Aharonov-Bohm 1
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- おきみち ひろもり
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1 Aharonov-Bohm 1. E x B z Jy c J c 1) y E x σ yx = Jy/E c x σ xx = Jx/E c x σ yx Fe,Co,Ni 2, 3) Ce,U f 1954 Karplus Luttinger KL 4) Smit Berger 5) 6) τ σ xx σ xy τ τ 2 7, 8) KL σ AH h/ τ 1954 KL 90 9) Ĥk e Ĵ k c = e kĥk Ĥk f 2000 Fe 10) 11) SrRuO 3 Ni Co 12) d f 14, 15) E x z J y s = ( h/2e) ( ) Jy Jy 16) 1
2 2. Dresselhaus 17) Rashba 18, 19) MOS / / 2 2DEG LS p Dresselhaus LS Luttinger Zhang 20) Rashba Sinova 21) Luttinger 22) 2DEG Rashba Rashba H = h2 k 2 2m + λ R(σ k) z (1) Rashba k Rashba Sinova 21) Rashba λ R e/8π λ R σ SH λ R ( h/ ) σ AH σ SH σxy αβ = ω ImKαβ (ω + i0), (2) ω=0 σ AH = σ cc xy σ SH = σ sc xy Kαβ (ω + i0) iω l = 2πilT l Jy α J x β α, β = c, s; c s K αβ (iω l ) = 1/T 0 J α x (τ)j β y (0) e iω lτ dτ (3) iω l ω + i0 (2) (3) 23) Rashba 2DEG 24, 25, 26) (1) Rashba J y(x) = +( )eλ R hσ x(y) Dresselhaus 3 Rashba 27, 28) Sr 2 RuO 4 t 2g 9 σ SH = e (τω) 2 8π 1 + (τω) 2 23, 29) τ ω 0 σ SH = 0 ω τ σ SH = e/8π 30, 31, 22) Rashba Fermi sea λ R e/8π 32) 2 Vol. 64, No. 1, 2009
3 d Pt Pt/Ni-Fe 33) / 34) n 10 4 d 4d Sr 2 RuO 4 LS Pt 35) 36) 37) Pt 38) 4d,5d (i) (ii) (iii) 3.1. Sr 2 RuO 4 Aharonov-Bohm 2 t 2g p Sr 2 RuO 4 Ru 3 xz yz xy xz yz 1(a) t = 0.2eV, t = 0.1t hopping integral xz, yz ( ) ξ(k x ) g(k) Ĥ K (k) =, (4) g(k) ξ(k y ) 1 2 xz, yz ξ(k x(y) ) = 2t cos k x(y), g(k) = 4t sin k x sin k y Ru LS ĤLS = λ i l i s i λ 0.4t(= 0.08eV) 39) 1(b) Sr 2 RuO 4 α, β xz, yz γ xy 3 0.5t -t d yz t t t d xz k y ( π,π) e 05 (π,π) e 05 k x ( π, π) γ β λ=0.4 α (π, π) 1 (a)sr 2 RuO 4 t 2g (b)sr 2 RuO 4 α, β xz, yz γ xy σ SH Sr 2 RuO 4 RuO 4 e/2π Sr 2 RuO 4 6 A Sr 2 RuO Ω 1 cm 1 Pt Ω 1 cm 1 xz t -t -t φ 0 /4 φ 0 /4 yz φ 0 /4 φ 0 /4 t xz l z = 1 i 2 xz yz AB i Aharonov-Bohm 57) 2 t 2g xy λl s l z = +1 = xz +i yz i xz yz π yz 3
4 Φ = ϕ 0 /4(ϕ 0 = hc/e ) Aharonov-Bohm(AB) l z = 1 = xz i yz AB i d, 5d Sr 2 RuO 4 Ru t 2g AB 4d,5d AB Pt 12 4d,5d Au Ag 38) Papaconstantopoulos Naval Research Laboratory tight-binding (NRL-TB) 40) full potential LDA 100K 9 s+p+d LS λ 41) Pt Pd λ 41meV 18meV (2) 3 38) n = n s + n p + n d n s + n p 1 d n 1 Au,Ag d d 3 Ir n n = 5, 6 n = 7, 8 n = n AB 2 l z = 1 AB 2 3 d half-filling n = 6 Pt Pd Nd Mo Ta 42) AB SHC (10 Ω cm ) γ = 0.02 Ry 4d 5d n d Nb Mo Tc Ru Rh Pd Ag 5d Ta W Re Os Ir Pt Au 3 NRL-TB 38) γ = h/2τ 0.02 Ry 3.3. p z π Dirac s, p x, p y σ LS 43) π undope σ LS 44) p 4 Vol. 64, No. 1, 2009
