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Kurkcuoglu, M E

Aytekin, H

An Investigation of the 16O+16O Elastic Scattering by Phenomenological and Double-Folding Potentials in Optical Model Formalism at the Energies Between Elab = 75 and 145 Mev

Utdian J. Phys. 80 (6). 683-684 (2006)
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Vol. 80 •  N o . 3 •  M a rc h  2006
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Front Contents

Ghosh, Dipak

Deb, Argha

Chattopadhyay (Dutta), Keya

Dutta, Srimonti

Lahiri, Madhumita Banerjee

English

Multi-dimensional Fluctuation Analysis of Target Residue in Nuclear Collisions

Devlal, Kamal

Khohya, Kuldeep

[lumJ 80(8), 801-805 (2006)
Analysis of equations of state for metals and rare gas solids
Kama! DevlaT and Kuldeep Kholiya 
Dcpaitmenl of Physics, G B Paul IJnivcisiiy of Agiiculluie and TcLhiiology. 
Paiiliiagar -363 145, DiUiianchal, India
H-mail k ,dcvlalQi>iedillmail com
ti<‘( M a n h 2 0 0 '^ a t I 21 J a m ’ 2 0 0 ()
A Lum|iaialivc sliidy ol dillcicnl cqualioiis ol slalc icscnlcd loi some melals and u ie gas solids ll is shown dial die Po 
and Sh.mkci equa -il state aie new appioaches In day do mil impiovi da lesidts lo impiession liLhavioi allhoiigh dasL
.Ki nis ia|iiiied a lot ol tOmpiiiaiion woik The lesidls ohiamcd by Poi ler-Taianiola sli...................... ............... .menl as tom pan.d wdh Su/uki aia.
Mkii Inimalaiuins The icsulls nhlamed by llam a-Sm lo EOS aie veiy igh The Tad EOS is lound lo give lai la t lu agiLemenl with llu available 
nineiilal ifsiills lhan these new equations In the pieseni study, ihe Ta 's EOS is liirthei ixlendcd lo study the Ihcimal expansion behavioi ol solids 
\liisiim III lliL u inetp l ol Iheimal piessuic The new modified 7'ail’s ohaiie hOS gives gooil agieemenl lalw een caludated and expeiimcntal data 
h ill inuiisliah Ihe validity ol the m odified EOS
MMirils Fqiialion of state melals laie gas solids, theimal piessme 
( S Nns 64 10 +h 64 30 -H
liilnxliietion
uaiioMol sUde(hOS) is basically a relation between pies.suie, 
Lime .iiul lemperatiiie Jt has a very important role lor analyzing 
ilicimopliyMcal pioperliesol different classes of solids The 
IS not only impoitant in the basic and applied condensed 
ttci physics but also in geophysics and eaith and planetary 
cni.es There aie many EOS’s available in the literature (1-4| 
inv wnrkei s have proposed their EOS’s on the basis of different 
s and continuous efforts are being made to formulate 
a TOS’s Most ol them are not capable to yield satisfactory 
alls ai high piessure Many times the theories and equations 
slalc aie very complicated, require many input parameter, 
iich are not always available and need very lengthy 
tuliitions Besides these problems, the EOS’s do not give 
>d icsulls Gaurav ei al |5] repotted the calculations using 
lu- well-known EOS’s without comparing the results with the 
e^iimental data Therefore, the study does not point out the 
icrioriiy ol any particular EOS In high-pressure, generally 
-d theory is the finite strain thcoiy, which means the theory 
- hi Birch [6J The first equation based on potential which 
