U Del

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High-performance computing for atomic physics
calculations
Marianna Safronova Department of Physics and
Astronomy February
14, 2006
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Outline

• Motivation for this work
• Method
• Computational challenges
• Future projects and future computational
  challenges

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What do we do?Calculate atomic properties!
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There are so many atomic properties!!!
and others ...
Lifetimes
van der Waals coefficients
Parity nonconserving amplitudes
Fine-structure intervals
Derived Weak charge QW, Anapole moment
Electron electric-dipole moment enhancement factor
s
Hyperfine constants
Isotope shifts
Energies
Line strengths
Branching ratios
Oscillator strengths
Transition probabilities
Atom-wall interaction constants
Wavelengths
Polarizabilities
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Motivation

• Development of new methodologies
• Theory Experiment
• Parity nonconservation
• Nuclear physics
• Astrophysics
• Variation of fundamental constants with time???
  
• Environmental studies
• Technology optical atomic clocks
• Quantum computation

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Motivation

• Development of new methodologies
• Theory Experiment
• Parity nonconservation
• Nuclear physics
• Astrophysics
• Variation of fundamental constants with time???
  
• Environmental studies
• Technology optical atomic clocks
• Quantum computation

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Theory Experiment
Level scheme of Ca
4p P3/2
854 nm
4p P1/2
3d D5/2
866 nm
393 nm
3d D3/2
397 nm
E2
729 nm
732 nm
4s S1/2
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Study of the 3d 2D-level 40Ca lifetimes
Experiment
Theory
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Comparison with all other results 3d 2D5/2
Theory
Experiment
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Standard Model
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Searches for new physics beyond the Standard Model
High energies
(1) Search for new processes or
particles directly (2) Study (very
precisely!) quantities which Standard Model
predicts and compare the result with its
prediction
Low energies
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Cost 3,000,000,000
High energies
The Large Hadron Collider (2007) particle
accelerator which will probe deeper into matter
than ever before. It will ultimately collide
beams of protons at an energy of 14 TeV . Beams
of lead nuclei will be also accelerated, smashing
together with a collision energy of 1150 TeV.
A TeV is a unit of energy used in particle
physics. 1 TeV is about the energy of motion of
a flying mosquito. What makes the LHC so
extraordinary is that it squeezes energy into a
space about a million million times smaller than
a mosquito.
http//public.web.cern.ch/
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Low energiesAtomic Parity violation
(1) Table-top experiments 100 000 (2)
Different sensitivities to new physics in
comparison with high-energy experiments
Atomic Parity Nonconservation experiment in
cesium C. Wieman group (Colorado)
Example lower bound for extra Z boson
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Atomic calculations
Very precise calculation of atomic properties
WANTED!
We also need to evaluate an uncertainty of a
theoretical value!
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So many properties ...
Atomic wave functions
Energies
E1,M1,E2, transitions
Matrix elements
Hyperfine
Spin-independent parity nonconserving
Lifetimes, branching ratios, line strengths,
oscillator strengths, transition probabilities
Polarizabilities Atom-wall interaction
constants van der Waals coefficients Parity-noncon
serving amplitudes and others ...
Spin-dependent parity nonconserving
p1p2 specific mass shift
and others
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Relativistic all-order method

• Problem High-precision calculations of atomic
  properties
• Solution Calculate Exact wave function
  by modifying lowest-order wave function
  in terms of all possible
  excitations, i.e. single-particle excitations,
  double excitations, triple excitations,
• Use resulting wave functions to calculate
  matrix elements.

S.A. Blundell, W.R. Johnson, Z.W. Liu, and J.
Sapirstein,Phys. Rev. A 40, 2233 (1989)
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Lowest order

• Cesium atom with single (valence)
  
• electron outside a closed core.

Cs Z55
valence electron
1s25p6
6s
core
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Lowest order

• Cesium atom with single (valence)
  
• electron outside a closed core.

Cs Z55
valence electron
1s25p6
6s
core
Valence electron
Core
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Lowest order

• Cesium atom with single (valence)
  
• electron outside a closed core.

Cs Z55
valence electron
1s25p6
6s
core
Lowest-order wave function
Core
Creation operator for state v
Core wave function
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Relativistic all-order method
core valence electron any excited orbital
Core
Lowest order
Single-particle excitations
core excitation
valence excitation
Double-particle excitations
core excitations
core - valence excitations
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Relativistic all-order method
core valence electron any excited orbital
Core
Lowest order
Single-particle excitations
Double-particle excitations
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Actual implementation Problem 1
The derivation gets really complicated if you add
triples!
Solution develop analytical codes that do all
the work for you!
Input ASCII input of terms of the type
Output final simplified formula in LATEX to be
used in the all-order equation
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Actual implementation Problem 2
PROBLEM A WITH EQUATIONS There are some many
of them !!!