5 LS 4. AB 2 AB LS z λl z s z LS z σ SH σ SH 45) σ SH σ SH + σ SH (5) σ AH 2e h (σ SH σ SH ) (6) σ SH = σ SH = σ SH/2 n NRL-TB Fe,Ni,Co σ AH, σ SH (5) (6) σ SH σ SH Fe,Ni Co 806 [Ω 1 cm 1 ], 1087 [Ω 1 cm 1 ], 341 [Ω 1 cm 1 ] 45) 4 Fe,Ni,Co σ SH σ SH 2n 2n 4 NRL-TB 3d σ para SH d n d 6.5 4d,5d Fe,Ni,Co σ SH σ SH 2σ SH σpara SH (2n ), 2σ SH σpara SH (2n ) AB [10 3 (Ωcm) 1 ] para σ SH γ=0.002ry 2σ SH (Fe) V 2σ SH (Ni) 2σ SH (Fe) 2σ (Co) 2σ SH (Ni) 2σ SH (Co) n Cr Mn Fe Co Ni Cu 4 NRL-TB Fe,Ni,Co σsh σ (σ =, ) NRL-TB 3d σ para SH 45) n d n 1 Nd 2 Mo 2 O 7 T c = 93K 46, 47, 48, 49, 50) 48) T N 30K Nd f d-f Mo 4d θ tilted ferromagnetism T N 5(a) Mo [111] T N Mo M Mo cos θ 3 θ 2 σ AH 47, 49) 46, 48, 50) AB 51) 5(b) Mo 3/2θ Φ θ AB non-collinearity θ Nd 2 Mo 2 O 7 θ 1 51) T N Nd M Nd M Nd θ tilted ferromagnetism 5. d s d k l, l z = 2, m d s-d k l, l z d Y m 2 (k) exp(imϕ k ) ϕ k = tan 1 (k y /k x ) k ϕ k = ( k y, k x, 0)/(k 2 x + k 2 y) Ĥk s-d Ĵ k = e k Ĥ k k 5
6 θ σ SH (e/4a) l s µ / h 2 2 ( l s µ / h 2 ) 10 3 Ω 1 cm 1 (7) A C B 57) a 3A s-d τ τ d τ = AB d 5 (a)nd 2 Mo 2 O 7 (1, 1, 1) θ tilt Mo (b)mo Aharonov-Bohm 9) σ AH σ SH d 57) 90 s d d s n d y E y 6(a) y µ ee y y d E d r d d n d y = +r d y = r d s d d s LS l s µ d l z = 1 l z = +1s-d d ±1 E y > 0 6(b) s-d x +x x l s µ 3 l s µ n d < 5 n d > 5 n d < 5 n d > 5 µ-ee yy E d (a) y +r d 0 -r d (b) 6 (a) E y µ ee yy d (virtual bound state) E d (b) 6. h/ τ 9) τ h/ τ K τ h/ ρ 100 µωcm σ SH(AH) (ρ 2 +ρ 2 ) 1 9) ρ σ SH(AH) ρ 0 σ SH(AH) ρ m m 2 53, 38) 7 Ta, W σ SH m 6 Vol. 64, No. 1, 2009
7 Rashba 2DEG σ AH 13) ρ 1.6 m = 2 9) 54, 55) m (i) (ii)ρ 100 µωcm (iii) m CrO 2 m = ) µωcm m 2 SHC (10 Ω cm ) W λ = Ta λ = γ γ (Ry) 7 Ta, W γ(= h/2τ) γ 0.05Ry ρ 100µΩcm σ SH constant σ SH γ 2 ρ 2 τ T 1000K NRL-TB T = 0K T = 1000K 10% 34) Kane Mele 44) HgTe Bi d 57) LS 57) LS l s µ d Kerr orbitronics 7.3. LS 3 T (k, k ) (k k ) z σsh skew τ 2 /τ skew τ skew τ τ tot τ skew σsh skew τ ρ 1 58) Fe 59) Pt 7
8 σ sj SH σ sj SH (7) 60) 8. d d AB l s µ d n d 3 σ SH σ SH d AB Prof. Gerrit Bauer 9) Prof. J. Sinova 1) E. H. Hall, Amer. J. Math. 2, 287 (1879). 2) E. H. Hall, Philos. Mag. 19, 301 (1880). 3) A. Kundt, Annalen der Phys. und Chemie, 49, 257 (1893). 4) R. Karplus and J. M. Luttinger: Phys. Rev. 95 (1954) ) J. Smit: Physica 24 (1958) 39. 6) L. Berger, Phys. Rev. B 2 (1970) ) J. M. Ziman: Electrons and Phonons (Clarendon, Oxford, 1960). 