(e ) (µ ) (τ ) ( (ν e,e ) e- (ν µ,µ ) µ- (ν τ,τ ) τ- ) ( ) ( ) ( ) (SU(2) ) (W +,Z 0,W ) * 1) [ ] [ ] [ ] ν e ν µ ν τ e µ τ, e R,µ R,τ R (2.1a
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1 (e ) (µ ) (τ ) ( (ν e,e ) e- (ν µ,µ ) µ- (ν τ,τ ) τ- ) ( ) ( ) ( ) (SU(2) ) (W +,Z 0,W ) * 1) [ ] [ ] [ ] ν e ν µ ν τ e µ τ, e R,µ R,τ R (2.1a) L ( ) ) * 2) W Z 1/2 ( - ) d u + e + ν e L L µ e + ν e + ν µ µ e * 1) * 2) SU(3) µ e + ν e + ν µ (2.2)
2 µ eγ µ e + γ < (2.3) ν e ν µ π π π + µ + + ν µ 2.1: µ eγ ( 2.2(b)) ν µ (ν e )( 2.2(a) ) ( 2.2(c)(d)) : (a) d (b) π + u d W + µ + ν µ (c)(d)(e) ν e,ν µ,ν τ ( ) e + e + τ + τ + (2.4a) e + ν e + ν τ τ (2.4b) µ+ ν µ + ν τ ν τ ν τ ν e (ν µ ) τ e(µ) + γ ν e (ν µ ) µ eγ, τ µγ e + X µ+y ( )
3 2 3 Z e + e + Z {(q i + q i ) + (l i + l + i ) + (ν i + ν i )} (2.5) i Z 2m i m Z * 3) BR = Γ(Z ) Γ(Z all) (2.6) e e + E(e e + ) = m z σ(e e + hadrons) = σ(e e + Z)BR(Z hadrons) (2.7) ( 2.3) N ν = ± (2.8) 2.3: e + e + Z N ν =3,4,5 m z /2 ( ) T D ( ) Ω B (= ρ B /ρ c, ρ c = 3H0 2 /8πG) D/H Ω B 2.4 D/H WMAP Ω B N ν WMAP ( 2.4 ) D/H = 2.6 ± 0.4, Y = ± N ν = (2σ ) * 4) * 3) m Z = 91GeV,m top = 185GeV m u 3MeV,m s 6MeV,m s 120MeV,m c 1.3GeV,m b 4.2GeV m e 0.51MeV,m µ = 105.7MeV,m τ 1777MeV * 4) V.Barger et al., Phys. Lett. B566 (2003) 8-18 hep-ph/
4 : (G.Steigman; Neutrino06) D/H Y(He) 2σ WMAP N ν N ν = (1930) 30 (1956) ν e + p (e + +W ) + p e + + n (2.9a) e + + e γ + γ (2.9b) n +Cd Cd Cd + (3 4) γ s W e + W p( u ) (d ) 2m e m ( ) ( ) 2.5 1kW /sec/cm ( ) 20
5 : Reines-Cowan(1954) γ (Cd) d(p d ) u(p u ) + e (p e ) + ν e (p ν ) (2.10) ( ) Z H f i =< f H (x)d 4 x i > = G Z β 2 G β = G F cosθ C d 4 xe i(p e+p ν )x < f u(x)γ µ (1 γ 5 )d(x) i > [u(p e )γ µ (1 γ 5 )v(p ν )] (2.11a) (2.11b) d u < u j µ (x) d > u(p u )γ µ (1 γ 5 )d(p d )e i(p d p u )x (2.12) (= E) u(p u )γ µ u(p d ) δ µ0, u(p u )γ µ γ 5 u(p d ) (0,σ) (2.13a) MeV/c 1/p m m (p e + p ν )x 1 e i(p e+p ν )x 1 Z Z < 1τ + >= d 3 xφ f (x)1τ + Φ i (x), < στ + >= d 3 xφ f (x)στ + Φ i (x), (2.14) τ ± n p eν 1 J = 0, J = 0,±1
