Quantum 1D coulomb problem with general connection condition at the origin
カテゴリ
講演資料
概要
"Quantum 1D coulomb problem with general connection condition at the origin"
by Axel Perez-Obiol & Taksu Cheon
Abstract:
We consider the solution of the quantum Coulomb problem in one dimension with the most general connection condition at the origin. The divergence of wavefunction at the origin invalidates the standard current conservation approach. We explore two approaches, Wronskian self-adjoint extension method and cutoff regulaization method, and establish their mutual relations, thereby clarifying the physical contents of the connection parameters. We show how to realize ``exotic'' non-Loudon connection conditions.
Talk presented at 6th Nanman Conference, Sept 11, 2019, Sv. Martin na Muri, Croatia
[last update 14:30, Sept 11, 2019]
Abstract
We consider a Bose-Einstein condensate with repulsive interactions confined in a 1D ring where a Dirac delta is rotating at constant speed. The spectrum of stationary solutions is analyzed in terms of the nonlinear coupling, delta velocity, and delta strength, which may take positive and negative values. Analytical expressions in terms Jacobi elliptic functions are provided for the wave functions, current, and chemical potential. The chemical potential is organized into a set of energy levels conforming a multiple swallowtail structure in parameter space, consisting in bright solitons, gray and dark solitonic trains, and vortices. We compute the critical velocities and perform a Bogoliubov analysis for the ground state and first few excited levels, establishing possible adiabatic transitions between the stationary and stable solutions. A set of adiabatic cycles is proposed in which gray solitons and vortices of arbitrary angular momenta are obtained from the ground state by setting and unsetting a rotating delta.
講演は次の原論文に基いている
[1] T.Cheon & S. Galam, "Dynamical Galam model", https://arxiv.org/abs/1802.05389
[2] S. Galam & T. Cheon, "Tipping point dynamics: a universal formula", https://arxiv.org/abs/1901.09622
Dynamical Galam model
by Taksu Cheon and Serge Galam
Abstract:
We introduce a model of temporal evolution of political opinions which amounts to a dynamical extension of Galam model in which the number of inflexibles are treated as dynamical variables. We find that the critical value of inflexibles in the original Galam model now turns into a fixed point of the system whose stability controls the phase trajectory of the political opinions. The appearance of two phases is found, in which majority-preserving and regime-changing limit cycles are respectively dominant, and the phase transition between them is observed.
Post arXiv version: referees' comments incorporated
[last update : Apr 20, 2018, 12:00, v5.0C, with critical typo corrections on eqs(4)-(6) over published version & arXiv version]
Classical analog for exotic quantum holonomy
Atushi Tanaka (TMU) and Taksu Cheon (KUT)
Talk to be presented at JPS 2017 meeting at Iwate Univ., 9/24/2017
Quantum vertices: Theory and applications
by Taksu Cheon
Invited talk presented at "3rd Dynamics Days in Central Asia", Astana
Sept. 5th, 2016 at Nazarbayev University, Astana, Kazakhstan
Spiral orbits and oscillations in historical evolution of empires
カテゴリ
講演資料
概要
Spiral orbits and oscillations in historical evolution of empires
by Taksu Cheon
Seminar presented at Math. Dept., Nazarbayev University, Astana, Kazakhstan, 1.9.2016
Spiral orbits and oscillations in historical evolution of empires
カテゴリ
研究論文
概要
Spiral orbits and oscillations in historical evolution of empires
by Taksu Cheon and Sergey S. Poghosyan
Abstract:
We introduce the concept of metaasabiya, the second non-material resource, to the asabiya theory of historical dynamics. We find that the resulting three variable dynamical system has peculiar structures of the repeller axis, the attractor string, and spiralling orbits in the phase space, which enable the system to go through multiple oscillatory rises and falls with nontrivial initial state dependence, mimicking the evolutions of real-world polities. These distinctive features, absent in conventional Lotka-Volterra type biological systems, reveal the hidden richness inherent in the asabiya theory.
KUT UQD Working paper, Aug. 25, 2016 (version 5)
[Last update 29.8.2016, v5.05]
Complete population inversion of Bose particles by an adiabatic cycle
カテゴリ
研究論文
概要
Complete population inversion of Bose particles by an adiabatic cycle
by Atushi Tanaka & Taksu Cheon
Abstract: We show that an adiabatic cycle excites Bose particles confined in a one-dimensional box. During the adiabatic cycle, a wall described by a -shaped potential is applied and its strength and position are slowly varied. When the system is initially prepared in the ground state, namely, in the zero-temperature equilibrium state, the adiabatic cycle brings all bosons into the first excited one-particle state, leaving the system in a nonequilibrium state whose energy is proportional to the number of bosons.
新論文arXiv公表までの限定公開 22.12.2015
Last update 24.12.2015 11:30PM
Path topology dependence of adiabatic time evolution
カテゴリ
研究論文
概要
Path topology dependence of adiabatic time evolution
by Atushi Tanaka & Taksu Cheon
Abstract: An adiabatic time evolution of a closed quantum system connects eigenspaces of initial and final Hermitian Hamiltonians for slowly driven systems, or, unitary Floquet operators for slowly modulated driven systems. We show that the connection of eigenspaces depends on a topological property of the adiabatic paths for given initial and final points. An example in slowly modulated periodically driven systems is shown. These analysis are based on the topological analysis of the exotic quantum holonomy in adiabatic closed paths.