8) τ H. Kontani, Rep. Prog. Phys. 71 (2008) ) H. Kontani and K. Yamada: J. Phys. Soc. Jpn. 63 (1994) ) Y. Yao, L. Kleinman, A.H. MacDonald, J. Sinova, T. Jungwirth, D.S. Wang, E. Wang and Q. Niu: Phys. Rev. Lett. 92 (2004) ) Z. Fang, N. Nagaosa, K. Takahashi, A. Asamitsu, R. Mathieu, T. Ogasawara, H. Yamada, M. Kawasaki, Y. Tokura, and K. Terakura, Science 302 (2003) ) X. Wang, D. Vanderbilt, J. R. Yates, and I. Souza, Phys. Rev. B 76, (2007). 13) N. Nagaosa, J. Sinova, S. Onoda, A.H. MacDonald, and N.P. Ong, arxiv: ) M. I. Dyakonov et al., Zh. Eksp. Teor. Fiz. Pis ma Red. 13, 657 (1971). 15) J. E. Hirsh et al., Phys. Rev. Lett. 83, 1834 (1999). 16) S. Takahashi et al., J. Phys. Soc. Jpn. 77, (2008). 17) G. Dresselhaus, Phys. Rev. 100, 580 (1955). 18) E. I. Rashba, Fiz. Tverd. Tela 2, 1224 (1960) [ Sov. Phys. Solid State 2, 1109 (1960)]. 19) Yu. A. Bychkov and E. I. Rashba, Pis ma Zh. Eksp. Teor. Fiz. 39, 66 (1984) [JETP Lett. 39, 78 (1984). 20) S. Murakami, N. Nagaosa, and S. C. Zhang, Science 301, 1348 (2003). 21) J. Sinova, D. Culcer, Q. Niu, N. A. Sinitsyn, T. Jungwirth, and A. H. MacDonald: Phys. Rev. Lett. 92 (2004) ) 62 (2007) 2. 23) J. Inoue, G. E. W. Bauer, and L. W. Molenkamp, Phys. Rev. B70 (2004) (R). 24) J. Inoue, T. Kato, Y. Ishikawa, H. Itoh, G. E. W. Bauer, and L. W. Molenkamp, Phys. Rev. Lett., 97, (2006). 25) T. Kato, Y. Ishikawa, H. Itoh, and J. Inoue, New J. Phys. 9, 350 (2007). 26) T. Kato, Y. Ishikawa, H. Itoh, and J. Inoue, Phys. Rev. B 77, (2008). 27) S. Murakami, Phys. Rev. B 69, (R)(2004). 28) B. A. Bernevig and S C. Zhang, Phys. Rev. Lett. 95, (2005). 29) J. Inoue, T. Kato, G. E. W. Bauer, and L. W. Molenkamp, Semicond. Sci. Technol. 24, (2009). 30) Y. K. Kato, R. C. Myers, A. C. Gossard, and D. D. Awschalom, Science 306, 1910 (2004). 31) J. Wunderlich, B. Kaestner, J. Sinova, and T. Jungwirth, Phys. Rev. Lett. 94, (2005). 32) H. Kontani, J. Goryo, and D. S. Hirashima: Phys. Rev. Lett. 102, (2009). 33) E. Saitoh, M. Ueda, H. Miyajima and G. Tatara, Appl. Phys. Lett. 88 (2006) ) T. Kimura, Y. Otani, T. Sato, S. Takahashi, and S. Maekawa: Phys. Rev. Lett. 98 (2007) ; L. Vila, T. Kimura, and Y. Otani, Phys. Rev. Lett. 99 (2007) Vol. 64, No. 1, 2009
9 35) H. Kontani, T. Tanaka, D.S. Hirashima, K. Yamada, and J. Inoue, Phys. Rev. Lett. 100, (2008). 36) G.Y. Guo, S. Murakami, T.-W. Chen, N. Nagaosa, Phys. Rev. Lett. 100, (2008). 37) H. Kontani, M. Naito, D.S. Hirashima, K. Yamada, and J. Inoue: J. Phys. Soc. Jpn. 76 (2007) ) T. Tanaka, H. Kontani, M. Naito, T. Naito, D. S. Hirashima, K. Yamada, and J. Inoue, Phys. Rev. B 77, (2008). 39) K.K. Ng and M. Sigrist., Europhys. Lett. 49, 473 (2000). 