The goal of this project is devlop a toolkit for computations and visualizations of Lattice Quantum Chromodynamics (LQCD). LQCD is an algorithmic formulation of QCD, the mathematical model that describes quarks and their interactions. Quarks are the basic components of most of the known matter, including protons and neutrons. LQCD is based on complex numerical algorithms derived from a mathematical analogy between "Feynman paths" in Quantum Mechanics and "steps" in the Markov Chain Monte Carlo algorithm. LQCD computationsare typically very expensive and run on dedicated supercomputers and large computer clusters for many months. [ read more ]
The typical outcomes of LQCD computations are predictions about properties of composite particles (such as their masses and lifetimes). These properties are then compared and confirmed in experiments. [ read more ]
The goal of this project is that producing a toolkit to complement those calculations and extract additional visual information from them. This important in order to better understand the physics behind this complex systems and properties of the algorithms that are used. This is also important to better communicate and educate both physicists and the general public about LQCD. [ read more ]
The following images show topological charge (instantons in blue and anti-instantons in red) as it evolves under the Markov Chain Monte Carlo. The initial gauge configuration is half cold (zero field) and half hot (random field). [ watch the video ]
The following images show the energy density in presence of a quark and an anti-quark (not shown). The energy density is computed and averaged on an increasing number of gauge configurations. Initially noise dominitates but eventually the correlation washes out the noise and the flux tube connecting the quark and anti-quark becomes visible. LQCD, in fact, predicts the existance of this flux tube and color confinement (a phenomenon by which isolated quarks do not exist in nature, only composite particles made of quarks do exist. Observations are consistent with this phenomenon). [ watch the video ]
The following images show different components of a staggered propagator on a cold gauge. Wilson quarks and Staggered quarks are different discreziations of Dirac quarks. LQCD in fact require that space and time be disceretized for the purpose of the computation.
The following images show different components of a heavy-light meson wave function in its ground state. The blue and red shapes are the analogous of the orbitals of an hydrogen atom execpt that a heavy quark and a light anti-quark play the role of the proton and the electron respectively.
The above images are meant to provide a sample of the capabilities of the toolkit we are developing and they are generated on relatively small lattices, compared to the ones used in real LQCD computations; nevertheless the resulting imeges and all qualitatively correct.
Video Tutorials and Visualizations
Fully Object Oriented
cout << U(x+mu,nu);
Natural Linear Algebra
cout << inv(A*A)+exp(3*I*A);
cout << lattice.random(x).SU(Nc);
Parallel but trasparent
Arbitrary lattice dimensions
Variety of fields
Variety of actions
Wilson, Clover, unisotropic,
Asqtad, Domain Wall, etc...
Minimum Residue, Stabilized Biconjugate Gradient, BiCGStabUML, Lanczos, etc.
New: SSE/SSE2 Optimizations
g++ test.cpp -DSSE2
New: Parallel simulator
(no MPI needed)
.. or just use MPI
mpiCC test.cpp -DPARALLEL
mpirun -np 4 a.out
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