6 2 6 H f i H fi 2 (2.14) dγ = G2 β 2π M 3 2 F(Z,E)p e E e p ν E ν de e (2.15a) p ν E ν = (E 0 E e ) (E 0 E e ) 2 m 2 ν, E 0 = M(Z,A) M(Z + 1,A) m ν = E e,max (2.15b) M 2 = < 1 > 2 + C GT 2 < σ > 2 (2.15c) F(Z,E) [ ] dγ/de 1/2 e K(E) = (2.16) F(Z,E)p e E e m ν = 0 K(E) E 0 E e ( 2.6) m ν 0 2.6: ( ) m ν 0 ( ) (σ) (1) E 0 m ν E 0 ( 3 H, E 0 = 18KeV ) E e = E 0 E 0 E e > E 0 ε = R E0 E 0 E2 (E 0 E) 2 ( ) de 3 R E0 0 E 2 (E 0 E) 2 de = 10 (2.17) E 0
7 2 7 = 1eV ε m ν 2.7: ) (2) E E 2.7 R OP (E) E EL(E) BS(E) N(E ) Z N(E) obs = N(E )R(E,E )de (2.18) ( 2.6 (3) V p ν E ν = P i (E 0 V i E e ) i (E 0 V i E e ) 2 m 2 ν) (2.19) P i i * 5) 2.8 p/p = 0.02%( E = 8eV ) E eV m ν = 0 m ν < 13eV KATRIN KATRIN 2.9 * 6) * 7) * 8) 10 m ν < 0.23eV (MAC-EF=Magnetic Adiabatic Collimator with Electrostatic Field) 2.10 B s B D B min ( ) ( 2π) E T = µ B, µ = E T B = (2.20) * 5) Phys. Lett. B187(1987) * 6) katrin/index.html * 7) Phys. Lett. B460 (1999) 219 * 8) Phys. Lett. B460 (1999)
8 : m ν = 0 m ν < 13eV 2.9: ATRIN: m ν < 0.2eV
9 : KATRIN ( µ ) (E T ) min = µb min (2.21) E 0 > E e > E 0 (E T ) min E (E T ) min = E e B min 18KeV T B max 6T m ν < 0.23eV 1eV (2.22) 2.10 (2006) m ν < 2.3eV π + (p) µ + (q) + ν µ (k) (2.23) π m π = q 2 + m 2 µ + k 2 + m 2 ν, k = k = q = q (2.24a)
10 : m ν < 2.3eV 90%CL q m π = ± MeV m µ = ± MeV m 2 ν = ± (2.25a) q = ± MeV m νµ < 0.17MeV (90%CL) (2.25b) * 9) e e + π + e + e + τ + τ m 2 ν = E(ν) 2 p(ν) 2 = (m τ i τ ± π ± + π + + π + ν τ E(π i )) 2 ( p(π i )) 2, E(π i ) = i p(π i ) 2 + m 2 π (2.26a) (2.26b) (2.26c) m τ = MeV m ν τ < 18.2MeV (95%CL) (2.27) m νi 0.3 1eV (2.28) i * 9) K.AssamaganPhys. Rev. D53(1996) 6065
11 2 11 Ω ν < (95%CL) Ω ν 2.12: ( ) ( ) (m) m m 2 23 = m 2 3 m (2.29a) m 2 12 = m 2 2 m (2.29b) m 2 23 m 1 < m 2 < m 3 (normal hierarchy) m 3 < m 1 < m 2 (Inverted hierarchy) m ( ) m 2 i j Max{m i 2,m 2 j } m ev 1eV m 1 << m 2 << m 3 m ν3 0.05eV, m ν2 0.01eV (2.30)
12 π π + µ + + ν µ, π + e + + ν e (2.31) π π π π µ + (e + ) ( 2.13 µ + (e + ) 1 v m 2 /p 2 π 2.13: π µ + µ Γ(π µ + ν) m 2 (m 2 π m 2 µ) 2 µ m 5 π (2.32) Γ(π e + ν) Γ(π µ + ν) = m2 e(m 2 π m 2 e) 2 m 2 µ(m 2 π m 2 µ) 2 = (2.33) ± µ eν * 10) ν e ν µ 2.14: π π ( ) * 10)
13 2 13 ( ) ( 2.14 ) (H = µ H) ( ( 2.14 ) MeV 2.15: #1, #2 #3( ) #4 #4 #3 #4 (Phys.Rev.Lett.7(1961)23) 10 ( ) (4) 3 10 P y A = L R L + R = ±0.09, f or P y = 1 (2.34) A = 0.09 ± P y = 0.9 µ 100% 2.5 * 11) 2ν 0ν ( 2.16(a),(b)) * 11)
