CONVERSION OF ENVIRONMENTAL HEAT INTO USABLE ENERGY

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1 my of Romnn nss uumnl sson 4 6 spmb 015 Onln IN Volum 7 Numb / CONVERION O ENVIRONMENL HE INO UBLE ENERGY El ENECU Rzum. znăm sop nă unu fnomn onvs ălu mulu mbn în ng âmp lomgn on ş m p în ng lă p bz ouă spozv p l-m num onvo ăluă un ş ssm nţ un. Un onvo ăluă un s bzză p upl ouă fnomn unosu no: supnţ ş ful l upl pn-un lmn v p l-m num nsso supn. Cân un un l s n în-un spozv onţn un numă sufn m nsso supn un âmp lomgn on s ms pn nzţ un în onţunl mo-bză p sm un bsopţ ăluă pn onţunl olo-bză. Eng ă s spozv po f ulză în unl plţ su onvă în ng lă pn ulz unu ssm nţ un. bs. W psn n sovy of phnomnon of onvson of h nvonmnl h no ohn lomgn ngy n fuh no l ngy on h bss of wo smonuo vs w ll qunum h onv n qunum non sysm. qunum h onv s bs on h ouplng of wo phnomn pvously known: h supn n h l ff oupl by v lmn w ll supn nsso. Whl n l un s n n v onnng suffnly lg numb of supn nssos ohn lomgn fl s m by qunum nsons n h m-bs unons on h oun of h bsopon by h ollo-bs unons. h ngy by hs v n b ly us n som pplons o onv no ly by qunum non sysm. Kywos: ohn fl ol nsons supn nsso qunum h onv qunum non sysm. 1. Inouon Ou vlzon s bs on lg ngy onsumpon mnly obn by bunng ffn fuls hml o nul. Howv hs posss poung lg hml o nul wss bgn o bom ngous fo ou lf onons on hs pln. Consqunly oh hnqus fo h ngy pouon fom ln sous s wflls wns mn s o sol on hv bn vlop. Howv hs hnologs gnlly bs on bg nsllons wh smll ffns n lly pnng on nl onons whh no ssf vywh on h Eh. muh mo ssbl ngy sou s h bu pvously ws blv h s onvson no usbl ngy s no possbl u o h son lw of hmoynms [1]. Howv ppomly n h ls hlf-nuy nw mkbl fl of sn hs bn vlop w

2 Convson of Envonmnl H no Usbl Engy 55 ll opn qunum physs [-10]. In hs fmwok w foun h onvson of h nvonmnl h no usbl ngy s possbl wh vy hgh ffny n h fmwok of h vy wll-known hnology of h opolon smonuo vs [11-15]. W show h pnpl of hmoynms os no hol ny mo n qunum m-fl sysm [16]. uh sysm w ll supn qunum non o [17] ompos of wo-lvl sysm wh h nsy m n oupl lomgn fl wh h mplu hs n nopy m von 11 1 E E K 11 Q (1) wh n pobbls fo fl mplu K volum E h sympo vlus of h oupon E whl s h fquny of hs fl s h qunzon numb of h sysm wh h qunzon V V n sonn lomgn fl wh wvlngh y fom h s 1 o h goun s 0 01 s h s h y of h lomgn ngy n h usul noons fo unvsl onsns. In hs psson w sngush h posvly fn om m popoonl o h y 01 n m pnng on fl whh n b ngv. Rlly whn h lomgn fl nss h populon of h ss lso nss nng o h sympo vlu fo hs fl whl h populon 00 qulbum vlu. Wh hs vlus 00 of h goun s ss o h w g posv fl m n h uly bk wh h ngv loghm fo mulplyng hs bk. 11 ln 11 ln 00 00

