Stochastic Fusion Dynamics of Heavy-Ions

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Ναβουχοδονόσορ Λαμπρόπουλος
5 χρόνια πριν
Προβολές:

1 CNP, Osaka U., Jaan Sochasc Fuson Dynacs o Havy-Ions Büln Yılaz Mddl Eas Tchncal U. & Ankara U.

2 OUTLINE PAT I Basc sochasc drnal uaons Brownan oon Sur-havy lns SHE and havy-on uson racons Quanu sascal cs on h oraon robably PAT II Inroducon o nurcal sulaon hods o SDE Mhod or nurcal sulaon o wo-r xonnally corrlad colord nos Concluson

3 Langvn Euaon n Markovan L: Dlud lk a dros ~μ n war dv γv d I δ V V d β V V V d β β β β d d β β 4β I V kt Flucuaon-Dssaon Thor γktδ

4 Langvn Euaon wh Mory Ecs Mor uaon: dv d γ V d ktγ Langvn Euaon wh Mory and Ponal Gnralzd Langvn Euaon: d U d d γ d d ktγ Drvaon o h GLE drc lnaon o rrlvan varabls Zwanzg s hod: P H U Q ω cq M Hcoll Hbah

5 Q& P M U P& ω c cq Q & & ω cq ω D dr arx & & ω cq θ ω ω ω L x θ y x& ω x ω cq y ω y & ω θ ω

6 cq Cosω SnωcQ Cosω ω P ' c Cosω ' d ' M U P' P& d ' γ ' Q M γ ω ω ' c Cos ' c ω Cosω Snω ω, rrlvan and n hral ulbru ' ktγ '

7 Th Fokkr-Planck uaon: kt wv, β β V wv, V V V β V d β σ kt β V wv, x πσv β V V σ V Krars uaon U w,, β βkt w,,

8 Island o Sably or SHE h://hyscswb.org Z N 4,,6 84

9 Synhss o SHE. Nuron-caur racons u o F Z. Havy-on uson racons - Ho uson acnd-basd uson - Cold uson B-O acnd arg SHE Cr- Zn Pb, B SHE Fuson Hndranc or Z > 6!!! Z W. sdor, J. Phys. G How o orula h uson racon? Nuclus s a any-body sys an-ld aroxaon. Dssav sys Sochasc oon D-nlasc collson Eulbru sascal hyscs Flucuaon-Dssaon Thor

10 Scannd ro Y. Ab. al., nucl-h/387 3 Havy-Ion Fuson acon D σ π E J. P E. P E A A SHE J J * E c J uson c surv longaon uas-sson

11 Quanu Sascal Ecs on Fuson Dynacs o Havy-Ions: Quanu dssaon usng sys rsrvor orals: MΩ H F H M Hcoll Vcou d d M d M Ω Tr F d ρ Lnarzd Transor Euaon h h F ρ ρ ρ [, ] h δρ h ρ F δρ [, ] [ δf, ρ] ρ ρ δρ d G FG, δρ δ ρ h G δρ G ρ G x h F

12 δρ j n ρ δρ j j δρ δ δ jj n nj nj n γ F j x ε j ε n nj nj n h h ξ F j x ε j ε j δρ h ρ n ξ ξ F j x ε j ε n nj nj n h d M d d δ Ω δ γ δ ξ δ δ δ cosh Ω snh Ω M Ω d M M d δ δ δ β δ ξ Ω Δ Ω

13 d M d Ω β ξ β dτ F j x τ ε j ε n njsnh Ω τ cc.. MΩ h ε j ε ε j ε F j n nj M Ω ε j ε Ω η ε j ε Ω η h h h h β Ω, Δ dω hω hω ξ ξ x [ ω ] coh Mβ ω π kt h Δ MV τ ω β D D MT hω D ω hω Mβ ω x hω / kt * kt

14 Gaussan cu-o β ω β x hω Δ Lornzan cu-o Drud gularzaon β ω β hω /Δ Markovan L ξ ξ D χ d ω h x [ ] ω h coh ω h χ ω x ω π kt kt Δ dω χ x [ ω ] x π Δ x πτ τ hω χ δ

15 T.5 MV T. MV T5. MV Δ5 MV. χ [MV] [/c]

16 Analyss o h Langvn uaon Th ovr-assng robably: d d M and d M d ± Ω β ξ ω ω ω M ± MΩ ω ω ω β ω ξ ω S ds ξ x β β coshω snhω Ω Ω Ω β β S x snhω M Ω σ σ σ S ds ds S s S s D χ s s

17 ducd Dsrbuon Funcon W, x πσ K M σ Ca U V B Foraon Probably P d x πσ σ rc σ V B 4 MV σ, σ, M Ω MV/ h β MV/c s 3.9 MV/ h