14 2 14 2ν : (Z) (Z + 2) + 2e + 2 ν e (2.35a) 0ν : (Z) (Z + 2) + 2e (2.35b) 2ν 2.16: 2 (a)2ν (b)0ν (3) 0ν 2.16(b) (1) ν L (ν c ) R (2) (m ν /m e ) 2 ) 2.17: (a)2ν (b)0ν (c) 1.29kg y. 90%CL 0ν 2ν ( 2.17 ) ( ) 100%
15 ( ) 0ν 180 NEMO3 * 12) : NEMO3 : ββ 10kg 20m 2 (40 60)mg/cm 2 10 (6180) σ i = 0.5mm, σ z = 1cm, 1940 PM.,FWHM(1MeV ) % (30G) (20cm)+ (30cm H 2 O) / τ y/m ν 0.1eV 2ν * 13) 100 Mo 100 Ru + 2e + 2 ν e τ 1/2 = 7.1 ± (2.36a) 76 Ge 76 Se + 2e + 2 ν e τ 1/2 = 1.5 ± (2.36b) 0ν (Ge) τ 0ν > (2.37) m ν < 1eV (2.38) * 12) * 13) A.S.Barabash Neutrino2006, SantaFe
16 : NEMO3 2ν 2ν 0ν 180 m j < m ν >= j Ue 2 jm j = η j U e j 2 m j (2.39) j η j CP < m ν >
( ) Note (e ) (µ ) (τ ) ( (ν e,e ) e- (ν µ, µ ) µ- (ν τ,τ ) τ- ) ( ) ( ) (SU(2) ) (W +,Z 0,W ) * 1) 3 * 2) [ ] [ ] [ ] ν e ν µ ν τ e
![( ) Note (e ) (µ ) (τ ) ( (ν e,e ) e- (ν µ, µ ) µ- (ν τ,τ ) τ- ) ( ) ( ) (SU(2) ) (W +,Z 0,W ) * 1) 3 * 2) [ ] [ ] [ ] ν e ν µ ν τ e](/thumbs/98/136160482.jpg "( ) Note (e ) (µ ) (τ ) ( (ν e,e ) e- (ν µ, µ ) µ- (ν τ,τ ) τ- ) ( ) ( ) (SU(2) ) (W +,Z 0,W ) * 1) 3 * 2) [ ] [ ] [ ] ν e ν µ ν τ e")
( ) Note 3 19 12 13 8 8.1 (e ) (µ ) (τ ) ( (ν e,e ) e- (ν µ, µ ) µ- (ν τ,τ ) τ- ) ( ) ( ) (SU(2) ) (W +,Z 0,W ) * 1) 3 * 2) [ ] [ ] [ ] ν e ν µ ν τ e µ τ, e R, µ R, τ R (1a) L ( ) ) * 3) W Z 1/2 ( - )
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
![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](/thumbs/92/109118076.jpg "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")
1 6 6.1 (??) (P = ρ rad /3) ρ rad T 4 d(ρv ) + PdV = 0 (6.1) dρ rad ρ rad + 4 da a = 0 (6.2) dt T + da a = 0 T 1 a (6.3) ( ) n ρ m = n (m + 12 ) m v2 = n (m + 32 ) T, P = nt (6.4) (6.1) d [(nm + 32 ] )a
July 28, H H 0 H int = H H 0 H int = H int (x)d 3 x Schrödinger Picture Ψ(t) S =e iht Ψ H O S Heisenberg Picture Ψ H O H (t) =e iht O S e i
July 8, 4. H H H int H H H int H int (x)d 3 x Schrödinger Picture Ψ(t) S e iht Ψ H O S Heisenberg Picture Ψ H O H (t) e iht O S e iht Interaction Picture Ψ(t) D e iht Ψ(t) S O D (t) e iht O S e ih t (Dirac
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TOP URL http://amonphys.web.fc.com/ 1 19 3 19.1................... 3 19.............................. 4 19.3............................... 6 19.4.............................. 8 19.5.............................
