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E-raamat: Advanced Course in Computational Nuclear Physics: Bridging the Scales from Quarks to Neutron Stars

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  • Sari: Lecture Notes in Physics 936
  • Ilmumisaeg: 09-May-2017
  • Kirjastus: Springer International Publishing AG
  • Keel: eng
  • ISBN-13: 9783319533360
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Advanced Course in Computational Nuclear Physics: Bridging the Scales from Quarks to Neutron StarsSuurem pilt
  • Formaat: EPUB+DRM
  • Sari: Lecture Notes in Physics 936
  • Ilmumisaeg: 09-May-2017
  • Kirjastus: Springer International Publishing AG
  • Keel: eng
  • ISBN-13: 9783319533360
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This graduate-level text collects and synthesizes a series of ten lectures on the nuclear quantum many-body problem. Starting from our current understanding of the underlying forces, it presents recent advances within the field of lattice quantum chromodynamics before going on to discuss effective field theories, central many-body methods like Monte Carlo methods, coupled cluster theories, the similarity renormalization group approach, Green"s function methods and large-scale diagonalization approaches.Algorithmic and computational advances show particular promise for breakthroughs in predictive power, including proper error estimates, a better understanding of the underlying effective degrees of freedom and of the respective forces at play. Enabled by recent improvements in theoretical, experimental and numerical techniques, the state-of-the art applications considered in this volume span the entire range, from our smallest components - quarks and gluons as the mediators of the

strong force - to the computation of the equation of state for neutron star matter.The lectures presented provide an in-depth exposition of the underlying theoretical and algorithmic approaches as well details of the numerical implementation of the methods discussed. Several also include links to numerical software and benchmark calculations, which readers can use to develop their own programs for tackling challenging nuclear many-body problems.

Motivation and overarching aims.- Quantum Chromodynamics.- Lattice quantum chromodynamics. - General aspects of effective field theories and few-body applications.- Lattice methods and effective field theory.- Lattice methods and the nuclear few- and many-body problem.- Ab initio methods for nuclear structure and reactions: from few to manyNucleons.- Computational Nuclear Physics and Post Hartree-Fock Methods.- Variational and Diffusion Monte Carlo approaches to the nuclear few- and many-body problem.- In-medium SRG approaches to infinite nuclear matter.- Self-consistent Green"s function approaches.
1 Motivation and Overarching Aims
1(4)
Morten Hjorth-Jensen
Maria Paola Lombardo
Ubirajara van Kolck
2 Quantum Chromodynamics
5(50)
Thomas Schafer
2.1 Introduction
5(1)
2.2 Path Integrals and the Metropolis Algorithm
6(5)
2.3 Quantum Chromodynamics
11(7)
2.3.1 QCD at Zero Temperature and Density
11(4)
2.3.2 QCD at Finite Temperature
15(2)
2.3.3 High Baryon Density QCD
17(1)
2.4 Lattice QCD
18(13)
2.4.1 The Wilson Action
18(3)
2.4.2 Fermions on the Lattice
21(2)
2.4.3 The QCD Vacuum
23(4)
2.4.4 Lattice QCD at Finite Baryon Density
27(2)
2.4.5 Real Time Properties
29(2)
2.5 Nonequilibrium QCD
31(17)
2.5.1 Fluid Dynamics
32(2)
2.5.2 Computational Fluid Dynamics
34(3)
2.5.3 Kinetic Theory
37(3)
2.5.4 Classical Field Theory
40(2)
2.5.5 Nonequilibrium QCD: Holography
42(6)
2.6 Outlook and Acknowledgments
