arXiv subjects
Publications and source records attributed to X. Q. Luo.
Based on a closed form expression for the path integral of quantum transition amplitudes, we suggest rigorous definitions of both, quantum instantons and quantum chaos. As an example we compute the quantum instanton of the double well potential.
Motivated by the computational demands of our research and budgetary constraints which are common to many research institutions, we built a ``poor man's supercomputer'', a cluster of PC nodes which together can perform parallel calculations at a fraction of the price of a commercial supercomputer. We describe the construction, cost, and performance of our cluster.
We discuss $QCD$ in the Hamiltonian frame work. We treat finite density $QCD$ in the strong coupling regime. We present a parton-model inspired regularisation scheme to treat the spectrum ($θ$-angles) and distribution functions in $QED_{1+1}$. We suggest a Monte Carlo method to construct low-dimensionasl effective Hamiltonians. Finally, we discuss improvement in Hamiltonian $QCD$.
We suggest a closed form expression for the path integral of quantum transition amplitudes. We introduce a quantum action with renormalized parameters. We present numerical results for the $V \sim x^{4}$ potential. The renormalized action is relevant for quantum chaos and quantum instantons.
We suggest how to construct an effective low energy Hamiltonian via Monte Carlo starting from a given action. We test it by computing thermodynamical observables like average energy and specific heat for simple quantum systems.
We construct an effective Hamiltonian via Monte Carlo from a given action. This Hamiltonian describes physics in the low energy regime. We test it by computing spectrum, wave functions and thermodynamical observables (average energy and specific heat) for the free system and the harmonic oscillator. The method is shown to work also for other local potentials.
We describe a nonperturbative method for calculating the QCD vacuum and glueball wave functions, based on an eigenvalue equation approach to Hamiltonian lattice gauge theory. Therefore, one can obtain more physical information than the conventional simulation methods. For simplicity, we take the 2+1 dimensional U(1) model as an example. The generalization of this method to 3+1 dimensional QCD is straightforward.
We review our new method, which might be the most direct and efficient way for approaching the continuum physics from Hamiltonian lattice gauge theory. It consists of solving the eigenvalue equation with a truncation scheme preserving the continuum limit. The efficiency has been confirmed by the observations of the scaling behaviors for the long wavelength vacuum wave functions and mass gaps in (2+1)-dimensional models and (1+1)-dimensional $σ$ model even at very low truncation orders. Most of these results show rapid convergence to the available Monte Carlo data, ensuring the reliability of our method.
We discuss the relevance of long wavelength excitations for the low energy spectrum of QCD, and try to develop an efficient method for solving the Schrodinger equation, and for extracting the glueball masses and long wavelength functions of the ground and excited states. Some technical problems appearing in the calculations of SU(3) gauge theory are discussed.
The chiral phase transition induced by a charged scalar field is investigated numerically in a lattice fermion-gauge-scalar model with U(1) gauge symmetry, proposed recently as a model for dynamical fermion mass generation. For very strong gauge coupling the transition is of second order and its scaling properties are very similar to those of the Nambu--Jona-Lasinio model. However, in the vicinity of the tricritical point at somewhat weaker coupling, where the transition changes the order, the scaling behavior is different. Therefore it is worthwhile to investigate the continuum limit of the model at this point.
We study the phase diagram of non compact $QED_3$ using the $MFA$ method and present evidence for a continuous phase transition line at small $N_f$. We also analyze the chiral structure of the vacuum by means of the computation of the probability distribution function of the order parameter in the exact chiral limit.
The reasons for the feasibility of the Microcanonical Fermionic Average ($MFA$) approach to lattice gauge theory with dynamical fermions are discussed. We then present a new exact algorithm, which is free from systematic errors and convergent even in the chiral limit.
We study the phase diagram of non compact $QED_3$ using the microcanonical fermionic average method described elsewhere. We present evidence for a continuous phase transition line in the $β, N$ plane, extending down to arbitrarily small flavour number $N$.
In the framework of (2+1)-dimensional compact lattice QED with light fermions, we investigate the phase diagram in the $(β, N)$ plane. The approximations involved are related to an expansion of the effective fermionic action as a power series of the flavor number $N$. We also develop a new mechanism for understanding the $N-$critical phenomenon in the full theory. Our results for the specific heat indicate that only one phase does exist. We give strong evidences that this qualitative result should not be changed with the inclusion of higher order terms in the $N$ expansion.