coed much attention was due to Morse f?l Tt was furthei
^“opunding Author
improved by Rydbeig|8| Vmet ct al 1^ 1 have icdiscovcied ihe 
Rydbeig potential as discussed by Stacey |3] Theic aie some 
othei lormulations viz Suzuki foimulalion [lO] based on Mie- 
Gruneisen theory, Shankei ct al loimulation |11| based on 
Gruneisen theory of theimal expansion
In present investigation, a compaiative study is made by 
using ditfeient EOS’s to identity the better equation ol state 
that gives satislactory agieement with the expeiiincntal data 
I'he Tait EOS f 1,2] is also used to predict the compiession in 
solids and the lesults aic compared with that obtained by othei 
EOS’s in the light ol expeiimcntal lesults It is found out that 
I'ait’s EOS gives better lesults The theoiy is tuiihei extended 
to study thermal expansion by applying the concept of theimal 
pressure 112-14] The thermal pressure (phonon picssuic) in 
crystal is developed by the lattice vibration inside the ciystals 
As the lempeiatuie increases, the amplitude ot the vibration 
also increases, which enhances the thermal pressure ol solids 
After inclusion of theimal pressure, the modified Tait isobaiic 
EOS can not only predict the lesults close to experimental data 
but also requires less number ot input paiameteis involving 
easy computational woi k In the present papei, we extend these 
studies for some important metals and rare gas solids to 
demonstrate the superiority of this EOS model
©20061ACS
802 Kamol Dcvlcil and KuUleep Kiwliya
The whole PVT (pressure, volume and temperature) surface 
ol a .solid can be predicted with the help of a universal EOS 
using a given set ol data at /eio pressure at a single reference 
temperature The analysis of the behavior of hydrogen solid (n- 
11^ ) IS a rigorous test 115| for any univeisal LOS, because it is a 
highly compressible solid Thus, relatively high values of 
compression are leached although the applied pressuie
IS not loo high
2. MethtNl of analysis
The first quantum-based potential to receive serious attention 
was due to Morse [7j The potential is based on the studies of 
molecular spectroscopy, which was used m a I mite strain theory 
|C1 For many years, the Moise potential was the most favored 
equation tor ft^ OS studies 7'he potential gives the following 
fomiol theFX)S|3|
P= K
V
P ^^K .
Ineq (4),
follows 1 19] 
x)exp|^ -^ - (A',; - 3) (1 - x) f ^/I, j(l - i)
Hama -Suito EOS reads as 
r
, V
k ;,-\ i - L
Va
The EOS based on Shanker formulation reads ,
|11J
•f'lk)*,
'I'he Tail's isothermal equation of state is given bv ih, 
expression (1,2|
(3)
(4)
v„ k ;, +1
whcie P IS the pressure, K the bulk modulus, K' the pressure 
del ivative of bulk modulus, v = p/pj, ~ V„/V and refers to 
then values at initial conditions
Vinet r tri/19,16,17] have obtained the following expression 
for pressure
P - ^K,,^^ ^ 1 - v)expj^^(AV, - l)(l- ' x " ') j (2)
Ineq (2),
Eqs ( I) and (2) are the same An excellent review on this 
suh|ect has been wiittcn by Stacey 13]
Poll ier-7'araniola EOS leads as follows [18]
Expanding the exponential term in eq (8) and neglectin{.'i^ 
higher order terms, we get the following relation
