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Thomas Luu
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I calculate finite-volume effects for three identical spin-1/2 fermions in a box assuming short-ranged repulsive interactions of `natural size. This analysis employs standard perturbation theory in powers of 1/L, where L^3 is the volume of the box. I give results for the ground states in the A_1, T_1, and E cubic representations.
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Majorana fermion dynamics may arise at the edge of Kitaev wires or superconductors. Alternatively, it can be engineered by using trapped ions or ultracold atoms in an optical lattice as quantum simulators. This motivates the theoretical study of Majorana fermions confined to a finite volume, whose boundary conditions are characterized by self-adjoint extension parameters. While the boundary conditions for Dirac fermions in $(1+1)$-d are characterized by a 1-parameter family, $lambda = - lambda^*$, of self-adjoint extensions, for Majorana fermions $lambda$ is restricted to $pm i$. Based on this result, we compute the frequency spectrum of Majorana fermions confined to a 1-d interval. The boundary conditions for Dirac fermions confined to a 3-d region of space are characterized by a 4-parameter family of self-adjoint extensions, which is reduced to two distinct 1-parameter families for Majorana fermions. We also consider the problems related to the quantum mechanical interpretation of the Majorana equation as a single-particle equation. Furthermore, the equation is related to a relativistic Schrodinger equation that does not suffer from these problems.
The residual mass of the pion in a finite spatial box at vanishing quark masses, the mass gap, is computed with two flavors of dynamical clover fermions. The result is compared with predictions of chiral perturbation theory in the delta regime.
The first observation is made of hadronic string breaking due to dynamical fermions in zero temperature lattice QCD. The simulations are done for SU(2) color in three dimensions, with two flavors of staggered fermions. The results have clear implications for the large scale simulations that are being done to search (so far, without success) for string breaking in four-dimensional QCD. In particular, string breaking is readily observed using only Wilson loops to excite a static quark-antiquark pair. Improved actions on coarse lattices are used, providing an extremely efficient means to access the quark separations and propagation times at which string breaking occurs.
New extended interpolating operators made of quenched three dimensional fermions are introduced in the context of lattice QCD. The mass of the 3D fermions can be tuned in a controlled way to find a better overlap of the extended operators with the states of interest. The extended operators have good renormalization properties and are easy to control when taking the continuum limit. Moreover the short distance behaviour of the two point functions built from these operators is greatly improved. A numerical comparison with point sources and Jacobi smeared sources on dynamical 2+1 flavour configurations is presented.
We present an exact dynamical QCD simulation algorithm for the $O(a)$-improved Wilson fermion with odd number of flavors. Our algorithm is an extension of the non-Hermitian polynomials HMC algorithm proposed by Takaishi and de Forcrand previously. In our algorithm, the systematic errors caused by the polynomial approximation of the inverse of Dirac operator is removed by a noisy-Metropolis test. For one flavor quark it is achieved by taking the square root of the correction matrix explicitly. We test our algorithm for the case of $N_f=1+1$ on a moderately large lattice size ($16^3times48$). The $N_f=2+1$ case is also investigated.
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