Hot Stuff

Tags: Context Theory, Wider context, lattice gauge theory, step, QCD, computational mode, quantum field theory, ti, relativistic quantum field theory, Strong Interactions, Fluctuations Experiment, particles, Nilmani Mathur, baby universe, thermal equilibrium, relativistic energies, specific heat, Gaussian distribution, Fluctuations, accurate measurements
Content: Context
Theory
Experiment
Hot Stuff Sourendu Gupta Wednesday Colloquium TIFR Mumbai October 3, 2012
Wider context
Context
Theory
Experiment
Wider context
Hot Stuff Sourendu Gupta Wednesday Colloquium TIFR Mumbai October 3, 2012 Saumen Datta, Rajiv Gavai, Nikhil Karthik, Xiaofeng Luo (CCNU), Nilmani Mathur, Pushan Majumdar (IACS), Bedangadas Mohanty (NISER), M. Padmanath, Hans-Georg Ritter (LBL), Nu Xu (LBL)
Context Outline
Theory
Experiment
1 Why study hot matter? 2 The theoretical puzzle 3 Looking for a critical point in a collider 4 The three revolutions in science
Wider context
Context
Theory
A hot big bang
Experiment
Wider context
The baby universe was very nearly in thermal equilibrium
Context
Theory
A hot big bang
Experiment
Wider context
The baby universe was very nearly in thermal equilibrium
Context
Theory
A hot big bang
Experiment
Wider context
The baby universe was very nearly in thermal equilibrium
Context
Theory
A hot big bang
Experiment
Wider context
The baby universe was very nearly in thermal equilibrium
Context
Theory
A hot big bang
Experiment
Wider context
The baby universe was very nearly in thermal equilibrium
Context
Theory
A hot big bang
Experiment
Wider context
The baby universe was very nearly in thermal equilibrium
Context
Theory
A hot big bang
Experiment
Wider context
The baby universe was very nearly in thermal equilibrium
Context
Theory
A hot big bang
Experiment
Wider context
The baby universe was very nearly in thermal equilibrium
Context
Theory
A hot big bang
Experiment
Wider context
The baby universe was very nearly in thermal equilibrium
Context
Theory
A hot big bang
Experiment
Wider context
The baby universe was very nearly in thermal equilibrium
Context
Theory
A hot big bang
Experiment
Wider context
The baby universe was very nearly in thermal equilibrium
Context
Theory
A hot big bang
Experiment
Wider context
The baby universe was very nearly in thermal equilibrium
Context
Theory
A hot big bang
Experiment
Wider context
The baby universe was very nearly in thermal equilibrium
Context
Theory
A hot big bang
Experiment
Wider context
The baby universe was very nearly in thermal equilibrium
Context
Theory
Choice of units
Experiment
Wider context
k =1 c =1 =1
temperature is energy length is time, mass is energy energy is frequency
Energy is the only dimensionful quantity
Context
Theory
Experiment
Relativity and particle production
Wider context
In thermal equilibrium particles have kinetic energy typically equal to their temperature: T . If two particles collide, their total kinetic energy is of order T . If the mass of the particles is M, and the kinetic energy in a collision is much larger (T M), then particles can be produced. So the Lorentz factor E /M T /M is much larger than 1 when particles are easily produced in a thermal medium. Maxwell, Boltzmann, Einstein
Context
Theory
Experiment
quantum mechanics and field theory
Wider context
Quantum mechanics perfectly fine for problems with fixed number of particles. Say, spectrum of acetylcholine, information transfer through entangled states, transport in nanowires ... Quantum mechanics fails when particle Number Changes: H H + . Then need quantum field theory. Thermal matter with M T requires relativistic quantum field theory. All matter that we know of obeys the Standard Model. So standard model at finite temperature. Pauli, Dirac, Bethe (1930s) ... Weinberg (1972)
Context
Theory
Experiment
The Discovery of the Strong Interactions
Wider context
The atomic nucleus discovered in the scattering of and particles by matter. Positively charged nucleus unstable unless there is a new force to keep it together: the strong interactions. Rutherford (1911) Half a century of discoveries of mesons and baryons. All attempts to understand strong interactions failed. Realization that the true constituents of matter were quarks and gluons. Nambu (1960); Gell-Mann, Ne'eman (1961) Forces between quarks and gluons hundred times stronger than electrodynamics; forces between nucleons is a shadow of these.