18 Q.D. C.F.D. Δ5 MV Probably..5 T. MV T5. MV. T.5 MV K -V B [MV]

19 PAT II Nurcal ngraon o Langvn-y uaons - Th Eulr-Maruyaa Mhod: Y. Ab al J. Phys C4-39 d d d d Δ U β gγ, Δ d Δ g Γ β T Γ Γ δ Δ Δ d, g d, g % Δ Γ Δ Γ Γ % Δ Γ % Δ ω ω ω

20 ,,... ~ ~ ~ Γ Γ Γ Δ Δ Δ Δ g g g... ~ ~ Γ Γ Δ Δ Δ Δ g g Taylor xanson around and

21 Δ ~ Γ d Γ Δ ~ Γ d dγ Δ ~ Γ3 d3γ 3 d d Γ % Δ Γ % Δ ω ~ ~ Γ Γ Δ ~ Γ Δ Γ % Δ ω ω 3 Γ% Γ % 3 Δ 6 3 ~ ~ Γ Γ 3 Δ 8 4 ~ Γ 3 5 Δ 5 3 Γ % 3 Δ ω ω ω3 6 5

22 Suary: Δ Δ Δ 3 Δ / g Δ ω g Δ ω ω g Δ ω ω ω Δ Δ Δ Δ... g 3 Δ ω ω 3 g 5 3 Δ ω ω ω

23 - Th Sochasc ung-kua Mhod:. Honycu, P.. A L x& x Δ Δ Δ x x F F d F x x DΔω F x ΔF x Δ F DΔω F DΔ ω DΔ ω... { ω...} F Δ DΔ DΔ ω DΔ ω... x x Δ Δ Δ Δ DΔω Δ DΔ ω ω Δ D ω ω

24 Δ Δ D ω ω Δ DΔ ω DΔ ω ω ω ω ω ω ω ω ω ω aψ ω aψ ω aψ a a a Suary: x& x x Δ x Δ F F DΔψ ψ ψ F x F xδ x DΔψ

25 3-Ingraon Mhod:. F. Fox al, P.. A L x x & D Γ x x & & Γ D Γ Γ δ s s ds Γ { } { } s s D D ds s ds s Γ Γ { } D

26 Γ x x & & ds s s Δ Δ Δ Γ Δ, h Δ D h Δ Δ,, Δ h Suary: L x x &, h Δ Δ Δ, h D Δ Δ Ψ D Ψ x x x Δ Δ { } D { } Ψ D Ψ

27 4-Mhod or nurcal sulaon o wo-r xonnal corrlaon P.. E accd Movaon: Quanu nos xhbs a ngav al whch canno b sulad only by osv xonnal rs. χ [MV] T.5 MV T. MV T5. MV Δ5 MV d χ D ω x ω coh ω [ ω ] π T T ω /Δ [/c] χ D Δ Δ Δ Tπ n Co 4T π T T n T π n Δ n

28 x& x D D x& x & Γ & Γ Γ,, Γ Γ D δ D < Γ Γ D δ D < { } % % % % D D D D Δ Δ Δs Δ Γ s ds h, Δ D% D% D D

29 h, Δ Th sulaon and rsrcons Δ h, Δ D% Δ h, Δ h, Δ D% { } { } { } D % D % D % Ψ % % D / D Ψ D% D% / D% Ψ Ψ Ψ D% Δ Δ Δ Ψ 3 F D% D% Δ Δ % Ψ Δ Δ Δ FΨ D F 3 4

30 D % > D % > D% DD %% < 4 D% DD %% Δ Δ Δ Δ l < Δ Δ Δ D% 4 D D% D D% D D% D% D D% D% D% D% D D D% DD 4 D% D D DD ax D D D % Th r arar s xd. ax

31 D D D% D D DD ax D D D D D D > For conssncy o h corrlaon uncon n h Markovan L. D D > For conssncy o h corrlaon uncon a. D D> Th drvav o h corrlaon uncon a us b ngav or zro ndcang h nal dcras o h corrlaon uncon.

32 4 unhyscal -τ -6-4τ 7 -τ -3-4τ 7-4τ -3 -τ unhyscal -4τ -6 -τ 3 χτ τ

33 D D D Th sulaon algorh D % D D % % D % D D % D % Ψ Ψ Ψ D% / D% Ψ D% D% / D% Ψ x Δ x x Δ F D% D% D% Δ Δ Δ Δ Δ Ψ 3 Δ Ψ % Ψ Δ Δ F D F 3 4

34 d d.8 d d Alcaon U χ d χ D D Analycal Nurcal Probably Inal Knc Enrgy

35 Argao Gozaasu

37 Nos wh any xonnal osv rs L x& x D N N x& x & Γ Γ,,,..., N Γ Γ j D δ δ j { } { } D N x Δ x x Δ Δ h, Δ D Ψ Ψ Ψ Δ Δ h, Δ

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