40) M.J. Mehl and D.A. Papaconstantopoulos: Phys. Rev. B 54 (1996) ) F. Herman and S. Skillman, Atomic Structure Calculations (Prentice-Hall, Englewood Cliffs, NJ, 1963). 42) 63 (2008) ) S. Onari, Y. Ishikawa, H. Kontani, and J. Inoue, Phys. Rev. B 78, (R) (2008). 44) C.L. Kane and E.J. Mele, Phys. Rev. Lett. 95, (2005). 45) T. Naito, D. S. Hirashima, and H. Kontani: unpublished. 46) S. Yoshii, S. Iikubo, T. Kageyama, K. Oda, Y. Kondo, K. Murata, and M. Sato, J. Phys. Soc. Jpn. 69 (2000) ) Y. Taguchi and Y. Tokura, Europhys. Lett. 54 (2001) ) Y. Yasui, Y. Kondo, M. Kanada, M. Ito, H. Harashina, M. Sato, and K. Kakurai, J. Phys. Soc. Jpn. 70 (2001) ) Y. Taguchi, T. Sasaki, S. Awaji, Y. Iwasa, T. Tayama, T. Sakakibara, S. Iguchi, T. Ito, and Y. Tokura, Phys. Rev. Lett. 90, (2003). 50) Y. Yasui, T. Kageyama, T. Moyoshi, M. Soda, M. Sato and K. Kakurai, J. Phys. Soc. Jpn. 75 (2006) ; θ 2 3 Tesla 51) T. Tomizawa and H. Kontani, Phys. Rev. B 80, (R) (2009); Nd 2 Mo 2 O 7 λj df / (J df ) 2 / J df 10K d-f λ 1000K Mo LS Nd 2Mo 2O 7 E 1000K θ J df /E 1 52) 59 (2004) ) H. Kontani, T. Tanaka and K. Yamada, Phys. Rev. B 75, (2007). 54) T. Miyasato, N. Abe, T. Fujii, A. Asamitsu, S. Onoda, Y. Onose, N. Nagaosa, and Y. Tokura, Phys. Rev. Lett. 99, (2007). 55) D. Satoh, K. Okamoto, and T. Katsufuji, Phys. Rev. B 77, (R) (2008). 56) W. R. Branford, K. A. Yates, E. Barkhoudarov, J. D. Moore, K. Morrison, F. Magnus, Y. Miyoshi, P. M. Sousa, O. Conde, A. J. Silvestre, and L. F. Cohen, Phys. Rev. Lett. 102, (2009). 57) H. Kontani, T. Tanaka, D. S. Hirashima, K. Yamada, and J. Inoue, Phys. Rev. Lett. 102, (2009). 58) T. Tanaka and H. Kontani, New J. Phys. 11 (2009) ) G.Y. Guo, S. Maekawa, and N. Nagaosa, Phys. Rev. Lett. 102, (2009). 60) T. Tanaka and H. Kontani: unpublished. ( ) Anomalous Hall effect and spin Hall effect in transiton metals Hiroshi Kontani, Dai S. Hirashima, and Jun-ichiro Inoue abstract: In metals, various kinds of Hall effects emerge, in addition to normal Hall effect under magnetic field. One example is the anomalous Hall effect in ferromagnets, and another example is the spin Hall effect in paramagnetic metals. These unconventional Hall effects without magnetic field have been attracting increasing attention, in terms of both fundamental interest and spintronics architecture. In this review article, we discuss the recent progress in intrinsic Hall effect that is essentially independent of randomness or impurities. We explain that the origin of commonly-observed giant intrinsic Hall effect in transition metals is the Berry phase induced by the d-orbital degrees of freedom. 9