P = /C„ll i - -
v „
Comparing eqs (5), (6) and (9), n iscleai that eqs (6),mJi' 
are the same
Now, the Tail hOS is modified by inclusion ol thciiii, 
pressure The thermal pressure Pj^ ^ is cxpiessed as 112-I4]
I ~ I
Now, if thermal pressure is taken in account, then the el lain 
pressure is reduced as
Vo Ko + \ K„ ' .
On integrating above equation for thermal pressuie ai 
putting the value of thermal pres.sure, the equation can I 
expressed as
y 1
Ko + i
and /li - ^ - 0(*« + 3 ) - | ^
The EOS ba.sed on the Suzuki theory of thermal expansivity 
reads as follow 110,201
It may be considered that if the reference pressure is /ef' 
then this equation can be expressed as
y _ I - - in{i-(Ar' + i)a„(r-r„)}
An + I
Analysis o f equations o f state for metals and rate gas solids 803
l-il (10) IS the final modified Tail's equations of state, which 
■nipcrafuie- dependent expression for thermal expansion in 
li IS also pointed out that the concept of thermal pressure 
,lsu be applied on bulk modulus equation for obtaining 
fn-raiure- dependent equations of slate
Kesults and discussion
. mpLii pjiameters [5J5J required foi present calculations 
,implied m Tables 1 We have selected four metals \>iz Cii, 
ph 1 I and tw'O rare gas solids viz Ai and Ne The choice ol 
,1. maiciials depends on the availability of the expeiimental
1 |ii|iiii paramt'icrs [SJS] used in compression
encouraging and compares well with the experimental data 120- 
23]. The percentage deviations calculated at the minimum value
KLkiLiice
knipL’ialuiL-
("Kl
K„ III
(DPj ) (in U )' K ')
11)0 135 5 03 -0 0K3 5 04
lOI) 72 () 4 H5 -0 104 0 96
1(10 41 7 5 70 3 07
40 b 2S 7 07 -2 52 100 8
Ml r> 36 7 6 1 2 HO 00 0
1 1 55 3 5 1 13 9H
FiKurc 2 Compiession bchavioi of jluminuin usiiip ditlcrcnl EOS modoK
) that the comparison can be made The results obtained 
om ip icss io n behavior are shown in bigures 1-5 It is 
irI ihai the T OS based on ihe Suzuki foimulalion (eq (5)1 
L‘, ilic iLsulis, which are very much low as compared with 
vxpmimcMital data 120-23] The EOS based on the Shankei 
niil.iiion |t‘t| (b)l slightly improves the results of Suzuki but 
I thciL IS a laigc deviation from the experimental data The 
ol both these EOS's arc improved by the EOS reporied 
lei-'laiantola leq (3)1 The results obtained by the Hama- 
i" I'OS |eq (4)1 are very high as compared with the 
iciimiMiial data It is pertinent to mention here that Hama- 
HXS needs the values ot Kq which are rarely available in 
iiiciatuie Perhaps Pb IS such a case Therefore in the present 
ic‘i vvi are not using this EOS for Pb Eq (8) based on the 
riTuidynamic analysis gives the results which are very much
v/v^
Figure 3. C'omprcssmn behaviui ol lead iisinji dillueni EDS modi Is
t t impression behaviour of copper using difterenl EOS
F ig u re 4. C'ompiession bchavim of argon using d illc icn t EOS 
mndds
of W/VO considered in the present woi k, are reported m Table 2 
The similar trend of variation found for all the solids studied m 
the present work, demonstrates the better agieemenl by Tail's 
BOS
A good agreement obtained for the compression behavioi 
of solids using eq (8), encouraged the authors to extend this