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 ±
![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 ±](/thumbs/91/106462075.jpg "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 ±")
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
1 223 KamLAND 2014 ( 26 ) KamLAND 144 Ce CeLAND 8 Li IsoDAR CeLAND IsoDAR ν e ν µ ν τ ν 1 ν 2 ν MNS m 2 21
1 3 KamLAND shimizu@awa.tohoku.ac.jp 014 ( 6 ) 1 31 1 KamLAND 144 Ce CeLAND 8 Li IsoDAR CeLAND IsoDAR.1 ν e ν µ ν τ ν 1 ν ν 3 3 3 MNS m 1 = 7.5 10 5 ev m 31 m 3 =.3 10 3 ev 100 m ν e [1] 71 Ga SAGEGallex
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August 26, 2005 1 1 1.1...................................... 1 1.2......................... 4 1.3....................... 5 1.4.............. 7 1.5.................... 8 1.6 GIM..........................
(Compton Scattering) Beaming 1 exp [i (k x ωt)] k λ k = 2π/λ ω = 2πν k = ω/c k x ωt ( ω ) k α c, k k x ωt η αβ k α x β diag( + ++) x β = (ct, x) O O x
![(Compton Scattering) Beaming 1 exp [i (k x ωt)] k λ k = 2π/λ ω = 2πν k = ω/c k x ωt ( ω ) k α c, k k x ωt η αβ k α x β diag( + ++) x β = (ct, x) O O x](/thumbs/104/162595168.jpg "(Compton Scattering) Beaming 1 exp [i (k x ωt)] k λ k = 2π/λ ω = 2πν k = ω/c k x ωt ( ω ) k α c, k k x ωt η αβ k α x β diag( + ++) x β = (ct, x) O O x")
Compton Scattering Beaming exp [i k x ωt] k λ k π/λ ω πν k ω/c k x ωt ω k α c, k k x ωt η αβ k α x β diag + ++ x β ct, x O O x O O v k α k α β, γ k γ k βk, k γ k + βk k γ k k, k γ k + βk 3 k k 4 k 3 k
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016 9 3 6 0 016 1 0 1 10 1 1 17 1..,,..,. 1 1 c = h = G = ε 0 = 1. 1.1 L L T V 1.1. T, V. d dt L q i L q i = 0 1.. q i t L q i, q i, t L ϕ, ϕ, x µ x µ 1.3. ϕ x µ, L. S, L, L S = Ld 4 x 1.4 = Ld 3 xdt 1.5
(1.2) T D = 0 T = D = 30 kn 1.2 (1.4) 2F W = 0 F = W/2 = 300 kn/2 = 150 kn 1.3 (1.9) R = W 1 + W 2 = = 1100 N. (1.9) W 2 b W 1 a = 0
1 1 1.1 1.) T D = T = D = kn 1. 1.4) F W = F = W/ = kn/ = 15 kn 1. 1.9) R = W 1 + W = 6 + 5 = 11 N. 1.9) W b W 1 a = a = W /W 1 )b = 5/6) = 5 cm 1.4 AB AC P 1, P x, y x, y y x 1.4.) P sin 6 + P 1 sin 45
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18 I ( ) (1) I-1,I-2,I-3 (2) (3) I-1 ( ) (100 ) θ ϕ θ ϕ m m l l θ ϕ θ ϕ 2 g (1) (2) 0 (3) θ ϕ (4) (3) θ(t) = A 1 cos(ω 1 t + α 1 ) + A 2 cos(ω 2 t + α
18 I ( ) (1) I-1,I-2,I-3 (2) (3) I-1 ( ) (100 ) θ ϕ θ ϕ m m l l θ ϕ θ ϕ 2 g (1) (2) 0 (3) θ ϕ (4) (3) θ(t) = A 1 cos(ω 1 t + α 1 ) + A 2 cos(ω 2 t + α 2 ), ϕ(t) = B 1 cos(ω 1 t + α 1 ) + B 2 cos(ω 2 t