概要：数学的言語の組織的な運用をもって社会科学を再構成することは、２１世紀の学問にとって必須の課題であると考えられる。そのような試みは経済学を除いては、未だ緒に着いたばかりである。本講演では、数理物理学的視点から社会学にアプローチする「社会物理学Sociophysics」について、筆者の最近の二つの研究、コンセンサス民主主義の分析「世論力学のバランサー理論(Balancer theory of opinion dynamics)」と民族集団興亡の数理モデル「歴史動力学のメタアサビーヤ理論(Metaasabiya theory of Cliodynamics)」とを軸にして紹介する。
参考文献：
[1] S. Galam, “Sociophysics” (Springer, 2012)
[2] T. Cheon & J. Morimoto “Balancer effects in opinion dynamics”, Phys. Lett. A 380 (2016) 429-434
[3] P. Turchin, “Historical dynamics” (Princeton, 2003)
[4] T. Cheon & S. S. Poghosyan “Spiral orbits and oscillations in historical dynamics”, KUT UQD working paper (2015)
Asymmetric quantum transport in a double-stranded Kronig-Penney model
カテゴリ
研究論文
概要
Asymmetric quantum transport in a double-stranded Kronig-Penney model
by T. Cheon & S. S. Poghosyan
We introduce a double-stranded Kronig-Penney model, and analyse its transport properties. The asymmetric fluxes between two strands with suddenly alternating localization patterns are found as the energy is varied. The zero-size limit of the internal lines connecting two strands is examined using quantum graph vertices with four edges. We also consider a two-dimensional Kronig-Penney lattice with two types of alternating layers with and connections, and show that there exist bands in which the quantum flux can flow only in select directions.
Bloch vector, disclination and exotic quantum holonomy
カテゴリ
研究論文
概要
Bloch vector, disclination and exotic quantum holonomy
by A. Tanaka & T. Cheon
Abstract
A topological formulation of the eigenspace anholonomy, where eigenspaces are interchanged by adiabatic cycles, is introduced. The anholonomy in two-level systems is identified with a disclination of the director (headless vector) of a Bloch vector, which characterizes eigenprojectors. The covering map structure behind the exotic quantum holonomy and the role of the homotopy classification of adiabatic cycles are elucidated. The extensions of this formulation to nonadiabatic cycles and -level systems are outlined.
2nd version, Last Updated on March 27, 2015, 15:30
A talk entitled "Singular vertices in quantum graphs", presented at the TMU workshop "new trend in complex quantum systems", Nov. 11, 2010 at International Hall, Tokyo Metropolitan University, Hachioji, Tokyo.
Extended version of previous quantum graph talks with some technical details, and also with updates on generalized Fulop-Tsutsui and PQRS forms.
Talk presente at NATO Advanced Research Workshop "New Challenges in Complex System Physics" at Samarkand, Uzbekistan, 20-24 May, 2013
*) quantum vertex in ST-form
*) scale anomaly and shell structure of parameters
*) scale invariant quantum graphs and Hermitian unitary S-matrix
*) inverse scattering of scale invariant graphs
*) extended Hadamard conjecture
*) threshold resonance in quantum graph with U-added control line
*) resonance coalescense and U-controlled band filter
*) U-controlled flat band filter
*) prospects of quantum graphs
Exotic quantum holonomy and non-Hermitian degeneracies in two-body Lieb-Liniger model
カテゴリ
研究論文
概要
A. Tanaka, N. Yonezawa, T. Cheon
An interplay of an exotic quantum holonomy and exceptional points is examined in one-dimensional Bose systems. The eigenenergy anholonomy, in which Hermitian adiabatic cycle induces nontrivial change in eigenenergies, can be interpreted as a manifestation of eigenenergy's Riemann surface structure, where the branch points are identified as the exceptional points which are degeneracy points in the complexified parameter space. It is also shown that the exceptional points are the divergent points of the non-Abelian gauge connection for the gauge theoretical formulation of the eigenspace anholonomy. This helps us to evaluate anti-path-ordered exponentials of the gauge connection to obtain gauge covariant quantities.
[in prettier format than the one in zrXiv; last update 16:45, 5/8/2013]
Theoretical methodology of designing equal-scattering quantum graphs with variable ratio of transmission and reflection amplitude is outlined. The key concept is the scattering matrix with generalized skew-symmetry, which guarantees the ratios between different non-diagonal elements of scattering matrix to remain independent of the incoming momentum.
人間の意思決定における背理的事象を「量子的」な確率を用いて記述しようとする試みがある。その代表例である「当然原理の破れ」および「連言錯誤」について、我々の二原著論文
T. Cheon & T. Takahashi, "Interference and inequality in quantum decision theory", Phys. Lett. A 375 (2010) 100-104
T. Cheon & T. Takahashi, "Quantum phenomenology of conjunction fallacy", J. Phys. Soc. Jpn 81 (2012) 104801(5pp)
を簡単にまとめた。
京大基礎物理研究所平成２２年度研究会「量子科学における双対性とスケール」に於ける "Egoistic-altruistic duality in quantum game theory" と題された１１月４日の講演。人間の意思決定過程の記述に量子確率を持ち込む試みを紹介する。何故量子確率なのか。量子的干渉は何を表し、量子的EPR相関は何を表すと考えられるか。そして人間の意思決定に真の意味での「量子性」がありうるのか。ハーサニィ不完備情報ゲームの量子化とベル不等式。量子確率で表された利他性とはいかなるものか。階級社会の単純ではあるが興味深い模型としての、利他的倫理を考慮したロトカ＝ヴォルテッラ系についても。
A talk entitled "Quantum mechanics in 21st century" presented in occasion for a guest appearance in RESCEU summer school "Dark energy in the universe" at Tosa Yamada, Aug. 31, 2010.
Its main assertion is that the seemingly arcane "quantum metaphysics", which had started as Bohr-Einstein debate a century ago, has gained the actual technological relevance, thanks to the increasing intrusion of quantum mechanics to our daily life.
The talk features such unconventional aspects of quantum mechnaics as quantum decision theory and Aravind's magic square.
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