Context
Theory
Experiment
Wider context
The Discovery of the Theory of Strong Interactions
A relativistic quantum field theory of quarks developed. Initially faced technical difficulties similar to electrodynamics, but problems resolved. Theory has an intrinsic momentum scale, 200 MeV. Well tested for log(p/) 1: perturbative QCD. Gross, Wilczek, Politzer (1973) Three "flavours" of quarks: light flavours up, down (mu, md ), strange (ms ). Later three heavy flavours discovered (m ). Quarks and gluons confined, seen together only in combinations of mesons and baryons. Remained a theoretical mystery; until a radically new approach developed. Strong interactions: 30 Nobel Prizes to about 50 people
Context
Theory
Particle content
Experiment
Wider context
Context
Theory
Little bangs
Experiment
Wider context
Recreate the conditions of the big bang in controlled experiments in a lab: relativistic collisions of heavy ions. Create a fireball which thermalizes at high temperature, then expands and cools. Size of the fireball 10 femto meters. Detectors placed 10 meters away. See only the late stages of the bang. Similar to today's telescopes looking back for traces of the big bang. Main difference: small bangs can be repeated. Statistical accuracy as high as you want. CERN SPS 1980s, BNL RHIC 2000s, CERN LHC 2010s, GSI FAIR 2020s ...
Context
Theory
A typical experiment
Experiment
Wider context
Context Outline
Theory
Experiment
1 Why study hot matter? 2 The theoretical puzzle 3 Looking for a critical point in a collider 4 The three revolutions in science
Wider context
Context
Theory
Experiment
Post-colonial quantum field theory
xi , ti |xf , tf
Wider context
time
space
Context
Theory
Experiment
Post-colonial quantum field theory
xi , ti |xf , tf
Wider context
time
space
Context
Theory
Experiment
Post-colonial quantum field theory
xi , ti |xf , tf
Wider context
time
space
Context
Theory
Experiment
Post-colonial quantum field theory
xi , ti |xf , tf
Wider context
time
space
Context
Theory
Experiment
Post-colonial quantum field theory
Wider context
xi , ti |xf , tf = xi , ti |xm, tm xm, tm|xf , tf xm
time
space
Context
Theory
Experiment
Post-colonial quantum field theory
Wider context
xi , ti |xf , tf = xi , ti |xm, tm xm, tm|xf , tf xm
time
space
Context
Theory
Experiment
Post-colonial quantum field theory
Wider context
xi , ti |xf , tf = xi , ti |xm, tm xm, tm|xf , tf xm
time
space
Context
Theory
Experiment
Post-colonial quantum field theory
Wider context
xi , ti |xf , tf = xi , ti |xm, tm xm, tm|xf , tf xm
time
space
Context
Theory
Experiment
Post-colonial quantum field theory
Wider context
xi , ti |xf , tf = xi , ti |xm, tm xm, tm|xf , tf xm
time
space
Context
Theory
Experiment
Post-colonial quantum field theory
Wider context
xi , ti |xf , tf = xi , ti |xm, tm xm, tm|xf , tf xm
time
space
Context
Theory
Experiment
Post-colonial quantum field theory
Wider context
xi , ti |xf , tf = xi , ti |xm, tm xm, tm|xf , tf xm
time
space
Context
Theory
Experiment
Post-colonial quantum field theory
Wider context
xi , ti |xf , tf = xi , ti |xm, tm xm, tm|xf , tf xm
time
space
Context
Theory
Experiment
Post-colonial quantum field theory
Wider context
xi , ti |xf , tf = xi , ti |xm, tm xm, tm|xf , tf xm
space
time Sum over all paths: path integral Dirac (1933), Feynman (1948)
Context
Theory
The grand synthesis
Experiment
Wider context
Notice a relation between quantum evolution operator (transition matrix) and the thermal density operator exp(iHt) and exp(-H/T ), Wick rotation t it. Makes path integral real; then use Monte Carlo to do the integral. Fisher, Kadanoff; Wilson (1974), Creutz, Jacobs, Rebbi (1979)
Opens the door to the study of almost any quantity in a field theory. Applied to the study of hadron masses and widths, hadron Form Factors, decay constants, weak matrix elements, muon g - 2, rare decays of hadrons, exotics and glueballs, nucleon-nucleon scattering, nuclear structure, equation of state of neutron stars, phase transitions at finite temperature ...