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
Chadwick [ 1 ] 1919,, electron number Q kinetic energy [MeV] 8.1: 8.1, 1 internal conversion electron E γ E e =
![Chadwick [ 1 ] 1919,, electron number Q kinetic energy [MeV] 8.1: 8.1, 1 internal conversion electron E γ E e =](/thumbs/104/162189465.jpg "Chadwick [ 1 ] 1919,, electron number Q kinetic energy [MeV] 8.1: 8.1, 1 internal conversion electron E γ E e =")
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医系の統計入門第 2 版 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. このサンプルページの内容は, 第 2 版 1 刷発行時のものです.
医系の統計入門第 2 版 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. http://www.morikita.co.jp/books/mid/009192 このサンプルページの内容は, 第 2 版 1 刷発行時のものです. i 2 t 1. 2. 3 2 3. 6 4. 7 5. n 2 ν 6. 2 7. 2003 ii 2 2013 10 iii 1987
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![II ( ) (7/31) II ( [ (3.4)] Navier Stokes [ (6/29)] Navier Stokes 3 [ (6/19)] Re](/thumbs/94/118770263.jpg "II ( ) (7/31) II ( [ (3.4)] Navier Stokes [ (6/29)] Navier Stokes 3 [ (6/19)] Re")
II 29 7 29-7-27 ( ) (7/31) II (http://www.damp.tottori-u.ac.jp/~ooshida/edu/fluid/) [ (3.4)] Navier Stokes [ (6/29)] Navier Stokes 3 [ (6/19)] Reynolds [ (4.6), (45.8)] [ p.186] Navier Stokes I Euler Navier
cm λ λ = h/p p ( ) λ = cm E pc [ev] 2.2 quark lepton u d c s t b e 1 3e electric charge e color charge red blue green qq
![cm λ λ = h/p p ( ) λ = cm E pc [ev] 2.2 quark lepton u d c s t b e 1 3e electric charge e color charge red blue green qq](/thumbs/89/98710373.jpg "cm λ λ = h/p p ( ) λ = cm E pc [ev] 2.2 quark lepton u d c s t b e 1 3e electric charge e color charge red blue green qq")
2007 2007 7 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 1 2007 2 4 5 6 6 2 2.1 1: KEK Web page 1 1 1 10 16 cm λ λ = h/p p ( ) λ = 10 16 cm E pc [ev] 2.2 quark lepton 2 2.2.1 u d c s t b + 2 3 e 1 3e electric charge
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A B A.70g/cm 3 B.74g/cm 3 B C 70at% %A C B at% 80at% %B 350 C γ δ y=00 x-y ρ l S ρ C p k C p ρ C p T ρ l t l S S ξ S t = ( k T ) ξ ( ) S = ( k T) ( ) t y ξ S ξ / t S v T T / t = v T / y 00 x v S dy dx
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
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
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1 20 9 19 2 1 5 1.1........................ 5 1.2............................. 8 2 9 2.1............................. 9 2.2.............................. 10 3 13 3.1.............................. 13 3.2..................................