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( 2) 3.4 5 (b),(c) [ 5 (a)] [ 5 (b)] [ 5 (c)] (extrinsic) skew scattering side jump [] [2, 3] (intrinsic) 2 Sinova 2 heavy-hole light-hole ( [4, 5, 6] ) Sinova Sinova 3. () 3 3 Ṽ = V (r)+ σ [p V (r)] λ
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5 S 2 tot = S 2 T (y, t) + S 2 (y) = const. Z 2 (4.22) σ 2 /4 y = y z y t = T/T 1 2 (3.9) (3.15) s 2 = A(y, t) B(y) (5.1) A(y, t) = x d 1+α dx ln u 1 ] 2u ψ(u), u = x(y + x 2 )/t s 2 T A 3T d S 2 tot S
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62 2017 7 25-29 - ARPES ARPES ARPES - ARPES 1 1.1 1.2 1.3 1.4 1.4.1 1.4.2 1.4.3 1.5 2 2.1 2.2 2.3 BCS 2.4 1 1.1 hν A(k,ε)[ k ρ(ω)] [1] A(k,ε) ε k μ f(ε) 1/[1 + exp( ε μ k B T )] A(k,ε)f(ε) ρ(ε)f(ε) A(k,ε)(1
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液晶の物理１：連続体理論（弾性，粘性）
The Physics of Liquid Crystals P. G. de Gennes and J. Prost (Oxford University Press, 1993) Liquid crystals are beautiful and mysterious; I am fond of them for both reasons. My hope is that some readers
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2005 9/8-11 2 2.2 ( 2-5) γ ( ) γ cos θ 2πr πρhr 2 g h = 2γ cos θ ρgr (2.1) γ = ρgrh (2.2) 2 cos θ θ cos θ = 1 (2.2) γ = 1 ρgrh (2.) 2 2. p p ρgh p ( ) p p = p ρgh (2.) h p p = 2γ r 1 1 (Berry,1975) 2-6
Gauss Gauss ɛ 0 E ds = Q (1) xy σ (x, y, z) (2) a ρ(x, y, z) = x 2 + y 2 (r, θ, φ) (1) xy A Gauss ɛ 0 E ds = ɛ 0 EA Q = ρa ɛ 0 EA = ρea E = (ρ/ɛ 0 )e
7 -a 7 -a February 4, 2007 1. 2. 3. 4. 1. 2. 3. 1 Gauss Gauss ɛ 0 E ds = Q (1) xy σ (x, y, z) (2) a ρ(x, y, z) = x 2 + y 2 (r, θ, φ) (1) xy A Gauss ɛ 0 E ds = ɛ 0 EA Q = ρa ɛ 0 EA = ρea E = (ρ/ɛ 0 )e z
2 1 1 α = a + bi(a, b R) α (conjugate) α = a bi α (absolute value) α = a 2 + b 2 α (norm) N(α) = a 2 + b 2 = αα = α 2 α (spure) (trace) 1 1. a R aα =
1 1 α = a + bi(a, b R) α (conjugate) α = a bi α (absolute value) α = a + b α (norm) N(α) = a + b = αα = α α (spure) (trace) 1 1. a R aα = aα. α = α 3. α + β = α + β 4. αβ = αβ 5. β 0 6. α = α ( ) α = α
変 位 変位とは 物体中のある点が変形後に 別の点に異動したときの位置の変化で あり ベクトル量である 変位には 物体の変形の他に剛体運動 剛体変位 が含まれている 剛体変位 P(x, y, z) 平行移動と回転 P! (x + u, y + v, z + w) Q(x + d x, y + dy,
変 位 変位とは 物体中のある点が変形後に 別の点に異動したときの位置の変化で あり ベクトル量である 変位には 物体の変形の他に剛体運動 剛体変位 が含まれている 剛体変位 P(x, y, z) 平行移動と回転 P! (x + u, y + v, z + w) Q(x + d x, y + dy, z + dz) Q! (x + d x + u + du, y + dy + v + dv, z +
1 9 v.0.1 c (2016/10/07) Minoru Suzuki T µ 1 (7.108) f(e ) = 1 e β(e µ) 1 E 1 f(e ) (Bose-Einstein distribution function) *1 (8.1) (9.1)