Context
Theory
A sample result
Experiment
Wider context
M[MeV]
2000 1500 1000 500 0
K p
K* r
X S L N
O X* S* D experiment width input QCD
Durr, Fodor, Katz, et al (2009)
Context
Theory
The sign problem
Experiment
Wider context
When there are Fermions in the external states, then the integrand of the path integral is complex. Monte Carlo method fails. Examples: QCD at non-zero particle density, high temperature superconductors, · · ·
Proposed workaround, use the Maclaurin expansion:
P(µ) = P(0) +
n
µn n!
n
1 is mean particle number, 2 is a particle number susceptibility, 3, · · · are non-linear susceptibilities. Developed methods to compute the coefficients n. Gavai, SG (2002)
Context
Theory
The QCD critical point
1.1
Experiment
Wider context
T/Tc
1
0.9
30 GeV 18 GeV (CERN SPS)
0.8
10 GeV
Freezeout curve
0.70
1
2
3
4
5
µB/T
Context
Theory
The QCD critical point
Experiment
Wider context
1.1 Critical point estimates: 1
T/Tc
0.9
30 GeV
Mumbai Nt=4
0.8
10 GeV
Freezeout curve
0.70
1
2
3
4
5
µB/T
Critical point for the onset of confinement and chiral symmetry breaking; note unspecified scale Tc Gavai, SG (2005, 2008), Datta, Gavai, SG (2012)
Context
Theory
The QCD critical point
Experiment
Wider context
1.1
1
0.9
30 GeV
Critical point estimates: Mumbai Nt=6 Mumbai Nt=4
T/Tc
0.8
10 GeV
Freezeout curve
0.70
1
2
3
4
5
µB/T
Critical point for the onset of confinement and chiral symmetry breaking; note unspecified scale Tc Gavai, SG (2005, 2008), Datta, Gavai, SG (2012)
Context
Theory
The QCD critical point
Experiment
Wider context
1.1
1
0.9
30 GeV
Critical point estimates: Mumbai Nt=8 Mumbai Nt=6 Mumbai Nt=4
T/Tc
0.8
10 GeV
Freezeout curve
0.70
1
2
3
4
5
µB/T
Critical point for the onset of confinement and chiral symmetry breaking; note unspecified scale Tc Gavai, SG (2005, 2008), Datta, Gavai, SG (2012)
Context Outline
Theory
Experiment
1 Why study hot matter? 2 The theoretical puzzle 3 Looking for a critical point in a collider 4 The three revolutions in science
Wider context
Context
Theory
Relativistic Collisions of Nuclei
Experiment
Wider context
At relativistic energies if two heavy nuclei (Au, Pb, etc) collide, then produced particles interact and form a dense hot fluid, which cools as it expands. The particles in the fluid are strongly interacting, matter is opaque: no knowledge of the early stages of the collision. When fluid becomes dilute then particles freeze out, and observations can be made. Fluctuations of conserved quantities possible, between one event and another. Asakawa, Heinz, Muller -- Jeon, Koch (2000)
Context
Theory
Thermodynamic Fluctuations
Experiment
Wider context
Since there are 1028 molecules of gas in this room, the pressure, entropy, heat content, etc can be accurately determined. Limits on our knowledge are due to instrumental limitations. If the number of molecules was 106 then there would be inherent limits on the accuracy. Repeated accurate measurements would not give the same value but would reveal a distribution of values. Fluctuations give physical information. Gaussian distribution of energy; width give specific heat. Specific heat can be computed from molecular properties. Carnot (1824), ... Einstein (1905)
Context
Theory
Observed fluctuations
Experiment
Wider context
Number of Events text STAR arxiv:1004.4959
106 Au+Au 200 GeV
105
0.4

|y|<0.5
104
103
102
0-5% 30-40% 70-80%
10
1 -20 -10 0 10 20 Net Proton (Np)
Central rapidity slice taken. Protons accepted with pT of 400­800 MeV.
Context
Theory
Shape of distribution
Experiment
Wider context
placeholder STAR: QM 2009
Shape of distribution captured in cumulants [Bn]. Cumulants change with volume (proxy: Npart ), by Central Limit Theorem.
