| 日時: | 2016-06-24 17:00 - 18:30 |
| 場所: | 研究本館 3階 セミナー室322 |
| 題目: | Thermodynamic entropy as a Noether invariant |
| 講演者: | 横倉 祐貴（理研） |
| 概要: | We study a classical many-particle system with an external
control represented by a time-dependent extensive parameter in a
Lagrangian. We show that thermodynamic entropy of the system is
uniquely characterized as the Noether invariant associated with a
symmetry for an infinitesimal non-uniform time translation $t\to
t+\eta\hbar \beta$, where $\eta$ is a small parameter, $\hbar$ is the
Planck constant, $\beta$ is the inverse temperature that depends on the
energy and control parameter, and trajectories in the phase space are
restricted to those consistent with quasi-static processes in
thermodynamics. References: [1]Phys. Rev. Lett. 116, 140601 (2016) |
| 日時: | 2016-02-25 15:00 - 16:30 |
| 場所: | 研究本館 3階 セミナー室322 |
| 題目: | 共変解析力学の基礎と応用 |
| 講演者: | 中嶋 慧（筑波大学大学院） |
| 概要: | 通常の解析力学のハミルトン形式は、時間を特別扱いし、共変が自明ではない。
また、ゲージ場や重力場は第1種の拘束系となり、ゲージ固定やDirac括弧の使用
が必要となる。共変解析力学は、微分形式を基本変数とすることで、明確に一般
座標共変(不変)に定式化され、時間と空間を平等に扱う。また、ゲージ場や重力
場は非拘束系となり、ゲージ固定は不要となる。共変解析力学のラグランジュ形
式は数十年前から知られていた[1,2]が、2002年に中村[3]によってハミルトン形
式へと拡張され、電磁場に適用された。2012年に神長[4]によって数学的に厳密
に定式化され、Dirac場と結合しない重力場へと応用された。また、Nesterも独
立にハミルトン形式に達した[5]。
私は、共変解析力学に初めてポアソン括弧を導入した[6,7]。また、De Donder-
Weyl理論[8]との関係を初めて明らかにした[7]。さらに、共変解析力学をDirac
場[6,7]と、Dirac場と結合した重力場[6]へ初めて適用した。先行研究とあわせ
て、全ての基本的な場の理論に共変解析力学が適用可能であることが分かった。
本講演では、共変解析力学を詳しく解説した後に、Dirac場, Dirac場と結合した
重力場への適用について報告する。 References: [1]B. Kuchowicz, , Acta Cosmologica, Zesz. 3, 109 (1975). [2]A. Trautman, Annals of the New York Academy of Sciences 262, 241 ( 1975). [3]中村匡, 物性研究79, 2 (2002). [4]Y. Kaminaga, EJTP 9, 199 (2012). [5]J. M. Nester, Classical and Quantum Gravity 21, S261 (2004). [6]S. Nakajima, arXiv:1510.09048 (EJTPに受理済). [7]S. Nakajima, 準備中. [8]I. V. Kanatchikov , Rept. Math. Phys. 41, 49 (1998). |
| 日時: | 2016-01-07 15:00 - 16:30 |
| 場所: | 研究本館 3階 セミナー室322 |
| 題目: | Spiral orbits and oscillations in historical dynamics - Can rise and fall of empires be understood mathematically? |
| 講演者: | 全 卓樹（高知工科大学） |
| 概要: | 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.
References: T.Cheon & S.S.Poghosyan, Spiral orbits and oscillations in historical dynamics, KUT UQD preprint (2015) |
| 日時: | 2015-10-29 15:00 - 16:30 |
| 場所: | 研究本館 3階 セミナー室322 |
| 題目: | Black Hole Information Paradox: a Door to New Physics? |
| 講演者: | Sujoy.K.Modak |
| 概要: | Black hole information paradox (BHIP) is an old but unsolved problem. There is an intense controversy regarding a satisfactory resolution of the problem, which, in our point of view may lead to new physics. We consider a novel approach to address this issue. The idea is based on adapting, to the situation at hand, the modified versions of quantum theory involving spontaneous stochastic dynamical collapse of quantum states, which have been considered in attempts to deal with shortcomings of the standard Copenhagen interpretation of quantum mechanics, in particular, the issue known as "the measurement problem". The new basic hypothesis is that this modified (stochastic) quantum behavior is enhanced in the region of high curvature so that the information encoded in the initial quantum state of the matter fields is rapidly erased as the black hole singularity is approached. We show that in this manner the complete evaporation of the black hole via Hawking radiation can be understood as involving no paradox.