1 9 v..1 c (216/1/7) Minoru Suzuki 1 1 9.1 9.1.1 T µ 1 (7.18) f(e ) = 1 e β(e µ) 1 E 1 f(e ) (Bose-Einstein distribution function) *1 (8.1) (9.1) E E µ = E f(e ) E µ (9.1) µ (9.2) µ 1 e β(e µ) 1 f(e )
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3 3. 3.. H H = H + V (t), V (t) = gµ B α B e e iωt i t Ψ(t) = [H + V (t)]ψ(t) Φ(t) Ψ(t) = e iht Φ(t) H e iht Φ(t) + ie iht t Φ(t) = [H + V (t)]e iht Φ(t) Φ(t) i t Φ(t) = V H(t)Φ(t), V H (t) = e iht V (t)e
main.dvi
6 FIR FIR FIR FIR 6.1 FIR 6.1.1 H(e jω ) H(e jω )= H(e jω ) e jθ(ω) = H(e jω ) (cos θ(ω)+jsin θ(ω)) (6.1) H(e jω ) θ(ω) θ(ω) = KωT, K > 0 (6.2) 6.1.2 6.1 6.1 FIR 123 6.1 H(e jω 1, ω
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9 7 A = A x x + A y y + A, B = B x x + B y y + B, C = C x x + C y y + C..6 x y A B C = A x x + A y y + A B x B y B C x C y C { B = A x x + A y y + A y B B x x B } B C y C y + x B y C x C C x C y B = A
) a + b = i + 6 b c = 6i j ) a = 0 b = c = 0 ) â = i + j 0 ˆb = 4) a b = b c = j + ) cos α = cos β = 6) a ˆb = b ĉ = 0 7) a b = 6i j b c = i + 6j + 8)
4 4 ) a + b = i + 6 b c = 6i j ) a = 0 b = c = 0 ) â = i + j 0 ˆb = 4) a b = b c = j + ) cos α = cos β = 6) a ˆb = b ĉ = 0 7) a b = 6i j b c = i + 6j + 8) a b a b = 6i j 4 b c b c 9) a b = 4 a b) c = 7
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4. ϵ(ν, T ) = c 4 u(ν, T ) ϵ(ν, T ) T ν π4 Planck dx = 0 e x 1 15 U(T ) x 3 U(T ) = σt 4 Stefan-Boltzmann σ 2π5 k 4 15c 2 h 3 = W m 2 K 4 5.
A 1. Boltzmann Planck u(ν, T )dν = 8πh ν 3 c 3 kt 1 dν h 6.63 10 34 J s Planck k 1.38 10 23 J K 1 Boltzmann u(ν, T ) T ν e hν c = 3 10 8 m s 1 2. Planck λ = c/ν Rayleigh-Jeans u(ν, T )dν = 8πν2 kt dν c
7 π L int = gψ(x)ψ(x)φ(x) + (7.4) [ ] p ψ N = n (7.5) π (π +,π 0,π ) ψ (σ, σ, σ )ψ ( A) σ τ ( L int = gψψφ g N τ ) N π * ) (7.6) π π = (π, π, π ) π ±
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7 7. ( ) SU() SU() 9 ( MeV) p 98.8 π + π 0 n 99.57 9.57 97.4 497.70 δm m 0.4%.% 0.% 0.8% π 9.57 4.96 Σ + Σ 0 Σ 89.6 9.46 K + K 0 49.67 (7.) p p = αp + βn, n n = γp + δn (7.a) [ ] p ψ ψ = Uψ, U = n [ α
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II Karel Švadlenka * [1] 1.1* 5 23 m d2 x dt 2 = cdx kx + mg dt. c, g, k, m 1.2* u = au + bv v = cu + dv v u a, b, c, d R
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II Karel Švadlenka 2018 5 26 * [1] 1.1* 5 23 m d2 x dt 2 = cdx kx + mg dt. c, g, k, m 1.2* 5 23 1 u = au + bv v = cu + dv v u a, b, c, d R 1.3 14 14 60% 1.4 5 23 a, b R a 2 4b < 0 λ 2 + aλ + b = 0 λ =