ThHIc 2. Pcrccniagc dcvutmns .it minmium in compresiiiun
804 Kamal Devlal and Kuldeep Klioliy
Solids Percentage deviations
Pi fscnl woik 
(eq M)
Su/iiki
(eq 5)
Slianker 
(tq 6)
Poiiicr- 
Taranlola 
(eq 3)
Hama Siiiio 
(cq 4)
('ll
(at P/F„~-0 4K) 3 3 77 8 72 8 30 0 390 3
Al
(at V/V^^M)M) 15 1 82 2 77 1 17 4 5H2 1
Pb
(at V/V,~{) 30) 26 (« 87 5 84 4 78 3 -
Al
(al P/V,-0 4l) ) 9 87 4 84 8 48 1 1968 7
model lot the thermal expansion al P=0 Good agreemeni is also 
obtained loi theimal expansion by using eq (10;
Figure 5 ('ompicssion behavmi nl luon usmt; iIiIKtciU EOS moilds
The lesults obtained using eq (10) are shown in Figuics 6- 
R tor the Cu,Li and Ar, The experimental data 124,25] are readily 
available in the case ot Cu, Li and Ar, which compare well with 
the present results Thus, a simple theory ol thermal pressure 
seems to be applicable undet high piessuic and high temperature 
for the solids considered in the present woik
Tamperalure (K)
Fif>ure 7, TtiL'inial cxpjnsion ol lilhium iisiny cq (III) 
’ T ------- Present work (eq 10)
Temperature (K)
Figure 6. Tlicrmal expansion of Lopper nsini; rq (10)
Figure 8. Thcimal exp.insion ol solid Ar horn u-feitnci. 
mtlling tL‘mpLr,]luiu usin^ eq (10)
Acknowledgment
The authois are thankful to Di D R K Gupta toi his \ 
guidance and suggestums
Heffrenccs
| l I J Freund and R Ingalls J riiv\ Chnn Solids 50 
12) L M Thomas and J .Shanker Phvs Sini Sol (b) 189 Mil'll*' 
n i F IJ Siaccy and P M Davis Pltys rnrtli Planet Inic' 1'^ - 
(2004)
|4 | F D Stacev Phvs Enith Planei Intel 128 179 (2001)
15) S Uaurav, B S Shaima and S C’ Upadhyayu PIiysiki II 
( 2002 )
fb| F Ditch J (jeophv.s Res 57 227 (1952)
|7J P N Morse Phvs Rev 34 57 (1929)
18] R Rydberg. Z Phvs l ^ 376 (1932)
|9 | P Vinel, J Ferranlc and I R Smith J Phvs f'19 L467 
IIOJ I Suzuki J Phvs Earth 23 145 (1975)
11 11 J Shankcr. S S Kushwah and P Kumar Phvsua B 233 7)^ ''
I 12J O L- Anderson in hqualion ol Stales of Solids for Geoph'^ '^^ ' 
( erainn s Sfietues (New York Oxford Univ, Press)
Analysis o f equations of state for metals and rare gas solids 805
1^ Pl'vIj I II R K Gupia DAE Solid Stale H iw k s 
(DiLLiiihci 20"' - 30'"*. ( ju ru tunak Hev University. Amnisui, 
InJM) <3004)
j,. K Y Singh and B R K Gupta Natl Conf on Advaiue\ in
, „ii,It lift'd Mailer Eliv\i(\ (Febiuaiy 11“' - 12'"*. Thapar Institute 
',1 luliiiology PaiMla, India) (2005)
M IjmmUo, V G Baolua, I E F Rubm, J Nunc/ and M Cacers J 
\ Sol,d\ 63 1705 (2002)
I* \mLi i H R**''*-' 3 Feirante and J R Smith J Phvs Cond Mattel
II .7S (1000)
1. vuiLl J R SiTiilh and J H Rose J Pliys CIM U 6 7 (1087)
) hiiiiL'i and A Taranlola Phvs F.tirlh Plane! Intel 109 I (1008)
[lOJ J Hama and K Suilo J Phvs ('ond Mailer 8 07 (10%)
[20J G Helfiich Phvs Earth Plaiiei Iniei 116 m (1099)
|2 I ] W J Nellis, J A Moiiaily, A C' Mitchell M Ross. R G Dandiea. 
N W Ashuoft, N r Holmes and G R Gathus Phvs Pev Lett 
60 1414 (198H)
122] MRoss H K Mao, PM Bell and J A Xu / Cheiii Phvs 85 1028 
(1986)
12'!] T A Hahn J Aiipl Phss 11 5006(1070)
[24] M S Andeison and r A Swenson Phvs Hev 1131 668(1085)
125] O G Peterson, U N Bateheldei and R C) Siinmuns Phvs Res 150 
703 (1966)