References: [1] S. K. Modak, L. Ortíz, I. Peña and D. Sudarsky, Phys. Rev. D 91, 124009 (2015). [2] S. K. Modak, L. Ortíz, I. Peña and D. Sudarsky, Gen. Rel. Grav. 47, 120 (2015). |
| 日時: | 2015-10-22 15:00 - 16:30 |
| 場所: | 研究本館 3階 セミナー室322 |
| 題目: | Quantum Energy Teleportation: Strong Local Passivity vs. LOCC |
| 講演者: | 堀田 昌寛 (東北大学) |
| 概要: | Quantum Energy teleportation (QET) is a protocol that allows one to teleport energy making use of pre-existing entanglement of the ground state of quantum many-body systems or quantum fields. I will review the latest results on QET and I will explain its implications on information thermodynamics, such as quantum Maxwell demons and Black Hole thermodynamics. I will also comment on current experimental prospects for QET via the quantum Hall effect. |
| 日時: | 2015-09-27 13:00 - 14:30 |
| 場所: | 研究本館 3階 セミナー室322 |
| 題目: | Counterfactual Communication |
| 講演者: | Lev Vaidman (Tel Aviv University) |
| 概要: | Counterfactual communication is a communication without particles in the transmission channel. Since there are no particles to observe, it apparently cryptographically secure because Eve has nothing to eavesdrop on. However, the issue is highly controversial. I will describe: interaction-free measurements, counterfactual key distribution, and direct counterfactual communication protocols. Analyzing the weak trace left in the transmission channel, I will argue that counterfactual communication is possible only for one bit value. |
| 日時: | 2015-09-25 15:00 - 16:30 |
| 場所: | 研究本館 3階 セミナー室322 |
| 題目: | Asking Photons Where They Have Been |
| 講演者: | Lev Vaidman (Tel Aviv University) |
| 概要: | Experimental evidence obtained from photons passing through a nested Mach-Zehnder interferometer shows that they have been in the parts of the interferometer through which they could not have possibly pass. The meaning of these results and numerous objections are discussed. It is argued that the most simple and clear explanation is given in the framework of the two-state vector formalism of quantum theory. |
| 日時: | 2015-07-28 13:30 - 15:00 |
| 場所: | 研究本館 3階 セミナー室322 |
| 題目: | BPS Monopole in the Space of Boundary Conditions |
| 講演者: | Satoshi Ohya (Institute of Quantum Science, Nihon-Univ) |
| 概要: | The space of all possible boundary conditions that respect self-adjointness of Hamiltonian operator is known to be given by the group manifold U(2) in one-dimensional quantum mechanics. In this talk we study non-Abelian Berry’s connections in the space of boundary conditions in a simple quantum mechanical system: We consider a system for a free spinless particle on a circle with two point-like interactions described by the U(2) ¥times U(2) family of boundary conditions. We show that, for a certain SU(2) ¥subset U(2) ¥times U(2) subfamily of boundary conditions, all the energy levels become doubly-degenerate thanks to the so-called higher-derivative supersymmetry, and non-Abelian Berry’s connection in the ground-state sector is given by the Bogomolny-Prasad-Sommerfield (BPS) monopole of SU(2) Yang-Mills-Higgs theory. We also show that, in the ground-state sector of this quantum mechanical model, matrix elements of position operator give the adjoint Higgs field that satisfies the BPS equation. It is also discussed that Berry’s connections in the excited-state sectors are given by non-BPS ‘t Hooft-Polyakov monopoles. |
| 日時: | 2015-07-08 15:00 - 16:30 |
| 場所: | 研究本館 3階 セミナー室322 |
| 題目: | 量子測定理論の数学的定式化・量子論と確率の諸解釈 |
| 講演者: | Shogo Tanimura (Graduate School of Information Science, Nagoya-Univ) |
| 概要: | 量子測定理論は，素朴な「波束の収縮」仮説に訴えることなく，量子系の測定に
おける確率と状態変化を記述する理論である．このセミナーでは、 量子測定理
論の基本概念である POVM (probability-operator valued measure), CP map
(completely positive map), instrument と，間接測定モデル表現を解説する．
また，量子論の解釈に関しては諸説あるが，波動関数の確率解釈を言うにして
も，確率自体の解釈に関しても諸説ある．確 率の解釈を吟味しないことには，
量子論の解釈を分析することもできないと思われるので，確率の解釈に関する議
論を整理したいと思う．ちなみ に，私は，波動関数や状態ベクトルやヒルベル
ト空間は，ミクロ系の内に宿った実体のようなものと捉えるべきではなく，ミク
ロ系とマクロ系の間 の橋渡し・窓口のようなものとみなすのがよいと考えてい
る．そういう意味で，代数的量子論におけるヒルベルト空間のGNS構成が適切な
数理だ と考えている．
References: [1] M. Ozawa, "Uncertainty relations for noise and disturbance in generalized quantum measurements", Ann. Phys. 311: 350-416 (2004). http://www.sciencedirect.com/science/article/pii/S0003491604000089 [2] 小澤正直「量子測定理論入門」（第56回物性若手夏の学校(2011年度) 講義 ノート），物性研究 97巻 1031-1057 (2012). http://ci.nii.ac.jp/naid/110009327893 [3] D. ギリース（中山智香子 訳）「確率の哲学理論」日本経済評論社 (2004). [4] 松原 望「入門ベイズ統計 : 意思決定の理論と発展」東京図書 (2008). [5] 谷村省吾「21世紀の量子論入門」 第15回：観測問題の基本概念（「理系への数学」（現代数学社）2011年7月号 pp.56-61）, 第16回：測定における確率則と遷移則（「理系への数学」（現代数学社）2011年 8月号pp.56-61）. [6] 谷村省吾「波動関数は実在するか ― 物質的存在ではない．二つの世界をつ なぐ窓口である」 数理科学2013年12月号 14-21. http://www.phys.cs.is.nagoya-u.ac.jp/~tanimura/paper/mathsci2013.pdf [7] 谷村省吾「量子力学 ― 歴史・骨子・展開，そして基礎付け」 数理科学2015 年2月号 26-32. |
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