• Cs a,b 1s22s22p63s23p63d104s24p
  64d105s25p6
• m,n finite basis set (35 ? 13) ? (35 ?
  13)
• Total actually 15412 ? 35 ? 35 19 000 000
  equations
• 
  to be solved iteratively!

Memory storage of it is a
really large file!
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Actual implementation Problem 3
PROBLEM B WITH EQUATIONS These are really
complicated equations !!!

• Quadruple term
• Program has to be exceptionally efficient!

a,b core (17 shells)
Indices mnrs can be ANY orbitals Basis set
nmax35, lmax6 17x17x(35x13)45 x 1012!
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Parallelization
15412 channels
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Current projects and computational challenges I
I. Development of the all-order method for more
complicated systems First, need to develop
third-order perturbation theory method
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Current projects and computational challenges I
I. Development of the all-order method for more
complicated systems First, need to develop
third-order perturbation theory method
Problem there are over 600 new TERMS !!!
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Current projects and computational challenges I
I. Development of the all-order method for more
complicated systems First, need to develop
third-order perturbation theory method
Problem there are over 600 new TERMS !!! Well,
they can be combined into 97 and then into
36. How do you write 36 subroutines without
spending too much time looking for bugs?
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Current projects and computational challenges I
I. Development of the all-order method for more
complicated systems First, need to develop
third-order perturbation theory method
Problem there are over 600 new TERMS !!! Well,
they can be combined into 97 and then into
36. How do you write 36 subroutines without
spending too much time looking for bugs?
Solution automated code generation !
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Code that writes codes
Input list of formulas to be programmed Output
final code (need to be put into a main shell)
Features simple input, essentially just type in
a formula!
Example
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end 1 subroutine
term1d(nvp,kvp,nwp,kwp,nv,kv,nw,kw,jtot,res) 2
Xk1(c,d,a,b) Xk2(vp,wp,c,d) Zk3(v,w,a,b)
3 none 4 4 xx z1(-1)(1jtotk1k2k3kap
ckapdkapwkapwp) xx z2d6j(2jtot,jc,jd,2
k2,jwp,jvp) xx z3d6j(ja,jb,2jtot,jw,jv,2k3) x
x z4d6j(jc,jd,2jtot,jb,ja,2k1) 5
(ec,d-evp,wp) (ea,b-evp,wp) 6 No
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Code that writes codes
Input list of formulas to be programmed Output
final code (need to be put into a main shell)
Features Simple input, essentially just type in
a formula! Efficient
codes are produced. Other features can be
easily added I already see several other
applications that it can be used
for. Safety features are build in attempts
to put a construct that is not allowed in the
formula will produce error message and no
code. To be completed latex wrapper for
the input. Future plans interface with
formula-writing codes.
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Current projects and computational challenges II
III. Further development of the all-order method
for systems with single valence electron
Non-linear terms
Triple excitations
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Triple excitations
core valence electron any excited orbital
Problem too many excitation coefficients
.
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Triple excitations
Problem too many excitation coefficients
.
Doubles

• Cs a,b 1s22s22p63s23p63d104s24p
  64d105s25p6
• m,n finite basis set (35 ? 13) ? (35 ?
  13)
• Smallest required basis set
• Need total about 300 MB (extra 150MB file)
• Extra index r gives at least a factor (35 ? 13)
  over 130GB!

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Triple excitations
Problem too many excitation coefficients
.

• Extra index r gives at least a factor (35 ? 13)
  over 130GB!

Solutions
Use symmetry of the coefficients to reduce needed
memory/storage Exclude inner core shells Use
single precision for the triples Deal with a very
large file
Suggestions are appreciated!
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Summary

• Development of new atomic physics
  methodologies
• Results are used for many different
  applications.

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Summary

• Development of new atomic physics methodologies
• Results are used for many different applications.

Codes that write formulas
Codes that write codes
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Summary

• Development of new atomic physics methodologies
• Results are used for many different applications.

Codes that write formulas
Codes that write codes
Parallelization
Efficiency
Current issue triple excitations!
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Graduate students Jenny Tchoukova
(poster) Rupsi Chandra Bindiya Arora Dansha
Jiang Matt Lammert
Other collaborations Walter Johnson
(University of Notre Dame) Hung-Cheuk Ho
(University of Notre Dame) Andrei Derevianko
(University of Nevada-Reno) Charles Clark
(NIST) Carl Williams (NIST)