Analysis of Equations of State for Metals and Rare Gas Solids

Haldar, Prabu Kumar

Guptaroy, Sima

Azimuthal Pion Fluctuation and Phase Transition in Ultra-relativistic Ring-like and Jet-like Events

Rajkhowa, Monisa

Das, Mrinal K

Singh, N Nimai

Possible Radiative Origin of Δ221 and Sinθ13 Revisited

Indian J  Phys. 80 (9), 949-950 (2006)
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Forthcoming Publications

Gopakumar, Rajesh

iP l i y , 80(11), 1071-1073 (2006)
Holography and hydrodynamics
Rajesh Gopakumar
Harish-Chandni Research Inslitule, ChliaUiag Road. Jliusi. Allahabad-21] 019. IJllai Pradesh. India 
E-mail gopakiiiiir@>mn cruet 111
Ui.lroil Wc describe some recent insiglils from slniiE llicory into holography, especially in the conlcxl of a liydrodynain 
mil ol hhitk hole physics
Quark gluon plasma, AdH/CFT conjecture, black holes, holography 
1*U'S Nos, I I I-*) Me, 11 10 Wx, 12 3H Mh. 04 70 Dy. 47 lO -q
|| Inlritduilion
i\S tem s lo sUind a[iarl from all Lhe oliter forces ol 
irr m nuiny d ifle rcn l ways Whereas lhe quantum 
.iniK.s (it lhe other forces are beautifu lly captured 
nil! [Jitr Iramework o f local quantum field theory, gravity 
rLsisied All such attenrqils lo lame it. Partly, the reason 
IS Imm Einstein’s observation that gravity is woven 
iht very labric o f spacetime. This suggests tliat 
rid,nvi the dynamics o f gravity m ight lie radically 
irruu Irom that of odver forces
'^'iL idea that gravity may be h o h ^ r a p h i c is one 
WA\ in which this difference may manifest iLself 
iivAioii was projxised by G ’ l H oo ft (1) and elaborated 
S Su,sskmtl [2] 111 the early nineties lo make sense o f 
"'.rii; AspeUs ol bUick holes It remained a tantalising idea 
very concrete realisa tion was proposed by11
describe how the h y d r o d y n a m ic behaviour ol such gauge 
theories is encoded in pmperties o f black hole honzons. 
Not only has tins led lo insights into the physics o f fie ld 
theories but it is also giving a new perspective on the 
membrane paradigm for black holes
AKR , 1 believe, would have been very happy lo see 
some o f tliese developments since they provide fresh 
illum ination on some o f the concepts that A K R himself 
helped develop This article is dedicated lo his memory
2. Holography
Tlie universal Bekenstein-Hawking expression fo r the 
entropy o f black holes
4Gv
(1)
for a theory o f gravity in an asymptotically 
'’■Jt Sitter (A^/S) spacetime. The rarrufications o l the 
conjeclure for the holographic nature o f gravity 
’iiiriae ui he unearthed and we seem to be uncovering 
hcduiilul picture
ihi.s ariide I w ill try and b rie fly sketch a few o f the 
notions that have emerged in the last few years 
!i)cus on some aspects o f black holes that are 
*’f''1'hically reflected m the dynamics o f strongly 
thermal fie ld theories In particular, we w ill
was one o f the first clues to the holographic nature o f 
gravity Recall that A „ is the a r e a o f the horizon and G f, 
IS Newtons’ constant The area dependence indicates that 
any microscopic accounting of this entropy in terms o f lhe 
number o f degrees o f freedom o f some underlying theory 
must have an unusual property. It cannot be extensive in 
the volume In fact, the area dependence seems to say that 
the degrees o f freedom must be more like those o f a local 
fie ld theory m one lower dimension The bold proposal o f 
’ I H ooft was that the e n t i r e g r a v i t a t i o n a l d y n a m ic s in d
© 2 0 0 6 lA C S
1 07 2 Rajesh Gopakumar
s p a c e t i u w d im e n s io n s is c o m p l e t e l y e r u o d e d in a l o c a l 
th e o r y in { d — \ ) d im e n s io n s Thus Qie origin ol the term 
“ holography”
The 1997 AdS/CFT conjecture o f Maldacena f3J offered 
the opiK)rtunity to flesh out this pr(»posal The conjecture 
liTose from developments in string theory luid describes iin 
exact duality between closed superstnng theory in the ten 
dimensional A d S ^ x spacetime find Uie m axim ally 
supersymmetnc Yang-Mills theory in lou r dimensions Tlie 
conjecture has sinced been generalised and is now 
understood to be valid lo r a large class o l asym iitotically 
A d S ^ spacetimes In all cases, a seniickLSsical gravitational 
description ol the spacetime dynamics is captured by the 
strong interaction dynmnics o f a 4d field theory
Tlie connection between dynamics in five dimensional 
AdS spacetime find lou r dimensional held theory is a 
rcHection o f the hologiaphic nature o f this duality In la d , 
the 4d spacetime in which the fie ld theory lives is the 