48(7)
Appendix: Z2 Gauge Theory
49(2)
References
51(4)
3 Lattice Quantum Chromodynamics
55(38)
Tetsuo Hatsuda
3.1 Introduction
55(2)
3.1.1 Euclidean QCD Action
56(1)
3.1.2 Quantum Fluctuations
57(1)
3.2 Lattice QCD: Theoretical Basis
57(15)
3.2.1 Wilson Line
57(2)
3.2.2 Lattice Gluons
59(1)
3.2.3 Lattice Fermions
60(3)
3.2.4 Partition Function on the Lattice
63(2)
3.2.5 Strong Coupling Expansion and Quark Confinement
65(3)
3.2.6 Weak Coupling Expansion and Continuum Limit
68(2)
3.2.7 Running Coupling
70(2)
3.3 Lattice QCD: Numerical Simulations
72(8)
3.3.1 Importance Sampling
72(1)
3.3.2 Markov Chain Monte Carlo (MCMC)
72(2)
3.3.3 Hybrid Monte Carlo (HMC)
74(2)
3.3.4 Error Estimate
76(1)
3.3.5 Heavy Quark Potential
77(1)
3.3.6 Masses of Light Hadrons
78(2)
3.4 Lattice QCD and Nuclear Force
80(5)
3.4.1 Master Equation for Baryon-Baryon Interaction
81(1)
3.4.2 Baryon-Baryon Interaction in Flavor SU(3) Limit
82(3)
3.5 Exercises
85(8)
Appendix
86(5)
References
91(2)
4 General Aspects of Effective Field Theories and Few-Body Applications
93(62)
Hans-Werner Hammer
Sebastian Konig
4.1 Introduction: Dimensional Analysis and the Separation of Scales
93(2)
4.2 Theoretical Foundations of Effective Field Theory
95(22)
4.2.1 Top-Down vs. Bottom-Up Approaches
96(4)
4.2.2 Nonrelativistic Field Theory
100(10)
4.2.3 Symmetries and Power Counting
110(7)
4.2.4 Matching
117(1)
4.3 Effective Field Theory for Strongly Interacting Bosons
117(16)
4.3.1 EFT for Short-Range Interactions
118(5)
4.3.2 Dimer Field Formalism
123(1)
4.3.3 Three-Body System
124(3)
4.3.4 Three-Body Observables
127(3)
4.3.5 Renormalization Group Limit Cycle
130(3)
4.4 Effective Field Theory for Nuclear Few-Body Systems
133(10)
4.4.1 Overview
133(1)
4.4.2 Pionless Effective Field Theory
133(1)
4.4.3 The Two-Nucleon S-Wave System
134(4)
4.4.4 Three Nucleons: Scattering and Bound States
138(5)
4.5 Beyond Short-Range Interactions: Adding Photons and Pions
143(12)
4.5.1 Electromagnetic Interactions
143(5)
4.5.2 Example: Deuteron Breakup
148(2)
4.5.3 Chiral Effective Field Theory
150(2)
References
152(3)
5 Lattice Methods and Effective Field Theory
155(82)
Amy Nicholson
5.1 Introduction
155(2)
5.2 Basics of Effective Field Theory and Lattice Effective Field Theory
157(19)
5.2.1 Pionless Effective Field Theory
157(6)
5.2.2 Lattice Effective Field Theory
163(13)
5.3 Calculating Observables
176(24)
5.3.1 Signal-to-Noise
178(7)
5.3.2 Statistical Overlap
185(5)
5.3.3 Interpolating Fields
190(5)
5.3.4 Analysis Methods
195(5)
5.4 Systematic Errors and Improvement
200(16)
5.4.1 Improving the Kinetic Energy Operator
200(3)
5.4.2 Improving the Interaction
203(8)
5.4.3 Scaling of Discretization Errors for Many-Body Systems
211(3)
5.4.4 Additional Sources of Systematic Error
214(2)
5.5 Beyond Leading Order EFT
216(13)
5.5.1 Tuning the Effective Range
217(5)
5.5.2 Including Pions
222(2)
5.5.3 3-and Higher-Body Interactions
224(4)
5.5.4 Final Considerations
228(1)
5.6 Reading Assignments and Exercises
229(8)
Appendix
230(1)
References
231(6)
6 Lattice Methods and the Nuclear Few- and Many-Body Problem
237(26)
Dean Lee
6.1 Introduction
237(1)
6.2 Recent Applications
238(1)
6.3 Scattering on the Lattice
239(2)
6.4 Lattice Formalisms
241(8)
6.4.1 Grassmann Path Integral
242(2)
6.4.2 Transfer Matrix Operator
244(2)
6.4.3 Grassmann Path Integral with Auxiliary Field
246(2)
6.4.4 Transfer Matrix Operator with Auxiliary Field
248(1)
6.5 Projection Monte Carlo
249(4)
6.6 Importance Sampling
253(4)
6.7 Exercises
257(1)
6.8 Codes and Benchmarks
258(5)
References
260(3)
7 Ab Initio Methods for Nuclear Structure and Reactions: From Few to Many Nucleons
