2,622 research outputs found
Effects of turbulent mixing on critical behaviour: Renormalization group analysis of the Potts model
Critical behaviour of a system, subjected to strongly anisotropic turbulent
mixing, is studied by means of the field theoretic renormalization group.
Specifically, relaxational stochastic dynamics of a non-conserved
multicomponent order parameter of the Ashkin-Teller-Potts model, coupled to a
random velocity field with prescribed statistics, is considered. The velocity
is taken Gaussian, white in time, with correlation function of the form
, where is
the component of the wave vector, perpendicular to the distinguished direction
("direction of the flow") --- the -dimensional generalization of the
ensemble introduced by Avellaneda and Majda [1990 {\it Commun. Math. Phys.}
{\bf 131} 381] within the context of passive scalar advection. This model can
describe a rich class of physical situations. It is shown that, depending on
the values of parameters that define self-interaction of the order parameter
and the relation between the exponent and the space dimension , the
system exhibits various types of large-scale scaling behaviour, associated with
different infrared attractive fixed points of the renormalization-group
equations. In addition to known asymptotic regimes (critical dynamics of the
Potts model and passively advected field without self-interaction), existence
of a new, non-equilibrium and strongly anisotropic, type of critical behaviour
(universality class) is established, and the corresponding critical dimensions
are calculated to the leading order of the double expansion in and
(one-loop approximation). The scaling appears strongly
anisotropic in the sense that the critical dimensions related to the directions
parallel and perpendicular to the flow are essentially different.Comment: 21 page, LaTeX source, 7 eps figures. arXiv admin note: substantial
text overlap with arXiv:cond-mat/060701
KMS states on Quantum Grammars
We consider quantum (unitary) continuous time evolution of spins on a lattice
together with quantum evolution of the lattice itself. In physics such
evolution was discussed in connection with quantum gravity. It is also related
to what is called quantum circuits, one of the incarnations of a quantum
computer. We consider simpler models for which one can obtain exact
mathematical results. We prove existence of the dynamics in both Schroedinger
and Heisenberg pictures, construct KMS states on appropriate C*-algebras. We
show (for high temperatures) that for each system where the lattice undergoes
quantum evolution, there is a natural scaling leading to a quantum spin system
on a fixed lattice, defined by a renormalized Hamiltonian.Comment: 22 page
Statistics of low-energy levels of a one-dimensional weakly localized Frenkel exciton: A numerical study
Numerical study of the one-dimensional Frenkel Hamiltonian with on-site
randomness is carried out. We focus on the statistics of the energy levels near
the lower exciton band edge, i. e. those determining optical response. We found
that the distribution of the energy spacing between the states that are well
localized at the same segment is characterized by non-zero mean, i.e. these
states undergo repulsion. This repulsion results in a local discrete energy
structure of a localized Frenkel exciton. On the contrary, the energy spacing
distribution for weakly overlapping local ground states (the states with no
nodes within their localization segments) that are localized at different
segments has zero mean and shows almost no repulsion. The typical width of the
latter distribution is of the same order as the typical spacing in the local
discrete energy structure, so that this local structure is hidden; it does not
reveal itself neither in the density of states nor in the linear absorption
spectra. However, this structure affects the two-exciton transitions involving
the states of the same segment and can be observed by the pump-probe
spectroscopy. We analyze also the disorder degree scaling of the first and
second momenta of the distributions.Comment: 10 pages, 6 figure
- …