24 research outputs found
Monte Carlo Hamiltonian
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.Comment: Contribution to Lattice'99 (Theoretical developments) Text (LaTeX
file) + 2 figures (ps files
The Massive Schwinger Model in a Fast Moving Frame
We present a non-perturbative study of the massive Schwinger model. We use a
Hamiltonian approach, based on a momentum lattice corresponding to a fast
moving reference frame, and equal time quantization.Comment: contribution to Lattice'98 including: 2 style files
(espcrc2.sty,psfig.sty) + text file (LaTeX) + 3 figures (ps) + complete
paper(ps
Measuring the Hausdorff Dimension of Quantum Mechanical Paths
We measure the propagator length in imaginary time quantum mechanics by Monte
Carlo simulation on a lattice and extract the Hausdorff dimension . We
find that all local potentials fall into the same universality class giving
like the free motion. A velocity dependent action () in the path integral (e.g. electrons moving in
solids, or Brueckner's theory of nuclear matter) yields if and if . We discuss the
relevance of fractal pathes in solid state physics and in , in particular
for the Wilson loop in .Comment: uuencoded and compressed shell archive file. 8 pages with 7 figure
Why Use a Hamilton Approach in QCD?
We discuss in the Hamiltonian frame work. We treat finite density
in the strong coupling regime. We present a parton-model inspired
regularisation scheme to treat the spectrum (-angles) and distribution
functions in . We suggest a Monte Carlo method to construct
low-dimensionasl effective Hamiltonians. Finally, we discuss improvement in
Hamiltonian .Comment: Proceedings of Hadrons and Strings, invited talk given by H.
Kr\"{o}ger; Text (LaTeX file), 3 Figures (ps file
Monte Carlo Hamiltonian from Stochastic Basis
In order to extend the recently proposed Monte Carlo Hamiltonian to many-body
systems, we suggest to concept of a stochastic basis. We apply it to the chain
of 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.Comment: revised version, new figures. Text (LaTeX), 4 Figs. (eps), style fil
Renormalisation in Quantum Mechanics
We study a recently proposed quantum action depending on temperature. We
construct a renormalisation group equation describing the flow of action
parameters with temperature. At zero temperature the quantum action is obtained
analytically and is found free of higher time derivatives. It makes the quantum
action an ideal tool to investigate quantum chaos and quantum instantons.Comment: replaced version with new figs. Text (LaTeX), 3 Figs. (ps
Quantum Instantons and Quantum Chaos
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.Comment: Extended version with new figures. Text (LaTeX), 5 Figures (epsi
files
Is Quantum Chaos Weaker Than Classical Chaos?
We investigate chaotic behavior in a 2-D Hamiltonian system - oscillators
with anharmonic coupling. We compare the classical system with quantum system.
Via the quantum action, we construct Poincar\'{e} sections and compute Lyapunov
exponents for the quantum system. We find that the quantum system is globally
less chaotic than the classical system. We also observe with increasing energy
the distribution of Lyapunov exponts approaching a Gaussian with a strong
correlation between its mean value and energy.Comment: text (LaTeX) + 7 figs.(ps
Scattering of Glueballs and Mesons in Compact in Dimensions
We study glueball and meson scattering in compact gauge theory in
a Hamiltonian formulation and on a momentum lattice. We compute ground state
energy and mass, and introduce a compact lattice momentum operator for the
computation of dispersion relations. Using a non-perturbative time-dependent
method we compute scattering cross sections for glueballs and mesons. We
compare our results with strong coupling perturbation theory.Comment: figures not included (hard copy only), LAVAL-PHY-94-05,
PARKS-PHY-94-0
Quantum Chaos at Finite Temperature
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 Poincar\'{e} sections of the quantum action at
finite temperature with those of the classical action.Comment: Text (LaTeX), Figs. (ps