263(30)
Giuseppina Orlandini
7.1 Introduction: Theory, Model, Method
263(1)
7.2 The Non-relativistic Quantum Mechanical Many-Nucleon Problem
264(2)
7.2.1 Translation and Galileian Invariance
265(1)
7.3 Classification of Ab Initio Approaches for Ground-State Calculations
266(8)
7.3.1 The Faddeev-Yakubowski (FY) Method
266(1)
7.3.2 Methods Based on the Variational Theorem (Diagonalization Methods)
267(3)
7.3.3 Methods Based on Similarity Transformations
270(3)
7.3.4 Monte Carlo Methods
273(1)
7.4 Two Diagonalization Methods with Effective Interactions
274(2)
7.4.1 The No Core Shell Model Method (NCSM)
274(1)
7.4.2 The Hyperspherical Harmonics Method with Effective Interaction (EIHH)
275(1)
7.5 Excited States
276(5)
7.5.1 Response Functions to Perturbative Probes
277(4)
7.6 Integral Transform Approaches
281(9)
7.6.1 Sum Rules
281(1)
7.6.2 Integral Transform with the Laplace Kernel
282(1)
7.6.3 Integral Transform with the Lorentzian Kernel
283(2)
7.6.4 Integral Transform with the Sumudu Kernel
285(2)
7.6.5 Integral Transform with the Stieltjes Kernel
287(1)
7.6.6 Methods of Inversion
288(2)
7.7 Conclusion
290(3)
References
290(3)
8 Computational Nuclear Physics and Post Hartree-Fock Methods
293(108)
Justin G. Lietz
Samuel Novario
Gustav R. Jansen
Gaute Hagen
Morten Hjorth-Jensen
8.1 Introduction
293(2)
8.2 Single-Particle Basis, Hamiltonians and Models for the Nuclear Force
295(17)
8.2.1 Introduction to Nuclear Matter and Hamiltonians
295(7)
8.2.2 Single-Particle Basis for Infinite Matter
302(3)
8.2.3 Two-Body Interaction
305(3)
8.2.4 Models from Effective Field Theory for the Two- and Three-Nucleon Interactions
308(4)
8.3 Hartree-Fock Theory
312(7)
8.3.1 Hartree-Fock Algorithm with Simple Python Code
315(4)
8.4 Full Configuration Interaction Theory
319(8)
8.4.1 A Non-practical Way of Solving the Eigenvalue Problem
324(2)
8.4.2 Short Summary
326(1)
8.5 Many-Body Perturbation Theory
327(9)
8.5.1 Interpreting the Correlation Energy and the Wave Operator
334(2)
8.6 Coupled Cluster Theory
336(10)
8.6.1 A Quick Tour of Coupled Cluster Theory
336(7)
8.6.2 The CCD Approximation
343(1)
8.6.3 Approximations to the Full CCD Equations
344(2)
8.7 Developing a Numerical Project
346(34)
8.7.1 Validation and Verification
347(2)
8.7.2 Tracking Changes
349(1)
8.7.3 Profile-Guided Optimization
349(10)
8.7.4 Developing a CCD Code for Infinite Matter
359(21)
8.8 Conclusions
380(1)
8.9 Exercises
381(9)
8.10 Solutions to Selected Exercises
390(11)
Appendix, Wick's Theorem
394(3)
References
397(4)
9 Variational and Diffusion Monte Carlo Approaches to the Nuclear Few- and Many-Body Problem
401(76)
Francesco Pederiva
Alessandro Roggero
Kevin E. Schmidt
9.1 Monte Carlo Methods in Quantum Many-Body Physics
401(3)
9.1.1 Expectations in Quantum Mechanics
401(3)
9.2 Variational Wavefunctions and VMC for Central Potentials
404(18)
9.2.1 Coordinate Space Formulation
404(1)
9.2.2 Variational Principle and Variational Wavefunctions
405(1)
9.2.3 Monte Carlo Evaluation of Integrals
406(8)
9.2.4 Construction of the Wavefunction and Computational Procedures
414(4)
9.2.5 Wave Function Optimization
418(4)
9.3 Projection Monte Carlo Methods in Coordinate Space
422(17)
9.3.1 General Formulation
422(1)
9.3.2 Imaginary Time Propagator in Coordinate Representation
423(6)
9.3.3 Application to the Harmonic Oscillator
429(3)
9.3.4 Importance Sampling
432(4)
9.3.5 The Fermion Sign Problem
436(3)
9.4 Quantum Monte Carlo for Nuclear Hamiltonians in Coordinate Space
439(16)
9.4.1 General Auxiliary Field Formalism
439(1)
9.4.2 Operator Expectations and Importance Sampling
440(5)
