70 research outputs found
Chaotic Dynamics of N-degree of Freedom Hamiltonian Systems
We investigate the connection between local and global dynamics of two
N-degree of freedom Hamiltonian systems with different origins describing
one-dimensional nonlinear lattices: The Fermi-Pasta-Ulam (FPU) model and a
discretized version of the nonlinear Schrodinger equation related to
Bose-Einstein Condensation (BEC). We study solutions starting in the vicinity
of simple periodic orbits (SPOs) representing in-phase (IPM) and out-of-phase
motion (OPM), which are known in closed form and whose linear stability can be
analyzed exactly. Our results verify that as the energy E increases for fixed
N, beyond the destabilization threshold of these orbits, all positive Lyapunov
exponents exhibit a transition between two power laws, occurring at the same
value of E. The destabilization energy E_c per particle goes to zero as N goes
to infinity following a simple power-law. However, using SALI, a very efficient
indicator we have recently introduced for distinguishing order from chaos, we
find that the two Hamiltonians have very different dynamics near their stable
SPOs: For example, in the case of the FPU system, as the energy increases for
fixed N, the islands of stability around the OPM decrease in size, the orbit
destabilizes through period-doubling bifurcation and its eigenvalues move
steadily away from -1, while for the BEC model the OPM has islands around it
which grow in size before it bifurcates through symmetry breaking, while its
real eigenvalues return to +1 at very high energies. Still, when calculating
Lyapunov spectra, we find for the OPMs of both Hamiltonians that the Lyapunov
exponents decrease following an exponential law and yield extensive
Kolmogorov--Sinai entropies per particle, in the thermodynamic limit of fixed
energy density E/N with E and N arbitrarily large.Comment: 29 pages, 10 figures, published at International Journal of
Bifurcation and Chaos (IJBC
Structural changes in water and Ar-water clusters under high pressure
1 pág.; 1 fig.; XXIX International Conference on Photonic, Electronic, and Atomic Collisions (ICPEAC2015); Open Access funded by Creative Commons Atribution Licence 3.0Specific size gas-water clusters are currently receiving considerable attention, as models for inclusion
compounds of different type of clathrate hydrates. As model microsolutions they retain many characteristics of
the bulk, are theoretically tractable, and can be used to probe the relevant guest/host interactions, as well as to
derive and to test intermolecular potentials that can be also used under different thermodynamic conditions.Peer Reviewe
Semiclassical Trace Formulas for Noninteracting Identical Particles
We extend the Gutzwiller trace formula to systems of noninteracting identical
particles. The standard relation for isolated orbits does not apply since the
energy of each particle is separately conserved causing the periodic orbits to
occur in continuous families. The identical nature of the particles also
introduces discrete permutational symmetries. We exploit the formalism of
Creagh and Littlejohn [Phys. Rev. A 44, 836 (1991)], who have studied
semiclassical dynamics in the presence of continuous symmetries, to derive
many-body trace formulas for the full and symmetry-reduced densities of states.
Numerical studies of the three-particle cardioid billiard are used to
explicitly illustrate and test the results of the theory.Comment: 29 pages, 11 figures, submitted to PR
Ab initio potential energy curves of the valence, Rydberg, and ion-pair states of iodine monochloride, ICl
We present for the first time a coherent ab initio study of 39 states of valence, Rydberg, and ion-pair character of the diatomic interhalogen ICl species through large scale multireference variational methods including spin-orbit effects coupled with quantitative basis sets. Various avoided crossings are responsible for a non-adiabatic behaviour creating a wonderful vista for its theoretical description. Our molecular constants are compared with all available experimental data with the aim to assist experimentalists especially in the high energy regime of up to ∼95 000 cm-1. © 2014 AIP Publishing LLC
Theoretical investigation of the He-I 2(E 3Π g) ion-pair state: Ab initio intermolecular potential and vibrational levels
We present a theoretical study on the potential energy surface and vibrational bound states of the E electronic excited state of the HeI 2 van der Waals system. The interaction energies are computed using accurate ab initio methods and large basis sets. Relativistic small-core effective core potentials in conjunction with a quintuple-zeta quality basis set are employed for the heavy iodine atoms in multireference configuration interaction calculations for the 3A ′ and 3A ″ states. For the representation of the potential energy surface we used a general interpolation technique for constructing potential surfaces from ab initio data based on the reproducing kernel Hilbert space method. The surface presents global and local minima for T-shaped configurations with well-depths of 33.2 and 4.6cm -1, respectively. Vibrational energies and states are computed through variational quantum mechanical calculations. We found that the binding energy of the HeI 2(E) T-shaped isomer is 16.85cm -1, in excellent agreement with recent experimental measurements. In lieu of more experimental data we also report our predictions on higher vibrational levels and we analyze the influence of the underlying surface on them. This is the first attempt to represent the potential surface of such a highly excited electronic state of a van der Waals complex, and it demonstrates the capability of the ab initio technology to provide accurate results for carrying out reliable studies to model experimental data. © 2012 American Institute of Physics
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