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C-2 NiS A, NSRRC B, SL C, D, E, F A, B, Yen-Fa Liao B, Ku-Ding Tsuei B, C, C, D, D, E, F, A NiS 260 K V 2 O 3 MIT [1] MIT MIT NiS MIT NiS Ni 3 S 2 Ni
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The Structure and Evolution of Stars I. Basic Equations. M r r =4πr2 ρ () P r = GM rρ. r 2 (2) r: M r : P and ρ: G: M r Lagrange r = M r 4πr 2 rho ( ) P = GM r M r 4πr. 4 (2 ) s(ρ, P ) s(ρ, P ) r L r T
リサイクルデータブック2016
AppendixEU SDGs2159EU 21512UNEPOECD2165G7 2165 213 Appendix 1 EU 2 EU 3 215 i CONTENTS i 1 213 1 213 2 1 4 2 2 6 3 3 6 4 213 7 4 5 9 6 213 9 5 7 1 8 213 1 9 11 1 213 11 11 213 11 6 6.1 12 213 14 6.2 13
23 1 Section ( ) ( ) ( 46 ) , 238( 235,238 U) 232( 232 Th) 40( 40 K, % ) (Rn) (Ra). 7( 7 Be) 14( 14 C) 22( 22 Na) (1 ) (2 ) 1 µ 2 4
23 1 Section 1.1 1 ( ) ( ) ( 46 ) 2 3 235, 238( 235,238 U) 232( 232 Th) 40( 40 K, 0.0118% ) (Rn) (Ra). 7( 7 Be) 14( 14 C) 22( 22 Na) (1 ) (2 ) 1 µ 2 4 2 ( )2 4( 4 He) 12 3 16 12 56( 56 Fe) 4 56( 56 Ni)
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X X 1 1 2 Free Electron Laser: FEL 2.1 2 2 3 SACLA 4 SACLA [1]-[6] [7] 1: S N λ [9] XFEL OHO 13 X [8] 2 2.1 2(a) (c) z y y (a) S N 90 λ u 4 [10, 11] Halbach (b) 2: (a) (b) (c) (c) 1 2 [11] B y = n=1 B
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C 3 C-1 Ru 2 x Fe x CrSi A A, A, A, A, A Ru 2 x Fe x CrSi 1) 0.3 x 1.8 2) Ru 2 x Fe x CrSi/Pb BTK P Z 3 x = 1.7 Pb BTK P = ) S.Mizutani, S.Ishid
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6 2 T γ T B (6.4) (6.1) [( d nm + 3 ] 2 nt B )a 3 + nt B da 3 = 0 (6.9) na 3 = T B V 3/2 = T B V γ 1 = const. or T B a 2 = const. (6.10) H 2 = 8π kc2
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128 3 II S 1, S 2 Φ 1, Φ 2 Φ 1 = { B( r) n( r)}ds S 1 Φ 2 = { B( r) n( r)}ds (3.3) S 2 S S 1 +S 2 { B( r) n( r)}ds = 0 (3.4) S 1, S 2 { B( r) n( r)}ds
127 3 II 3.1 3.1.1 Φ(t) ϕ em = dφ dt (3.1) B( r) Φ = { B( r) n( r)}ds (3.2) S S n( r) Φ 128 3 II S 1, S 2 Φ 1, Φ 2 Φ 1 = { B( r) n( r)}ds S 1 Φ 2 = { B( r) n( r)}ds (3.3) S 2 S S 1 +S 2 { B( r) n( r)}ds
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9 AR (i) (ii) MA (iii) (iv) (v) 9.1 2 1 AR 1 9.1.1 S S y j = (α i + β i j) D ij + η j, η j = ρ S η j S + ε j (j =1,,T) (1) i=1 {ε j } i.i.d(,σ 2 ) η j (j ) D ij j i S 1 S =1 D ij =1 S>1 S =4 (1) y j =
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33 Non-destructive Measurement of Retained Austenite Content in Austempered Ductile Iron Yoshio Kato, Sen-ichi Yamada, Takayuki Kato, Takeshi Uno Austempered Ductile Iron (ADI) 100kg/mm 2 10 ADI 10 X ADI
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