9.4.3 Application to Standard Diffusion Monte Carlo
445(2)
9.4.4 Fixed-Phase Importance-Sampled Diffusion Monte Carlo
447(1)
9.4.5 Application to Quadratic Forms
448(1)
9.4.6 Auxiliary Field Breakups
449(2)
9.4.7 AFDMC with the υ'6 Potential for Nuclear Matter
451(3)
9.4.8 Isospin-Independent Spin-Orbit Interaction
454(1)
9.5 GFMC with Full Spin-Isospin Summation
455(2)
9.6 General Projection Algorithms in Fock Space and Non-local Interactions
457(14)
9.6.1 Fock Space Formulation of Diffusion Monte Carlo
458(3)
9.6.2 Importance Sampling and Fixed-Phase Approximation
461(2)
9.6.3 Trial Wave-Functions from Coupled Cluster Ansatz
463(2)
9.6.4 Propagator Sampling with No Time-Step Error
465(5)
9.6.5 Results
470(1)
9.7 Conclusions and Perspectives
471(2)
9.8 Problems
473(4)
Appendix
474(2)
References
476(1)
10 In-Medium Similarity Renormalization Group Approach to the Nuclear Many-Body Problem
477(94)
Heiko Hergert
Scott K. Bogner
Justin G. Lietz
Titus D. Morris
Samuel J. Novario
Nathan M. Parzuchowski
Fei Yuan
10.1 Introduction
477(3)
10.1.1 Organization of This
Chapter
480(1)
10.2 The Similarity Renormalization Group
480(28)
10.2.1 Concept
480(3)
10.2.2 A Two-Dimensional Toy Problem
483(3)
10.2.3 The Pairing Model
486(8)
10.2.4 Evolution of Nuclear Interactions
494(14)
10.3 The In-Medium SRG
508(32)
10.3.1 Normal Ordering and Wick's Theorem
509(4)
10.3.2 In-Medium SRG Flow Equations
513(4)
10.3.3 Decoupling
517(4)
10.3.4 Choice of Generator
521(6)
10.3.5 Implementation
527(8)
10.3.6 IMSRG Solution of the Pairing Hamiltonian
535(4)
10.3.7 Infinite Neutron Matter
539(1)
10.4 Current Developments
540(21)
10.4.1 Magnus Formulation of the IMSRG
540(3)
10.4.2 The Multi-Reference IMSRG
543(9)
10.4.3 Effective Hamiltonians
552(8)
10.4.4 Final Remarks
560(1)
10.5 Conclusions
561(1)
10.6 Exercises and Projects
561(10)
Appendix: Products and Commutators of Normal-Ordered Operators
564(2)
References
566(5)
11 Self-Consistent Green's Function Approaches
571(65)
Carlo Barbieri
Arianna Carbone
11.1 Introduction
571(2)
11.2 Many-Body Green's Function Theory
573(13)
11.2.1 Spectral Function and Relation to Experimental Observations
575(3)
11.2.2 Perturbation Expansion of the Green's Function
578(8)
11.3 The Algebraic Diagrammatic Construction Method
586(16)
11.3.1 The ADC(n) Approach and Working Equations at Third Order
591(5)
11.3.2 Solving the Dyson Equation
596(3)
11.3.3 A Simple Pairing Model
599(3)
11.4 Numerical Solutions for Infinite Matter
602(16)
11.4.1 Computational Details for ADC(n)
603(10)
11.4.2 Spectral Function in Pure Neutron and Symmetric Nuclear Matter
613(5)
11.5 Self-Consistent Green's Functions at Finite Temperature in the Thermodynamic Limit
618(16)
11.5.1 Finite-Temperature Green's Function Formalism
619(5)
11.5.2 Numerical Implementation of the Ladder Approximation
624(6)
11.5.3 Averaged Three-Body Forces: Numerical Details
630(4)
11.6 Concluding Remarks
634(2)
Appendix 1 Feynman Rules for the One-Body Propagator and the Self-Energy 636(2)
Appendix 2 Chiral Next-to-Next-to-Leading Order Three-Nucleon Forces 638(5)
References 643
Morten Hjorth-Jensen is a professor in theoretical nuclear physics at the University of Oslo since 2001. He shared the University of Oslo Excellence in Teaching Award for 2000, and became a fellow of the American Physical Society in 2007. In 2008, together with collaborators, he received the Oak Ridge National Laboratory award in the category for "Scientific Research" for the development and implementation of coupled-cluster theory for medium mass and neutron-rich nuclei. 
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