HAI HOA PHA TO'

BAI BAO KHOA HQC

CHUYtN PHA UrglNG TO' TRONG Hf BOSON HAI THANH PHAN KHI TSt HOA HQC THAY DOI

Ding Thj Minh Huf', Nguyin Tuin Anh'

Tom tit: Chigdn pha luang tii Id he chuyin tic trgng thai lugng tic niy sang trgng thdi lugng H, khdc kht thi hod hodc hdng s6 liin kit thay 061, dgt din gid tri t&i hgn (di qua diim chuyin pha) i nhiit do gdn OK. Cdc kich bdn chuyin pha lugng til dugc xdc dinh qua viic khdo sdt suphv thupc vdo thi hod hodc hdng sd lien kit & mSi gid tri nhiit dg cue thip cda cdc tham so trat ttf dgc trung cho he. Bai bdo nay trinh bay nhiing kit qud nghiin cuu vi chuyin pha lugng tic trong hi boson hai thdnh phan hod tan nh& sic dung phuong phdp tdc dtcrig hiiu dgng Cornwall-JacUw-Tomboulis trong gdn diing bong bong kep edi tiin Kit qud cho thdy chuyin phalugrig tu trong he Id chuyen pha logi hai, xdy ra theo mgt trong hai kjch bdn: chuyin pha phgc hdi dSi ximg hogc chuyin pha phd vd ddi xdng nghich ddo.

Tir khda: gii hi tdi han, tham sd hrit ty, thi hieu dung, phyc hdi doi xirng, phi vo ddi xikg nghich dao.

lupng td trong cac he boson dang l i mpt trong nhung bai toan hay, mang tinh cap thidt thdi dai.

6 nghien ciiu trudc (Dang Thi IVImh Hue, Nguyen Tuan Anh, 2016) chung tdi da khao sal cic kich bin chuyin pha lupng tir trong cic he boson ddng nhit. CJ bai bio niy, chung tdi tiep tuc nghien cu:u cic kieh ban chuyen pha luong tii doi vdi h^ boson hai thanh phan khi the hoa thay ddi dl tim ra cic lii?n tupng mdi. Sir dyng phucmg phip the hieu d\mg Comwall-Jackiw- Tomboulis (CJT) - li phuong phap hifin dai, chinh xac va phu hpp vdi cac nghien cdu ve chuyen pha (Amelino G. and So - Young Pi, 1993; Comwall, J. M. et al, 1974) dl khao sat cac kjch ban chuyen pha lupng tu.

De dat dupe muc tieu nghien ciiu, chung toi su dung mo hlnh tuong tac cua he boson hai thanh phan dupe bieu diln bdi Lagrangian ciia h? dudi day:

I.D^TVANDB;

Nhihig nim gin day, ed nhilu cong hlnh nghien ciiu ve chuyen pha nhiet trong h? boson hai thinh phin ca vl ly thuyit lan thuc nghiem (Alexander L. F. and Christopher J. F., 2012;

Anderson R. P et al, 2009; Comell E. A. and Weiman C. E., 2002; Tran Huu Phat et al, 2009), Tuy nhien, doi vdi h? lupng td d nhift dp c\rc thap, khi the hoi hpc ho$c hang so lien ket thay doi, itsX den gia tri tdi han se xay ra chuyen pha lupng tu trong he (Moshe Gitterman, 2014), Nhung, cho den nay, co rat It cdng trinh nghien cim ve chuyen pha lupng tu trong cac he boson, dac biet la he boson hai thanh phin hoa tan.

Trong khi do, su phat trien cua nganh cdng nghe lupng tir rat can thong tin day du vl chuyin pha lupng tu trong cac vat chit lupng tu, la vat lieu quan trpng trong cac may tinh lupng tir trong tucmg lai. Nhu vay, nghien ciiu vl chuyin pha

V'

^ = *' -'5;-5;;rK + v--a V' \ I a v^\

(1)

trong do fii, (fjij la ki hieu thi hoa hoc

J Khoa Nang lufng, Truang Bai hfc Thuy tffi Khoa Cong nghi nang iwjng. Trudng Dai hpc Difn luc.

cda trudng ^, (v/); mi, {mi) li khdi lupng cua nguyen tu boson loai thii nhit vi thii hai; X^ Xi, X la cac hang so lien ket va ludn duong: A. =

KHOA Hpc Kt THUAT THUY Lpi VA Mdl TRUdNC . 5d 56 (3/20171

I = 1, 2; a, l i cic dp dii tin x j sdng im tuomg Nho v|y,_cic tham sd dilu khien li nhi$t dO, dng vdri va ch^im giOa cic nguySn td khic loai. thS hoi va hing so lito ket.

