg Lie algebra are determined by using the Yang-Baxter operators.

DIFFERENTIAL GEOMETRIC PROPERTIES ON THE HEISENBERG GROUP

Park, Joon-Sik Korean Mathematical Society 2016 대한수학회지 Vol.53 No.5

In this paper, we show that there exists no left invariant Riemannian metric h on the Heisenberg group H such that (H, h) is a symmetric Riemannian manifold, and there does not exist any H-invariant metric $\bar{h}$ on the Heisenberg manifold $H/{\Gamma}$ such that the Riemannian connection on ($H/{\Gamma},\bar{h}$) is a Yang-Mills connection. Moreover, we get necessary and sufficient conditions for a group homomorphism of (SU(2), g) with an arbitrarily given left invariant metric g into (H, h) with an arbitrarily given left invariant metric h to be a harmonic and an affine map, and get the totality of harmonic maps of (SU(2), g) into H with a left invariant metric, and then show the fact that any affine map of (SU(2), g) into H, equipped with a properly given left invariant metric on H, does not exist.

Differential geometric properties on the Heisenberg group

Joon-Sik Park 대한수학회 2016 대한수학회지 Vol.53 No.5

In this paper, we show that there exists no left invariant Riemannian metric $h$ on the Heisenberg group $H$ such that $(H,h)$ is a symmetric Riemannian manifold, and there does not exist any $H$-invariant metric $\bar h$ on the Heisenberg manifold $H/\Gamma$ such that the Riemannian connection on $(H/ \Gamma, \bar h)$ is a Yang-Mills connection. Moreover, we get necessary and sufficient conditions for a group homomorphism of $(SU(2),g)$ with an arbitrarily given left invariant metric $g$ into $(H,h)$ with an arbitrarily given left invariant metric $h$ to be a harmonic and an affine map, and get the totality of harmonic maps of $(SU(2),g)$ into $H$ with a left invariant metric, and then show the fact that any affine map of $(SU(2),g)$ into $H$, equipped with a properly given left invariant metric on $H$, does not exist.

VOLUMES OF GEODESIC BALLS IN HEISENBERG GROUPS ℍ⁵

Kim, Hyeyeon Chungcheong Mathematical Society 2019 충청수학회지 Vol.32 No.3

Let ${\mathbb{H}}^5$ be the 5-dimensional Heisenberg group equipped with a left-invariant metric. In this paper we calculate the volumes of geodesic balls in ${\mathbb{H}}^5$. Let $B_e(R)$ be the geodesic ball with center e (the identity of ${\mathbb{H}}^5$) and radius R in ${\mathbb{H}}^5$. Then, the volume of $B_e(R)$ is given by $${\hfill{12}}Vol(B_e(R))\\{={\frac{4{\pi}^2}{6!}}{\left(p_1(R)+p_4(R){\sin}\;R+p_5(R){\cos}\;R+p_6(R){\displaystyle\smashmargin{2}{\int\nolimits_0}^R}{\frac{{\sin}\;t}{t}}dt\right.}\\{\left.{\hfill{65}}{+q_4(R){\sin}(2R)+q_5(R){\cos}(2R)+q_6(R){\displaystyle\smashmargin{2}{\int\nolimits_0}^{2R}}{\frac{{\sin}\;t}{t}}dt}\right)}$$ where $p_n$ and $q_n$ are polynomials with degree n.

ON THETA FUNCTIONS

YANG, JAE-HYUN 경북대학교 위상수학 기하학연구센터 1995 硏究論文集 Vol.6 No.-

In this paper, we identitfy theta functions with smooth functions on the Heisenberg group with certain conditions and give a connection of theta functions with lattice representations.