3 56 El ENECU mosop spon of hs phnomnon hs bn pfom n h fmwok of nly vlop hoy bs on ms quons wh pl sspon offns whh pn on h non ponls bwn h sysm n nvonmnl pls nss of ss n mpu [18-1]. W show h hs spon wh opos fo sysm wh N ss N N 1 nson s no only mo pl bu lso mo o omp o h mos hol ppohs sng n lu whh k no oun only wo non-ohogonl opos oon n momnum []. In son w psn h h ms quons of h sysms of ns fo smonuo opolon suu: h v lons h ohn lomgn fl n h opl phonons. In son 3 w psn h opon of qunum h onv. W obn h oupu pow s funon of h v hss n physl onsns n vlu hs pow fo ls sysm.. Qunum ms quons fo supn nsso supn nsso s smonuo suu wh n y of qunum non os s n m-bs unon n p--n p-lvl ph s bsollo unon (g. 1). g. 1. upn nsso wh n n-n b-n --p -p b-p supn unon n p--n unon wh p-lvl ph bsobng h by l ff. qunum non o s ono-po p mb n wo n n p hn lys of low bn gp wh n -ly of hgh bn gp bwn hs lys. h qunum o nsy m N h hknsss 0 1 n 4 of

4 Convson of Envonmnl H no Usbl Engy 57 h wo lys n n p h hknss n U 4 wh h hknsss 1 3 n n n p wh h onuon n vln bn mgns hosn fo qunum o gnngs E1. U E0 U v of h -ly n h bs U 3 bwn h onuon gons U n U v (g. ) E 0 g.. Qunum non o wh h ngy lvls E 0 n E 1 oupl o ohn lomgn fl E G G n vy wh mo nsmsson offns 0 0 n whl n lon un I I Ih s n n hs qunum o. h wo ponl bs whh sp h qunum o lvls n fom h hgh nsy lvls of h onuon gons n n p mnsh h sspv ouplng of h v qunum o lons o h onuon lons n hols. Of ous h mnsons of h spon bs hosn fo suffn hgh pnbly o pov h nssy lon flow fo h v opon. Whn suffnly hgh un s n n h v ohn lomgn fl of n mplu E s gn by qunum nsons fom h s 1 wh h ngy E 1 E 1 o h goun s 0 wh h ngy 0 E. Whn hs lons oss h bs-ollo unon h low ss of h p lvl ph nhn whl h hgh ss of hs ph pl whh mns mpu s of hs unon. hs ls o h bsopon n hs unon nng o mk h lon sbuon fo h nvonmnl mpu. h fl mplu E s mn by h

5 58 El ENECU ouplng of hs fl o h qunum nsons 1 0 n oh ouplngs n hs m-fl sysm: 1. h sspv ouplngs of h v lons wh h ysl l vbons h onuon lons n hols n h f lomgn fl sng n mpu ;. h ouplng of h lomgn fl wh h opl vbons of h ysl l n h sspv ouplngs wh h onuon lons n hols; 3. h sspv ouplngs of h opl vbons of h ysl l wh h vln lons. Consqunly w sb hs physl sysm by h ms quons [10]: 1. Ms quon fo sysm of mons nng wh n lomgn fl wh sspv offns fo ouplngs o oh mons Bosons n f lomgn fl;. Ms quon fo n lomgn fl mo nng wh sysm of v mons n h opl vbons of ysl l wh sspv offns fo ouplngs o n nvonmn of oh mons; 3. Ms quon fo h opl vbons of ysl l by n lomgn fl wh sspv offns fo h ouplng o h vln lons. W ons sysm of mons sb by h on-nnhlon opos oon - n n ngy spum n ponl wll su of by-o vy wh h sonn lomgn fl mos of h vy - fo h fow wv n - fo h bkw wv. H w k no oun mnsons of hs wll muh smll hn h lomgn fl wvlngh. hs sysm s sb by Hmlonn H H 0 V () wh s h Hmlonn of h sysm of mons n k k V K H s h non ponl of hs sysm n lomgn fl wh h nson fquns n h pol momns. h k k 0 (3) (4)