Hay, Dvra tren (Tran Huu Phat et al, 2009), chung , tdi thu dupe thi hipu dung CJT trong gin dung

^ _ « n i _ o ^ j ^ ^ _ " t * ^ (2) bong bong kep cii t i l n - l i phdp gin dung phvc m mt+mi hoi dinh 1;^ Goldstone:

<T(*.,fl) = - M 5 + | * J - ft*? + | * J + 5*S«5 + | p f i +^PJ2 +^P^^P^, + ^Qh + f «lj +^(2iiO,2 + I J trpnD->m + DoHWW-1]

h^j tr[ln(;-»(k) + CJH*)C(*) - 1]

+ 2 J

(3) trong do;

Di

,!(,, /^-'^-3..*5 -.„ \ „..,,, / ^ ^ « i - » V

Ml* = -Jii + ^ * o + 2*« +-2^''ii + Y ' ' 2 2 + 4 0 I I + j0z2;

, , ! ( , ) , (^-"^-^^A^t^S _^-'^ ),a-Hk)J^^''' . - - ^ l

Mj = - f e + 3^2.^? +|./iS^ + ^ I 2 „ + H i i 2 „ + i p , j + | p , , :

''a. = | D ^ C f c ) . Q . . = | c ^ ( * ) ; a,i. = l ; 2 /I C

//(*) = 7- ^ I J ^ /K,t), <^ = 2rar.

J "—"

Tir (3) chiing toi nhan dupe

a. Cdc phicang trinh khe b. Cdc phuong trinh Schtvinger - Dyson a'?-^C»..»..P.g) _ _ j j j Kit hpp vdi phuong trinh (4) nhan dupe

—£ r: = 0 => M,j, = 0.

S?s"(.<t'c.'P„,D,G) , Z ^ + Mi -<„,

= 0 =» G ' ( * ) = I ^">

KHOA HpC KY T H U A T THUY Lpi VA Mdl TRUpNC - S6 56 (3/2017)

(6)

Sd dvmg thi h o i hifu dung

liic niy cic phucmg trinh khe dirpc viet l i

* . « + i * l = ^ , •»>*•'*i*5='^.

Do do chung t6i thu dugc

Cac c6ng thiic (4) va (8) se duoc sir dung de k h ^ sat gian d6 pha. Tu do dua ra cac kich ban chuyin pha luong tu kha di trong h€.

Bai bao nay dugc trinh bay vdi cau tnic gom ba muc voi muc 2 la phSn chinh, trinh bay cdc kk qua tinh s6 vh cac kich ban chuyen pha luong tii va loai chuyen pha tuong ling. Ket luEin ciia bai bao duoc trinh bay 6 muc 3.

2. CHUYEN PHA LU*<?NG TU" TRONG R^ BOSON HAI THANH PHAN

6 phan nay, chung toi thu duoc cac kich ban chuySn pha ciia h$ boson hai thanh phan hai thanh phan trgn lan khi the hoa hoc ciia mot thanh phan thay doi trong khi nhiet do va hang so lien ket khong thay doi. Cu the, chiing toi khao sat bai toan mau doi vol he hon hgp g6m vo so cac nguyen tu ^^Rb va *'i?6 (co kh6i lugng rut gpn mi2 = 80 GeV).

De CO dugc biic tranh tong quat ve cac kich ban chuyen pha khi hang so lien ket bang hang so, chung toi vg gian do pha tren mat phSng (T,

^2) ling vcri bo tham so dugc chgn nSm trong vimg gia tri thuc nghiem ciia chiing (Alexander L. F. and Christopher J. F., 2012; Ketterle W., 1999) va thoa man dieu kien he gdm hai thanh phan trgn lan (Tran Huu Phat et al, 2009). Vi dy,;., = 5.I0•'^eV-^ A, - 0,4.10-'^eV-^ X = 2.10"

%W-\ fji = 5.10"'^eV. Kk qua cho 6 hinh 1 duoi day.

U^ 2Pi2AA-iiiA B 2 " 4XiAa-A2 4^X^-i?

