X.Q. Luo

Quantum Instantons and Quantum Chaos

We suggest a closed form expression for the path integral of quantum transition amplitudes to construct a quantum action. Based on this we propose rigorous definitions of both, quantum instantons and quantum chaos. As an example we compute the quantum instanton of the double well potential.

Quantum chaos at finite temperature

Abstract We use the quantum action to study quantum chaos at finite temperature. We present a numerical study of a classically chaotic 2-D Hamiltonian system — harmonic oscillators with anharmonic coupling. We construct the quantum action non-perturbatively and find temperature-dependent quantum corrections in the action parameters. We compare Poincare sections of the quantum action at finite temperature with those of the classical action.

Closed path integrals and the quantum action.

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

Monte Carlo Hamiltonian from stochastic basis

V \sim x^{4}

Glueball masses in quantum chromodynamics

potential. The renormalized action is relevant for quantum chaos and quantum instantons.

Renormalisation in quantum mechanics

Abstract In order to extend the recently proposed Monte Carlo Hamiltonian to many-body systems, we suggest the concept of a stochastic basis. We apply it to the chain of N s =9 coupled anharmonic oscillators. We compute the spectrum of excited states in a finite energy window and thermodynamical observables free energy, average energy, entropy and specific heat in a finite temperature window. Comparing the results of the Monte Carlo Hamiltonian with standard Lagrangian lattice calculations, we find good agreement. However, the Monte Carlo Hamiltonian results show less fluctuations under variation of temperature.

New way to compute excited states and thermodynamics: Monte Carlo hamiltonian

Abstract We review the recent glueball mass calculations using an efficient method for solving the Schrodinger equation order by order with a scheme preserving the continuum limit. The reliability of the method is further supported by new accurate results for (1+1)-dimensional σ models and (2+1)-dimensional non-abelian models. We present first and encouraging data for the glueball masses in 3+1 dimensional QCD.

Thermodynamical observables in a finite temperature window from the Monte Carlo Hamiltonian

We study a recently proposed quantum action depending on temperature. At zero temperature the quantum action is obtained analytically and reproduces the exact ground state energy and wave function. This is demonstrated for a number of cases with parity symmetric confining potentials. In the case of the hydrogen atom, it also reproduces exactly energy and wave function of a subset of excited state (those of lowest energy for given angular momentum l) and the quantum action is consistent with O(4) symmetry. In the case of a double-well potential, the quantum action generates the ground state of double-hump shape. In all cases we observe a coincidence (in position) of minima of the quantum potential with maxima of the wave function. The semi-classical WKB formula for the ground state wave function becomes exact after replacing the parameters of the classical action by those of quantum action.

Variational study of vacuum structure with fermions ind+1 dimensional Hamiltonian lattice gauge theory

Abstract We present a new way to compute thermodynamical observables on the lattice. We compute excited states and thermodynamical functions in the scalar model via the Monte Carlo Hamiltonian technique. We find agreement with standard Lagrangian lattice calculations, but observe lesser fluctuations in the results from the MC Hamiltonian.

Hopping-parameter expansion and the Schwinger model with Wilson fermions

The Monte Carlo (MC) Hamiltonian is a new stochastic method to solve many-body problems. The MC Hamiltonian represents an effective Hamiltonian in a finite energy window. We construct it from the classical action via Monte Carlo with importance sampling. The MC Hamiltonian yields the energy spectrum and corresponding wave functions in a low energy window. This allows to compute thermodynamical observables in a low temperature window. We show the working of the MC Hamiltonian by an example from lattice field theory (Klein-Gordon model).