8,761 research outputs found
Editorial: The pre-history of Chaos—An Interdisciplinary Journal of Nonlinear Science
Published versio
Spin-Peierls transition in the Heisenberg chain with finite-frequency phonons
We study the spin-Peierls transition in a Heisenberg spin chain coupled to optical bond phonons. Quantum Monte Carlo results for systems with up to N=256 spins show unambiguously that the transition occurs only when the spin-phonon coupling α exceeds a critical value α_c. Using sum rules, we show that the phonon spectral function has divergent (for N→∞) weight extending to zero frequency for α<α_c. The phonon correlations decay with distance r as 1/r. This behavior is characteristic for all 0<α<α_c and the q=π phonon does not soften (to zero frequency) at α=α_c.First author draf
Behavior and Breakdown of Higher-Order Fermi-Pasta-Ulam-Tsingou Recurrences
We investigate numerically the existence and stability of higher-order
recurrences (HoRs), including super-recurrences, super-super-recurrences, etc.,
in the alpha and beta Fermi-Pasta-Ulam-Tsingou (FPUT) lattices for initial
conditions in the fundamental normal mode. Our results represent a considerable
extension of the pioneering work of Tuck and Menzel on super-recurrences. For
fixed lattice sizes, we observe and study apparent singularities in the periods
of these HoRs, speculated to be caused by nonlinear resonances. Interestingly,
these singularities depend very sensitively on the initial energy and the
respective nonlinear parameters. Furthermore, we compare the mechanisms by
which the super-recurrences in the two model's breakdown as the initial energy
and respective nonlinear parameters are increased. The breakdown of
super-recurrences in the beta-FPUT lattice is associated with the destruction
of the so-called metastable state and hence is associated with relaxation
towards equilibrium. For the alpha-FPUT lattice, we find this is not the case
and show that the super-recurrences break down while the lattice is still
metastable. We close with comments on the generality of our results for
different lattice sizes
Critical Entanglement for the Half-Filled Extended Hubbard Model
We study the ground state of the one-dimensional extended Hubbard model at
half-filling using the entanglement entropy calculated by Density Matrix
Renormalization Group (DMRG) techniques. We apply a novel curve fitting and
scaling method to accurately identify a order critical point as well
as a Berezinskii-Kosterlitz-Thouless (BKT) critical point. Using open boundary
conditions and medium-sized lattices with very small truncation errors, we are
able to achieve similar accuracy to previous authors. We also report
observations of finite-size and boundary effects that can be remedied with
careful pinning.Comment: 10 pages, 12 figure
Tunneling in the self-trapped regime of a two-well Bose-Einstein condensate
Starting from a mean-field model of the Bose-Einstein condensate dimer, we reintroduce classically forbidden tunneling through a Bohr-Sommerfeld quantization approach. We find closed-form approximations to the tunneling frequency more accurate than those previously obtained using different techniques. We discuss the central role that tunneling in the self-trapped regime plays in a quantitatively accurate model of a dissipative dimer leaking atoms to the environment. Finally, we describe the prospects of experimental observation of tunneling in the self-trapped regime, both with and without dissipation.We wish to thank Wolfgang Muessel, Markus Oberthaler, Kaspar Sakmann, Andrea Trombettoni, Stephanos Venakides, and Tilman Zibold for helpful discussions. We are also grateful for the hospitality of Joshua E. S. Socolar and the Duke University Physics Department. This work was supported in part by Boston University. D.W. acknowledges support from the Helmholtz Association (Grant No. VH-NG-1025). (Boston University; VH-NG-1025 - Helmholtz Association)First author draf
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