(7)

(8)

Aft < 0 A / i < 0

*o=0 1*0=0

• ft^O

• Mj > 0 0 0 * 0 Wi<0(fro = 0

^

11

^

\ TCP

Ml <0

*o=0 iAo*0

^ j ( l 0 - ' = e V )

Hinh 1. Gidn dSpha trin mdt phdng (T.iii) ung v&i bg tham so mdu dugc chgn d trin.

Trong do (po, ij/o Id cdc tham sd trat ti/t, cite duang pha irng vai cdc tham so dgng luc Mi,

M2 bdng khong. TCP Id diim ba l&i hgn.

Hlnh 1 cho thiy, vdi mpt g i i trj khong doi cua nhiet dp, h? sS h i i qua chuyin pha lupng tii khi thi hoi thay ddi, x i y ra khi thi hoi in d?t gia tri tdi han, //j= it2c - l i hoinh dp dilm giao cua dudng thing T = const vdi dudng ^4 = 0, S = 0. Ro rang, fijci 2.10"'^ eV phu hpp vdi khoang gia tri cd the dieu chinh h-ong thuc nghiem ciia the hoa. Nhu vay, trong thuc nghiem, bing cacli giir nguyen s6 hat cua thinh phin thii nhit va thay ddi sd hat cua thanh phin thu hai trong hj den khi H2 dat gia tri tdi han sa quan sat dupe chuyen pha lupng tii d moi gia tri nhiet dp cm thap cua he. Nlu t h i hoa ldn hon gia trj 2.10"'^

eV, se khong xuit hien chuyin pha lupng tii trong he. Die bipt, vdi nhipt dp cua he dupe giO khong ddi va thip hon 400nK, khi dilu chinh the hoa, se ddng thdi xiy ra chuyin pha lupng KHOA HQC KY T H U A T THUY Lpi VA Mdl TRUdNC - SS 56 (3/2017)

td dli vdi c i hai thinh phin d ^ hp. Nlu nhipt dd ciJa h$ cao hem 400iiK, khi thay dli tbi hoi, chi tdn t ^ v i xiy ra chuyin pha lupng tiit dli vdi thinh phin thd hai cda h$. , . .

•—^^,£0

T = S n K

/

tfia

•

«!» . .

K,(10-«eV) Hinh 2. Stjcphif thudc vdo p2 cita cdc

tham sd trgt tu.

De minh hpa ket l u i n rut ra tir giin d l pha v i ed dupe s\r h i l u day du ve c i c kjch b i n chuyin

T>SnK

- « . 2.5.10-'^aV, 4>o. 3.85 eV*^

- l a . 2 . 0 . 1 0 - " #V, ( W . a - l B e V " ,."' -n «1.5-10-"oV, (po.229eV''5*'

*o(eV='

pha cd thi xiy ra, hudc tito chdng tdi xdt svr phy thuOc vio thi hoi cda cic tham s6 trat tv (|io,

\|iot?d gii hi cvK thip cda nhi^t dO vi bd tham so dupe chpn cda hlnh 1, vi dp T= 5nK. Kit qui cho dr hinh 2.

Hhih 2 cho thiy ring doi xting cua h? bi phi vd (tham s6 trfit tvt tpo khic khong) tai gii hi tdi han ciia thi hoa 112 = Item = 0,93.I0""eV > 0.

Turc l i xiy ra hito tupng chuyin pha phi vd doi xdng nghich dio (ISB) dli vdi thinh phin thd hai khi thi hoi dat tdi gid tri tdi ban, trong khi xiy ra hito tupng chuyin pha khdi phvc ddi xdng (SR) dli vdi thinh pMn thd nhit khi thi hoi dat gia hi tdi ban iicv = 2.10""eV. Sv biln thito dcm dito cda cic tham so trit t\r theo ^2 cimg cho thiy svt chuyin pha l i loai hai. Dilu dd dupe khing dinh mdt lan niia d hinh 3, bilu dien su phy thudc vio cic tham si trit t\r ciia thi hito dvmg V^" - i f ^ quanh gii frj tdi h?n cua the hda tgi r = 5nK.

2.!

5-20

5 "

. .