6 Convson of Envonmnl H no Usbl Engy 59 ynms of suh sysm n sspv sysm of of ss mn numb ponl g V B numb f f Y sysm of Bosons wh nsy of ss mons wh nsy of mons on hs ss n V B B g mn on hs ss n ponl n f lomgn fl m p u s sb by h qunum ms quon [10151]: (5) hs quon pns on h sspv ponl fluuons mplu mn-vlu h mmoy m sspv offns 1 1 V Y n h nom phss of h (6) of hs fluuons n h o n nson ngs muh lg hn h hml ngy h ms of hs offns of h fom V 1 f g (8) V f g B f g. (7)

7 60 El ENECU fo h ouplng wh h nvonmnl mons B B B V 1 f g B B B B V f g B (9) fo h ouplng wh h nvonmnl Bosons n / 1 fo h ouplng wh h f lomgn fl mpu. hs offns sb sonn sspon whn nson of mon of h sysm of ns s ol o nson of n nvonmnl pl wh n pobbly (g. 3). (10) V ( ) g. 3. Rsonn sspon. hs pobbls ospon o h l bln pnpl []. o sysm of v lons n smonuo suu h sspon offns sn non n of h ouplng wh onuon lon su n onuon gon s obn wh h Coulomb ponl of o wo-lvl qunum o n ysl l whh s of ns fo ou pplon h sspon offns of h ouplng o h vbonl mos of hs l of h fom [15]: 4 5 M (1) / v V ( ). M v / 1 (11) (13)

8 wh M s h lon mss Convson of Envonmnl H no Usbl Engy 61 - phonons of fquny n polzon 1 on-nnhlon opos of s h ysl nsy n s h soun vloy n ysl wh Young lsy offn E. In suh sspon poss n lon y/on wh n ngy s ol o phonon on/nnhlon of h sm ngy. om h ms quon (5) w v quons of h nsy m lmns fo wo-lvl sysm wh nson ngy 10 0 whh pn on qus-sonn lomgn fl of mplu n fquny 0 E E E o h polzon mplu v E * E E 10 (14) (15) n h populon ffn 1 w obn h polzon-populon quons w (16) (17) w 1 g w 0 E * * w w E E whh pn on h ouplng offn g 01 1 E h phsng h y h qulbum populon w mpu h non-mkovn fluuon g 0 n offn n n h lv om unng. h supn fl gn by h qunum nsons of hs sysm whh n (18)

9 6 El ENECU popgs hough h smonuo s hghly nflun by h unnl hg of vln lon sbuon ov h on sbuon of hs ml whh ls o n mpon von of h fl popgon vloy ong o fv n 1 (g. 4). g. 4. n nl lomgn fl ng n nnl fl of h unnl hg n h ysl n n opl vbon of hs ysl whh popgs wh h soun vloy v. Rlly h Hmlonn p H U (19) M of n lon n ponl n n lomgn fl of vo ponl K k k k k wh K 1 E s h fl V K qunzon vo nlus fl m W 1. M M U K hs mns n onl fl ngy W 4Nf u n h fl qunzon M volum V wh N oms n n unnl hg o bss h phoon ngy.. fv n W f (0) u MM wh M s h om mss. W obn ms quons fo h lomgn fl popgng fow f u

10 Convson of Envonmnl H no Usbl Engy 63 (1) n h lomgn fl popgng bkw () wh wv numb k. hs quons oupl wh ms quons fo h opl vbons popgng fow (3) n bkw (4) 0 k k k Kv K 0 L k k k Kv K 0 Kv k 0 Kv k

11 64 El ENECU gn by h lomgn fl wh h sm wvlngh o wv vo (g. 4) whh mns fquny k k v E (5). h ms quons (1)-() of n lomgn fl n qunzon volum V 3 1 L h nson opos sb h ouplngs of hs fl o h v lons wh h opl vbons wh h on-nnhlon opos - n - n h qus-f lons/hols noun n h onuon gons by popgon bwn h wo sufs of h v n wh h sspon offn 0 L 4 L M. (6) 1L h ms quons (3)-(4) of h opl vbons of ysl l wh l onsn n n unnl hg o sb h ouplng o h lomgn fl ng hs vbons wh h onnnhlon opos - n - n h vln lons by hs vbons o f ss mpu wh h sspon offn M U v / f (7) u 1L L om h ms quons (1)-() of h lomgn fl n (3)- (4) of h opl vbons fo h mn vlus of h fl k n h m lmns h mplu quons f u k 1 w obn 1 3 k 1 0K 01 R (8) (9) (30)

