Staying Thermal with Hartree Ensemble Approximations

We study thermal behavior of a recently introduced Hartree ensemble approximation, which allows for non-perturbative inhomogeneous field configurations as well as for approximate thermalization, in the $\phi^4$ model in 1+1 dimensions. Using ensembles with a free field thermal distribution as out-of-equilibrium initial conditions we determine thermalization time scales. The time scale for which the system stays in approximate quantum thermal equilibrium is an indication of the time scales for which the approximation method stays reasonable. This time scale turns out to be two orders of magnitude larger than the time scale for thermalization, in the range of couplings and temperatures studied. We also discuss simplifications of our method which are numerically more efficient and make a comparison with classical dynamics.Comment: 19 pages latex; extensively rewritten to improve presentation, data essentially unchanged, analysis sharpened and one table adde

The Hartree ensemble approximation revisited: The "symmetric phase"

The Hartree ensemble approximation is studied in the ``symmetric phase'' of 1+1 dimensional lambda phi^4 theory. In comparison with the ``broken phase'' studied previously, it is shown that the dynamical evolution of observables such as the particle distribution, energy exchange and auto-correlation functions, is substantially slower. Approximate thermalization is found only for relatively large energy densities and couplings.Comment: 17 pages RevTeX, 16 figures, 3 tables, uses amsmath and feynmp. Extended some sections, reordered Sec.IV, added 3 refs, numerical typo corrected, published versio

Self-assembled electron-rich receptors: from molecular polygons to polyhedra

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Finite Temperature Simulations from Quantum Field Dynamics?

We describe a Hartree ensemble method to approximately solve the Heisenberg equations for the \phi^4 model in 1+1 dimensions. We compute the energies and number densities of the quantum particles described by the \phi field and find that the particles initially thermalize with a Bose-Einstein distribution for the particle density. Gradually, however, the distribution changes towards classical equipartition. Using suitable initial conditions quantum thermalization is achieved much faster than the onset of this undesirable equipartition. We also show how the numerical efficiency of our method can be significantly improved.Comment: Lattice 2000 (Finite Temperature), 4 pages, 5 figures; title correcte

Coordination-driven self-assembly of electron-rich tetrathiafulvalene-based architectures

Date du colloque : 12/2010International audienc