Context
Theory
Experiment
QCD predictions needed at finite µB
Wider context
Shape variables: [Bn] = (VT 3)T n-4n(T , µ). Ratios of cumulants are thermodynamic state variables:
m0 :
[B 2 ] [B ]
=
T 2 1
m1 :
[B 3 ] [B 2 ]
=
T 3 2
m2 :
[B 4 ] [B 2 ]
=
T 24 2
m3 :
[B 4 ] [B 3 ]
=
T 4 3
SG, 2009; Athanasiou, Rajagopal, Stephanov, 2010
Context
Theory
Checking the match
Experiment
S
79 140 (A) 720 420 2 m1 1.5 1 0.5 0 (B) 2 m2 1 0 -1 -2 4 5 6 10
T (MeV)
160
165
µ (MeV)
210 B
54
166 20 10
Exp. Data
Lattice QCD
HRG
20 30
100 200
sNN (GeV)
2
Gavai, SG (2010) -- STAR (2010)
T2 (4)/(2)
T (3)/(2)
Wider context
Context
Theory
Experiment
Tuning lattice scale to match data
Wider context
/S 2 placeholder text GLMRX (2011)
(A) 10
Lattice QCD Tc=165 MeV Tc=170 MeV Tc=175 MeV Tc=180 MeV Tc=190 MeV
5
Exp. Data
(B) Tc =175-+71 (MeV) 30
20
0
5 10 20
100 200
sNN (GeV)
10
2 min
+
1
0
160 170 180 190 Tc (MeV)
Context
Theory
Conclusions
Experiment
Wider context
Thermalization After 1 parameter tuning agreement of thermodynamic predictions with data for 2 ratios at 3 energies. Indicates thermalization of the fireball at freezeout. Tc Comparison of lattice and data along the freezeout curve gives Tc = 175+-71 MeV, in agreement with other scale settings on the lattice. Indicates that non-perturbative phenomena in single hadron physics and strong interaction thermodynamics are mutually consistent through QCD.
Context
Theory
Implications for QCD
Experiment
T=0 lattice T>0 lattice Hadron properties Bulk matter
Wider context
Context
Theory
Implications for QCD
Experiment
step (a)
T=0 lattice T>0 lattice Hadron properties Bulk matter
Wider context
Context
Theory
Implications for QCD
Experiment
step (b) T=0 lattice T>0 lattice
step (a)
Hadron properties Bulk matter
Wider context
Context
Theory
Implications for QCD
Experiment
step (b) T=0 lattice T>0 lattice
step (a)
Hadron properties Bulk matter step (c)
Wider context
Context
Theory
Implications for QCD
Experiment
step (a)
step (b) T=0 lattice T>0 lattice Tc Hadron properties Bulk matter step (c)
Wider context
Context
Theory
Implications for QCD
Experiment
step (a)
step (b) T=0 lattice T>0 lattice Tc Hadron properties Bulk matter step (c)
step (d)
Wider context
Context
Theory
Implications for QCD
Experiment
Wider context
step (a)
step (d)
step (b) T=0 lattice T>0 lattice Tc Hadron properties Bulk matter step (c) Beginning of quantitative theory for hot relativistic matter. Extend this method to the search for the critical point of QCD.
Context Outline
Theory
Experiment
1 Why study hot matter? 2 The theoretical puzzle 3 Looking for a critical point in a collider 4 The three revolutions in science
Wider context
Context
Theory
Experiment
The beginning of experimental sciences
Wider context
Usually attributed to Galileo, often dated to 1609, but could be a little earlier.
Context
Theory
Experiment
The start of mathematical sciences
Wider context
Usually attributed to Newton and dated to the establishment of the inverse square law of gravity in 1686.
Context
Theory
Experiment
The founding of Computational Sciences
Wider context
Often attributed to Alan Turing, and traced to his 1937 proof that the behaviour of computer programs is observable but not mathematically predictable.
Context
Theory
Experiment
Wider context
The computational mode is a conceptual revolution
Quantum mechanics was the first revolution of modern science. Conceptual unification of physically totally different fields: atomic spectroscopy, chemistry, Solid State Physics, etc.
Today the computational aspects of very large scale problems creates a methodological unification of lattice gauge theory with fermions, Google search and data mining, extraction of sky maps from noisy radio telescopes, atomic spectroscopy, Fluid Dynamics of nanorobots, ... Conceptual advances in one can cross fertilize other problems.
Similar methodological unification also occurring elsewhere within the computational mode of doing science.
Context
Theory
A pedagogical shortcoming
Experiment
Wider context
Work in every area of science today involves an interplay of these three modes of science.
The science training programs developed in the 1920s and 30s still persists in Our country today with updated content but little structural change. Not a problem earlier since the founding generations of the computational mode of doing science grew up with the subject.
This is a problem because a new generation is entering the sciences now. We need to train them in the computational mode of doing science: new course work, new text books. Computatiion must be embedded into course work.

File: hot-stuff.pdf
Title: Hot Stuff
Author: Sourendu Gupta
Published: Fri Oct 5 07:45:44 2012
Pages: 68
File size: 0.81 Mb


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