12 Convson of Envonmnl H no Usbl Engy 65 (31) 1 3 R k 1 0K 01 whh sb Rmn fquny shf R. om hs quons wh (0) n (5)-(7) n h polzon-populon quons (18) wh (6)-(8) n (10)-(14) w obn n nlyl spon of supn smonuo suu pnng on h ysl om mss M h ysl nsy h unnl hg o h qus-sonn qunum o fquny f u h onuon lon/hol nsy onnons N n N g 0 0 h ono n po of h onuon gons whh mn h ponls n h Coulomb ponl of h onuon lons n hols n h fl of qunum o h lsy offn E h qunum o nson pol momn of h v suu. U U v 01 n h hknss 3. Qunum h onv qunum h onv s v ompos of pk of supn nssos n by-o vy wh ol flon mo 0 0 n n oupu mo wh nsmsson offn n nm on wh h bsobn (g. 5) [10] [1-17]. h qunum o ys of hs nssos su n h nnos of qus-sonn lomgn mo of h vy whl h h bsobng unons pl n nos. n lomgn fl flow s gn by song lon-fl ouplng n nnos whl h bsopon of hs fl by h wk lon-fl ouplng n nos s nglgbl. wo vsons of hs v onvbl: (1) longunl v wh h wo mos on h wo sufs of h smonuo hp n () nsvsl v wh h wo mos on wo ll sufs of h hp. V L g. 5. Qunum h onv s pk of supn nssos n by-o vy wh h supn m-bs unons n h nnos of qus-sonn lomgn mo of h vy n h h bsobng bs-ollo unons n nos.

13 66 El ENECU Wh hp of v nssos wh qunum o nsy longunl v n hknss N L nlung N supn w obn h ngy flows fo n nsvsl on pnng on hshol uns L K K R R N 1L 1 N 1L 1 L I I0L I I0 (3) (33) I 0 n offn I phsng K R 1 w (34) (35) fo o h Rmn ff whh fo suffnly low s K 1 R R 4 N N 0L N N 1 w 4 N N 1. W no h h un I n n w h v mus b low hn h mmum vlu I N M ohws h qunum o nuly s no mo sp. hus w obn n opon onon fo h hshols of h populon nvsons n h pssons (34) n (35) of h hshol uns: w I w IL 4 N N 4 N N E 1 E.. fo h qunum o nsy N h numb of supn nssos N h pol momn 01 h phsng n h y of h fl. L 01 1 E 01 E 1L L 1L w 1L 1 L w 1 1 (36) (37)

14 Convson of Envonmnl H no Usbl Engy 67 o sonbl vlus of Gs - lg1 s smonuo suu wh n v zon 4 m n hknss L mm ono n po onnons os N N m 3 whh mn nsy of supn N m n nson fquny V fquny N s 1 whh fo h fv n.. fl 3.3 mns supn nssos n hs suu nson pol momn 6 nm phsng s s 1 n fl y whh mns nsmsson offn of h oupu mo 0.10 w obn h populon nvson hshol m s s m s w IL s nm 5 10 nm 137 (38) s s Wh y fom (34) wh (36) n (38) w obn h hshol I0 L un C m m s o un ssn 0. m / R C I 34 IM n n hs hp wh n l fom (3) w obn n lomgn pow L muh lg hn h l pow un non. 4 m m 16 m E m V V KW 6 1 1m s m s (39) (39) RI 8. W whh s nssy fo hs s