asymptotic boundary ol the A d S ^ spacetime There is then 
a precise dictionary [4,5] between observables in the gauge 
theory on the b o u n d a r y and those o f the gravity theory 
m the h u lk . In the semiclassical lim it fo r gravity, this 
dictionary takes the fo rm
(2)
Here the le ft hand side is the gravity side in which we 
perform an integral over bulk fields (including the metric) 
taking specified values on the boundary The right 
hfind side is the gauge theory in which we have the patli 
integral over gauge fields A . The boundary value nets 
as a source term fo r a gauge invariant operator o f the 
field theory Thus the gravity theory may be viewed <is the 
generating functional fo r correlators in the boundary gauge 
theory
What does tins holographic description tell us about 
black holes, the orig ina l m otivation o f ’ tH ooft and 
Susskind'^ One finds that the Schwfirzschild black hole in 
A d S s , lo r instance, is described by the same gauge theory 
hut now at a lin ite temi^erature, w hich is the Hawking 
teriifieralure o f the b lfick ho»le [6J Tlius we can Irfinslatc 
questions about black hole physics (in five dimensions) 
in to questions in the strongly interacting dynfimics o f hot 
gauge Lhcones (in four dimensions) and v ic e v e r s a '
For instance, the equilibnum tliermcidynamics o f the 
gauge theory desenbes black hole thermodynamics In 
particular, the Bekenstein-Hawking entropy o f blfick holes
is the same as the entropy o f the thermal gauge Uit 
in the deconfined phase The latter, l:)eing extensive * 
three spatial dimensions is actually proportioiiHi 
area o f the horizon o f the five dimensional , 
(which IS a three dimensional sphere) Other thermcxivi, 
features such as phase transitions in the gauge ilieon, 
also liave their reflection in the gravity side
This connection to strongly interacting gauge ihtn, 
took on a new significance because o f recent exiTerirnLi 
results from die Relativistic Heavy Ion Collider (RH|(' 
Bronkhaven In these experiments, the high 
collusions ol gold nuclei seem to have creaicil a 
teniiwature phase o f deconlined strongly mterdctiiiy t|Ui 
and gluons (see [7.8] for overviews) Tins Slr^ n 
interacting Quark-Gluon Plasimi (SQGP) is very dil'm 
describe using the Uxils o f perturbative gauge lliAm 
appears as i f the dual description in terms 
gravitational physics o f five dimeiiMonal AdS bhu.k 
IS better at reproducing some o f the features tlial ihi R1 
data exlubit'
3. Hydrodynamics
One o f the challenges o f understanding the RHIC l 
was in describing phenomena w inch go somewhat W\ 
etiu ilibrium dynamics In fact, the prcx;ess of fornviiiuii 
e vo lu tion o f the SQGP phase are best 
hydrodynam ically Remarkably, it api^ears that ihc SQ 
behaves a lm ost lik e a p e rfe c t flu id To j 
approximation, it is as il the shear visctxsity rj is ncj/lin 
The dimensionless parameter
j 10
where s is the entropy per unit volume If this tlesair 
oi the data is indeed correct then this would be the n 
perlect flu id observed in nature
Such a small value fo r the shear viscosity is 
to explain using perturbative calculations in the 
Lheoj7 These give a behaviour
Infor small values o f the gauge coupling 
calculations, the shear viscosity is extracted from 
frequency pole in the tw o point function of comi^ on 
o f the energy momentum tensor
Holography and hydrodynamics 1073
Using ihc A d S i C F T d ic lion iiry for gauge tlieory 
,n-el:ilorN mentioned in the previous section, this two 
(unction has a gravity interpretation in the live 
jiniensional black hole geometry It can be related to the 
cross section tor polarised gravitons by the 
hLitk hole [9] This latter calculation yields a simple 
prediUion for the shear viscosity at very strong coupling
(5)? An
this IS very close to the value that best fits
J.ii.i
111 (act, there seems to be something universal about 
[Ills value ol the viscosity extracted Irom gravity calculations 
.i Lirge class o f black holes, the absor]Uion calculations 
mlIiJ this same value, somewhat like the universality ol the 
ilia lormula lo r the entropy It has been conjecturetl that 
il,L nUive value lo r T]/s is a universal lower bound See 
:|0 | 11)1 an overview and references to tlie literature on 
topics
N'lsLOMly IS a him iliar notion in a field theory, but docs 
' iKD'e a direct interpretation in the gravity side‘s Tii fact, 
itvsiLisis studying black holes m llie 1970's came up with 
iliL‘ iioiioii ol a membrane paradigm The horizon o f the 
