counting statistics in thermal transport in nanojunctions

Transcription

1 rs bhvor d fll cog sscs hrml rspor ojcos J-Shg Wg Dp PhysNUS

2 Ol of h lk rodco Mhod of oqlbrm r s fcos Applcos hrml crrs D ch d obs rs problm Fll cog sscs MS workshop

3 Forr s lw for h codco J [ ] f f d Forr J Bps Josph Bro

4 hrml codcc SJ S whr : hrml crr : : : mprr of codcc codcvy S : cross sco r J : crr dsy lf d rgh ld 4

5 Eprml rpor of Z Wg l 7 h prmlly msrd hrml codcc s 5pW/K for lk chs K. From Z Wg l Scc

6 hrml rspor of jco Jco f d gh d sm-f MS workshop 6

7 Modls m K j V m j V k j jk jk 3 Jco MS workshop 7 f d gh d

8 Forc cos mr k k k k k V V K V k k V k k k k k K MS workshop 8

9 Dfos of r s fcos rr/lssr r s fco j k jk k j jk m-ordrd/-m ordrd r s fco rdd/dvcd r s fco r MS workshop 9

10 oor-ordrd r s fco jk j k d r k j oor ordr: h oprors rlr o h coor r o h rgh. τ τ MS workshop

11 lo o h rl-m r s fcos or or τ τ MS workshop

12 Eqos for r s fcos K K K r r K K K K MS workshop K

13 Solo for r s fcos sg Forr rsform: r r K r r [ ] [ ] K r K c K d K [ ] r [ ] [ ] K r f r c d d c b fd by l/bodry codo. MS workshop 3

14 oor-ordrd r s fco k j jk d k j r d j k j r τ τ MS workshop 4

15 Prrbv pso of coor ordrd r s fco ordrd r s fco d d k j jk 3 k j d d d lm m l lm k j k j d d d d d d q p o m l k j jk opq q p o opq d d d Wck horm k o q p m l j MS workshop 5

16 rl pso rl = + { } 3 3 Sgl l 3-l vr -dobl l vr jk j k jj j j j j MS workshop

17 Dgrmmc rprso of h pso = = + dd MS workshop 7

18 Eplc prsso for slf-rgy d jk[ ] jlmrsk lr [ ] ms[ ] lmrs jkl mrs lm rs lmrs 4 d [] [ ] O jk MS workshop 8

19 Jco sysm hr yps of r s fcos: g for sold sysms wh lds d cr r dcopld for bllsc sysm for fll olr sysm ovrg mlos + + +V V g g = Eqlbrm α r s fco = Noqlbrm sdy s sblshd MS workshop

20 hr rgos MS workshop

21 Dyso qos d solos V g V V g V g g r r K r r r r r r r MS workshop r

22 Ergy crr d V d r V [ ] d r r [ ] [ ] [ ] [ ] d MS workshop

23 rol forml d r r f f d d r r f f r r MS workshop 3

24 Bllsc rspor D ch Forc coss k k k k k K k k k k k k k k Eqo of moo j j j j k k k k j MS workshop 4

25 Solo of g Srfc r s fco K g k k k k k k k K k k k k k j g j j k k k / k MS workshop 5

26 d slf rgy d rsmsso k [ω] r r jk K k jk ω r k 4k k [ ] r ohrws MS workshop 6

27 crr d codcc dr forml [ ] f f d m f d lm f m k B k 3hh MS workshop 7

28 rbo ob olr ffc h rsmssos o--cll crbo ob jco of 8 3K. From J-S Wg J Wg N Zg Phys. v. B MS workshop 8

29 rs problms sm-f lf ld sm-f rgh ld coplg s swchd o = V k km MS workshop 9

30 Dyso qo o coor from o = τ τ τ τ τ g τ g τ + τ τ g g τ b τ oor d g V g d d g V g V MS workshop 3

31 rs hrml crr crr [W] 8 8 h m-dpd frs-ordr crr wh h mssg 4 ll ordrs 4 sprg s sddly cocd. rr flow o of lf ld b ll ordrs o of rgh ld. Dos -4-4 r wh prdcd from dr forml. frs-ordr -8-8 =3K k =.65 V/Å wh smll - b - os k =.k. From E.. sg d J.-S. Wg Phys. v. B S lso m [ -4 s] m [ -4 PE 8 6. s] MS workshop 3

32 Fll cog sscs Wh s h mo of rgy h Q rsfrrd gv m? hs s o fd mbr b gv by probbly dsrbo PQ rg fco Q Z P Q dq All moms of Q c b compd from h drvvs of Z. h objcv of fll cog sscs s o comp Zξ. MS workshop 3

33 A brf hsory o fll cog sscs. S. vov d. B. sovk proposd h cocp for lcros 993; rdrvd d for orcg lcro problms by. Klch K. Schöhmmr d ohrs K. So d A. Dhr obd h frs rsl for phoo rspor 7 J.-S. Wg B. K. Agrwll d. PB ; B. K. Agrwll B. d J.-S. Wg rxv:.68 MS workshop 33

34 Dfo of grg fco bsd o wo-m msrm bsd o wo-m msrm r Z r P P Z P P P P U U /.g. U U U MS workshop 34 g

35 Approchs o comp Z Eprss Z s pco vl of som ffcv volo opror ovr coor Evl h prsso sg Fym ph grl/flc fcol Fym dgrmmc pso MS workshop 35

36 Prodc l s P ] [ Z r ] [ U U Z r r U U r / / U U r / / U U MS workshop 36

37 U U d d V MS workshop 37

38 Schrödgr sbrg d rco pcrs rco pcrs U w U Schrödgr pcr U U p A A AU U A ] [ sbrg pcr A ] [ S rco pcr d S S S MS workshop 38 A A

39 omp Z rco pcr d U U Z ] r[ / / τ -ξ/ d d d d r ] r[ τ +ξ/ V V d d d ] [ r V g V g ] r[ A g g Z ] l d[ ] r l[ l A A ] r l[ MS workshop 39 A g g

40 mpor rsl l r l A Z l r l Z A g g A f / M ohrws f / M MS workshop 4 ohrws

41 og-m rsl vov-sovk forml forml A l r l Z K r A b b l r d b b l d 4 f f f f d r M ] [ ] [ whr b / / k f B r MS workshop 4

42 Arbry m rs rsl l Z r l A Q Q Q l Z Q Q A l Z r Q l Z Q M log m MS workshop 4

43 Nmrcl rsls D ch <<Q Q>> V <<Q 3 >> > V M -4 s M -4 s <<Q >> V <<Q 4 >> > V 4 D ch wh sgl s s h cr. k= V/Å k =.k =3K =3K =9K. d l rgh ld; blck lf ld. B. K. Agrwll B. d J.-S. Wg rxv:.68. MS workshop 43

44 Ohr rsls Wclsocomphcmls lso comp h cmls for h projcd sdy s ρ Eropy prodco Flco horm Zξ = Z-ξ +β -β h hory s ppld qlly wll o lcro mbr of lcro rgy rspor MS workshop 44

45 Smmry rmrks NEF s powrfl ool o hdl hrml rspor problms osrcrs Sdy s crr s obd from dr d rol forml Nw rsls for rs d fll cog sscs. A ky qy s h slf-rgy Σ A MS workshop 45

46 hk yo