15 68 El ENECU Conlusons W popos nw hnologl vlopmn fo h ngy pouon by h bsopon fom h nvonmn. In hs fmwok hgh ffny vs fsbl: fo nsn w obn fom supn hp 4 m mm 1 KW wh n of n hknss of. mosop hoy s vlbl fo ompl nlyl spon. In hs fmwok h ssnl hss of h v ly unsnbl fom physl sons. hus w foun h h supn pow s popoonl o h nson ngy of h v qunum os h l un n ov hshol vlu n h numb of supn nssos n s nvs popoonl o m sbng h bsopon of h fl n s popgon hough h vy n m pnng on h nspny of h oupu mo. hs nspny s mn fom h onon of sony wvs popgon n h vy pnng on h bsopon offn of hs wvs. h hshol un s popoonl o h qunum o nsy h of h v zon n h y of h v lons. h qunum o nsy s mn fom h nson ngy onon fo h lon non fom h n-zon of h m o h p-zon of h bs. h hshol un ssnlly pns on h populon nvson whh s popoonl o h phsng n h sum of h oupu mo nspny wh h fl bsopon m n nvs popoonl o h nson fquny h numb of supn nssos h qunum o nsy n h squ of h nson pol momn. hs hss obn s pl funons of h ysl pops n v pms. R E E R E N C E [1] E. H. Lb n J. Yngvson h physs n mhms of h son lw of hmoynms hys. Rp (1999). [] E. B. vs Qunum hoy of opn sysms (m ss Lonon Nw Yok n nso 1976). [3] R. lk n K. Ln Qunum ynml mgoups n pplons In: Lu Nos n hyss 86 (png-vlg Bln Hlbg Nw Yok s okyo 1987). [4] U. Wss Qunum sspv sysms (Wol nf ngpo Nw Jsy Lonon Hong Kong 1999). [5] R. lk n R. nns Qunum ynml sysms (Ofo Unvsy ss 001). [6] H.. Bu n. uon h hoy of opn qunum sysms (Ofo Unvsy ss 00). [7] K. H. L hyss of Opn sysms hys. Rp (1986).

16 Convson of Envonmnl H no Usbl Engy 69 [8] M. Rzvy n. mpl Qunum unnlng: gnl suy n mulmnsonl ponl bs wh n whou sspv ouplng hys. Rp. 168(6) 305 (1988). [9]. Is. nulsu H. uu E. fnsu n W. h Opn Qunum ysms In. J. Mo. hys. E (1994). [10] E. fnsu Opn Qunum hyss n Envonmnl H Convson no Usbl Engy (Bnhm n ublshs hh UE Bussls Blgum nvs U 014). [11] E. fnsu n W. h 'upn sspv unnlng n oubl p--n smonuo hosuu wh hml non of lons' hys (007). [1] E. fnsu n L. E. Consu Longunl Qunum H Conv U n Off U (009). [13] E. fnsu n L. E. Consu nsvsl Qunum H Conv U n Off U (010). [14] E. fnsu n L. E. Consu Qunum Inon ysm U n Off U (009). [15] E. fnsu Ms quon n onvson of nvonmnl h no ohn lomgn ngy ogss n Qunum Elons (010). [16] E. fnsu Opn Qunum ysms of ls n npl of hmoynms J. hys.: Conf (013). [17] E. fnsu Qunum Inon os In: ngpns n h Opl n nspo ops of Qunum os E.: l-hm (INECH 01). [18] E. fnsu. nulsu n h W h ollsonl y of m sysm nng wh mny-mo lomgn fl In. J. Mo. hys. E 9 17 (000). [19] E. fnsu n. nulsu Mosop offns fo h qunum ms quon of m sysm In. J. Mo. hys. E (00). [0] E. fnsu n. nulsu ynms of m sysm n blkboy on fl In. J. Mo. hys. E (00). [1] E. fnsu W. h n. nulsu Non-Mkovn ms quon fo sysm of mons nng wh n lomgn fl nn. hys (008). [] E. fnsu ynms of m sysm wh sonn sspon n ynml l bln hys (005).

SYMMETRICAL COMPONENTS

SYMMETRICAL COMPONENTS SYMMETRCA COMPONENTS Syl oponn llow ph un of volg n un o pl y h p ln yl oponn Con h ph ln oponn wh Engy Convon o 4 o o wh o, 4 o, 6 o Engy Convon SYMMETRCA COMPONENTS Dfn h opo wh o Th o of pho : pov ph