T-5nK

(J2 «a43.10-"«V, ^ ^IXliM^

n .O.B3"10-"eV, A] "1.35 eV"2 in . 1.43.10-12 ev, * ) • 1 01 BV3'2y

, '~"'T"

/ / / /

i(/o(ev"'

4

Hinh

Hinh 3. Suphu thugc cua thi hi$u dicing vdo cdc tham so trat tu xung quanh gid tri tdi han cua thi hod dT = 5nK.

Tiep theo, chiing toi xet su phu thugc vao th^

hod fj2 ciia cac tham so trat t\r 6 nhiet do T = 650 nK > 400 nK. Kat qua cho 6 hinh 4: R5 rang chi xay ra chuyen pha lugng tu ddi voi thanh phan thii hai trong h? khi the hoa //^ = 0,77.10"'^ eV ting voi kjch ban chuyin pha la ISB va su chuyen pha tuong ung cung la lo^i hai. Tiic la, co the tao ra cac kich ban pha mong muon bang each don gian la dieu chinh cac tham so.

3. K E T LUAN

Bang each khao sat cac kich ban chuyin pha lugng tu dua tren gian d6 pha ve tren m3t phing

.

•

li-o

r = 650 n K

.

^0^.'-'^

i » 0 / ? ! - ' • = ' .

4. Suphu thupc vdo the hod fi2cua cdc tham so trat tu tai T =650nK.

KHOA HOC K? THUAT THOY LQI VA HOI TRlrtfflG - Sfi 56 (3/2017)

(T n) Chung tdi iH thu duoc cic kit qui mdi lupng td khi thay ddi thi hoi d?t < ^ gii trj tdi nhu sau- h?n. Dd l i chuyen pha phyc hdi ddi xdng hojc

I Hoin toin cd thi quan sit dupe bing thyc chuyin pha phi vd dli xiing nghjch dio.

nghiem chuyin pha luong hi trong h? boson hai 3. Ket qui nghito ciiu so gdp phin cung cip thanh phin vi chuyin pha li log! hai. thdng tin cho cic nhi thyc nghi?m ttong IM,

2. Tin tai hai kilu kich ban chuyin pha vyc miy tinh lupng td.

TAI LlfU THAM KHAO

Alexander L. F. and Christopher J. F. (2012), Bose gas: Theory and Experiment, Contemporary Concepts of Condensed Matter Science 5, pp. 27-67.

Amelmo G. and So - Young Pi (1993), Self- consistent improvement of the finite - temperature effective potential, Phys. Rev. D 47,2356.

Anderson R. P., Ticknor C, Sidorov A. I., and Hall B. V. (2009), Spatially inhomogeneous phase evolution of a two -component Bose - Einstein condensates, Phys. Rev. ASO, 023603.

Comell E. A. and Wehnan C. E. (2002), Nobel Lecture: Bose -Einstein condensation in a dilute gas, the first 70 years and some recent experiments. Rev. Mod. Phys. 74, 875.

Comwall, J. M., Jackiw, R. and Tomboulis (1974), Effective Action for Composite Operators, Phys.

Rev. DIO, 2428.

Dang Thi Minh Hue, Nguyen Tuan Anh (2016), Quantum phase transition in homogeneous boson systems, annual conference of Thuy Loi university.

Ketterle W. (1999), Experimental studies of Bose-Einstein condensation. Physics Today, December, pp.30-35.

Moshe Gitterman (2014), Phase Transitions Modern Application, Worid Scientific, Smgapore Tran Huu Phat, Le Viet Hoa, Nguyen Tuan Anh, and Nguyen Van Long (2009), Bose - Einstein condensation in binary mixtures of Bose gases, Ann. Phys. (NY) 324, 2074.

Abstract:

QUANTUM PHASE TRANSITION IN BINARY - MIXTURE BOSON SYSTEMS WHEN CHEMISTRY POTENTIAL CHANGED

Quantum phase transition in binary-mixlure boson systems is studied by means of the Cornwall- Jackiw-Tomboulis effective potential approach in the improved double-bubble approximation which preserves the Goldstone theorem. Its main feature is that the transition is second order occurring when the chemistry potential is approached lo critical value associating with two types including inverse symmetry breaking transition and symmetry restoration transition.

Keywords: Critical Value, Order Parameter, Effective Potential, Symmetry Restoration (SR), Inverse Symmetry Breaking (ISB).

BBT nhdn bdi: 12/01/2017 Phdn biin xong: 06/3/2017

KHOA HQC KY THUAT THUY Lpi VA Mdl TBlrtNO - S6 56 (3/201JI