ω 0 m(ẍ + γẋ + ω0x) 2 = ee (2.118) e iωt x = e 1 m ω0 2 E(ω). (2.119) ω2 iωγ Z N P(ω) = χ(ω)e = exzn (2.120) ϵ = ϵ 0 (1 + χ) ϵ(ω) ϵ 0 = 1 +
2.6 2.6.1 ω 0 m(ẍ + γẋ + ω0x) 2 = ee (2.118) e iωt x = e 1 m ω0 2 E(ω). (2.119) ω2 iωγ Z N P(ω) = χ(ω)e = exzn (2.120) ϵ = ϵ 0 (1 + χ) ϵ(ω) ϵ 0 = 1 + Ne2 m j f j ω 2 j ω2 iωγ j (2.121) Z ω ω j γ j f j
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( ; ) C. H. Scholz, The Mechanics of Earthquakes and Faulting : - ( ) σ = σ t sin 2π(r a) λ dσ d(r a) =
1 9 8 1 1 1 ; 1 11 16 C. H. Scholz, The Mechanics of Earthquakes and Faulting 1. 1.1 1.1.1 : - σ = σ t sin πr a λ dσ dr a = E a = π λ σ πr a t cos λ 1 r a/λ 1 cos 1 E: σ t = Eλ πa a λ E/π γ : λ/ 3 γ =
Gmech08.dvi
145 13 13.1 13.1.1 0 m mg S 13.1 F 13.1 F /m S F F 13.1 F mg S F F mg 13.1: m d2 r 2 = F + F = 0 (13.1) 146 13 F = F (13.2) S S S S S P r S P r r = r 0 + r (13.3) r 0 S S m d2 r 2 = F (13.4) (13.3) d 2
1 I 1.1 ± e = = - = C C MKSA [m], [Kg] [s] [A] 1C 1A 1 MKSA 1C 1C +q q +q q 1
![1 I 1.1 ± e = = - = C C MKSA [m], [Kg] [s] [A] 1C 1A 1 MKSA 1C 1C +q q +q q 1](/thumbs/94/121802164.jpg "1 I 1.1 ± e = = - = C C MKSA [m], [Kg] [s] [A] 1C 1A 1 MKSA 1C 1C +q q +q q 1")
1 I 1.1 ± e = = - =1.602 10 19 C C MKA [m], [Kg] [s] [A] 1C 1A 1 MKA 1C 1C +q q +q q 1 1.1 r 1,2 q 1, q 2 r 12 2 q 1, q 2 2 F 12 = k q 1q 2 r 12 2 (1.1) k 2 k 2 ( r 1 r 2 ) ( r 2 r 1 ) q 1 q 2 (q 1 q 2
5 5.1 E 1, E 2 N 1, N 2 E tot N tot E tot = E 1 + E 2, N tot = N 1 + N 2 S 1 (E 1, N 1 ), S 2 (E 2, N 2 ) E 1, E 2 S tot = S 1 + S 2 2 S 1 E 1 = S 2 E
5 5.1 E 1, E 2 N 1, N 2 E tot N tot E tot = E 1 + E 2, N tot = N 1 + N 2 S 1 (E 1, N 1 ), S 2 (E 2, N 2 ) E 1, E 2 S tot = S 1 + S 2 2 S 1 E 1 = S 2 E 2, S 1 N 1 = S 2 N 2 2 (chemical potential) µ S N
20 4 20 i 1 1 1.1............................ 1 1.2............................ 4 2 11 2.1................... 11 2.2......................... 11 2.3....................... 19 3 25 3.1.............................