iiliik hole, as viewed by an ouLside observer, appeiirs to 
hiM ill the pmperlies ol a physical membrane Among 
'ilicr tilings the membrane lias an energy momentum 
itHMir which IS that o f a flu id Essentially, tins follows 
Irnin the behaviour o f geodesics in the vic in ity o f the 
!.>>ii7ou Tlie shear, rotation e tc of these gecxlesics, as
i. imiluted liy AKR , are instrumental m the identification 
.1 lluul The respective coetficenls then give the 
.^inoLis viscosity coelficents Amazingly, the ordinary 4d 
Sdiwurzschdd black hole also has a ratio o f t] / s = l/4 ;r in 
'll'!' menibrjine paradigm
It therelore seems that the hydrtxlynamics ol the gauge 
iliiory IS ho lographica lly capturing the membrane 
dcNcnpiion ol black hole horizons We have grown familiar 
'''iih the notion o f associating an entropy to black hole 
'ii'n^ons and now understand it as the entropy ol the 
'•U'^ ruscopic gauge description o f the system Simihirly, we 
now viewing the hydrodynamic properties that can be 
't'nbuied to the horizon as those o f the hydrodynamics o f 
gauge theory Thus the hologra|ihic gauge theory 
^^''tnpuon gives a physical meaning and sharper picture 
h^e ideas o f the membrane paradigm
IS an aspect o f this connection that the attentive 
might liave found puzzling We had mentioned
earlier that tile gauge theory is to be viewed as liv ing on 
tile iLsymplolic boundary ol the AdS spacetime Whereas 
we are now connecting its properties with those o f the 
honzon which is a dilferent lour dimensional surface in tlie 
interior ol tlie spacetime While we don’ t understand tins 
sharply enough, it appears that long wavelength 
phenomena ol the gauge theory (such as hydrtxlynamics) 
capture the dynamics near the horizon Tlie boundary 
description is mure appropriate as a UV or microscopic 
one This dichotomy is a reflection o f the la d that the 
radial direction in Uie AdS siiacelime jilays the role o f the 
energy scale in the gauge theory, with asymptotic in lin ity 
being the UV iind the deep interior ne^ir the horizon being 
the tfje IR
To summarise, the realisation o f holography in A d S 
spacetimes has enabled us to gel a belter hantlle on nnuiy 
aspects ol this miraculous conneclitm Tlie understanding 
o f hydrodynamic phenomena is a step beyond the 
conventional IMack hole ihernx'idynamics and shows us 
how lar reaching the connection between the gauge and 
gravity iheones are It hits already provided qualitative 
and probably quantitative understanding ol the SQGP 
phase discovered at RHJC The comprehensive nature o f 
the connection pronuses to id so shed light on hir from 
ec]uihbnum situations such as in black hole lormalion This 
has yet to be explored
[1] U ’I Hwfl Dimenstonnl redutnon in i/iumiurn grnvirv [arXiv gr- 
qc/y310026)
[2] L Susskind Thr World At A Hologram, J Malh I'hyj, 36 6377 
(1995) [diXiv liep-lh/y4090K9]
[3] J M Malilucuia ’[ht> large N limn o f supertonfnrmal field theories 
rind snprrgravily Adv Thei/r Malh Phys 1 2J1 fl99B) Ini J, 
Thenr. Phys 38 1113 (1999) [arXiv liep-Ui/97112001
|4 | S S Gubter, 1 R Klebanov and A M Polyakov Phys Lett B428 
105 (199H) [arXiv bi-p-d>/y«02!O9I
(51 L WiUeii Anh-de Siller space and holography, Adv Theor 
Math Phys I 253 (1998) (arXiv liep-lli/9R02150|
(61 II WiUen Anli-de Sitter spare, thermal phase Irnnsilion, and 
confinement m gauge thrones, Adv Theor Math. Phys 2 505 
(1998) (arXiv hep-lli/98031311
(7 1 II Shury'ok ^h y does the quark gluon plasma at RW C behave 
as a nearly ideal fluids Prog Part Nucl Phys S3 273 (2004) 
IarXivlicp-pli/0312227]
[8] E V Shuryak What RHlC experiments and theory tell us about 
properties o f r/uark-gluon plasma? Nucl Phys, A7S0 64 (2005) 
(arXjv hep-pb/0405006]
|9 | U Pulicjsim, D T Son and A O Slanncls The shear viscosity o f 
strongly coupled N = 4 supersymmetric Yang-Mills plasma 
Phys Rev U tt 87 081601 (2001) farXiv hep-lli/01040661 
110) A O Slannels Transport coefficients of strongly coupled gauge 
theories ■ Insights from string theory [arXiv nndiUlhAlSl 1073]

Holography and Hydrodynamics

Kar, Soumitra

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Chaudhuri, Subhadra

Mn-Doped Zn2SiO4 Thin Films Prepared by a Simple Sol-Gel Route: Photoluminescence Properties

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An Investigation of the 16O+16O Elastic Scattering by Phenomenological and Double-Folding Potentials in Optical Model Formalism at the Energies Between Elab = 75 and 145 Mev

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