1,380 research outputs found
Soliton turbulences in the complex Ginzburg-Landau equation
We study spatio-temporal chaos in the complex Ginzburg-Landau equation in
parameter regions of weak amplification and viscosity. Turbulent states
involving many soliton-like pulses appear in the parameter range, because the
complex Ginzburg-Landau equation is close to the nonlinear Schr\"odinger
equation. We find that the distributions of amplitude and wavenumber of pulses
depend only on the ratio of the two parameters of the amplification and the
viscosity. This implies that a one-parameter family of soliton turbulence
states characterized by different distributions of the soliton parameters
exists continuously around the completely integrable system.Comment: 5 figure
Super Schrodinger algebra in AdS/CFT
We discuss (extended) super Schrodinger algebras obtained as subalgebras of
the superconformal algebra psu(2,2|4). The Schrodinger algebra with two spatial
dimensions can be embedded into so(4,2). In the superconformal case the
embedded algebra may be enhanced to the so-called super Schrodinger algebra. In
fact, we find an extended super Schrodinger subalgebra of psu(2,2|4). It
contains 24 supercharges (i.e., 3/4 of the original supersymmetries) and the
generators of so(6), as well as the generators of the original Schrodinger
algebra. In particular, the 24 supercharges come from 16 rigid supersymmetries
and half of 16 superconformal ones. Moreover, this superalgebra contains a
smaller super Schrodinger subalgebra, which is a supersymmetric extension of
the original Schrodinger algebra and so(6) by eight supercharges (half of 16
rigid supersymmetries). It is still a subalgebra even if there are no so(6)
generators. We also discuss super Schrodinger subalgebras of the superconformal
algebras, osp(8|4) and osp(8^*|4).Comment: 19pp; references added and title changed. version to appear in J.
Math. Phy
Interacting SUSY-singlet matter in non-relativistic Chern-Simons theory
We construct an example of supersymmetric Chern-Simons-matter theory with a
matter field transforming as a singlet representation of the supersymmetry
algebra, where the bosonic and fermionic degrees of freedom do not match. This
is obtained as a non-relativistic limit of the N=2 Chern-Simons-matter theory
in 1+2 dimensions, where the particle and anti-particle coexist. We also study
the index to investigate the mimatch of bosonic and fermionic degrees of
freedom.Comment: 11page
Disordered Regimes of the one-dimensional complex Ginzburg-Landau equation
I review recent work on the ``phase diagram'' of the one-dimensional complex
Ginzburg-Landau equation for system sizes at which chaos is extensive.
Particular attention is paid to a detailed description of the spatiotemporally
disordered regimes encountered. The nature of the transition lines separating
these phases is discussed, and preliminary results are presented which aim at
evaluating the phase diagram in the infinite-size, infinite-time, thermodynamic
limit.Comment: 14 pages, LaTeX, 9 figures available by anonymous ftp to
amoco.saclay.cea.fr in directory pub/chate, or by requesting them to
[email protected]
Families of IIB duals for nonrelativistic CFTs
We show that the recent string theory embedding of a spacetime with
nonrelativistic Schrodinger symmetry can be generalised to a twenty one
dimensional family of solutions with that symmetry. Our solutions include IIB
backgrounds with no three form flux turned on, and arise as near horizon limits
of branewave spacetimes. We show that there is a hypersurface in the space of
these theories where an instability appears in the gravitational description,
indicating a phase transition in the nonrelativistic field theory dual. We also
present simple embeddings of duals for nonrelativistic critical points where
the dynamical critical exponent can take many values z \neq 2.Comment: 1+25 pages. References adde
AdS/CFT duality for non-relativistic field theory
We formulate a correspondence between non-relativistic conformal field
theories (NRCFTs) in d-1 spatial dimensions and gravitational theories in
AdS_{d+2} backgrounds with one compactified lightlike direction. The breaking
of the maximal SO(2,d+1) symmetry of AdS_{d+2} to the non-relativistic
conformal group arises from boundary conditions on bulk fields, without the
need to introduce non-vacuum sources of energy-momentum. As a check of the
proposal, we use the gravitational theory to reproduce the NRCFT state-operator
correspondence between scaling dimensions of primary operators and energy
eigenstates of the non-relativistic system placed in an external harmonic
potential.Comment: 19 pages LaTeX, no figure
Dynamically-Coupled Oscillators -- Cooperative Behavior via Dynamical Interaction --
We propose a theoretical framework to study the cooperative behavior of
dynamically coupled oscillators (DCOs) that possess dynamical interactions.
Then, to understand synchronization phenomena in networks of interneurons which
possess inhibitory interactions, we propose a DCO model with dynamics of
interactions that tend to cause 180-degree phase lags. Employing an approach
developed here, we demonstrate that although our model displays synchronization
at high frequencies, it does not exhibit synchronization at low frequencies
because this dynamical interaction does not cause a phase lag sufficiently
large to cancel the effect of the inhibition. We interpret the disappearance of
synchronization in our model with decreasing frequency as describing the
breakdown of synchronization in the interneuron network of the CA1 area below
the critical frequency of 20 Hz.Comment: 10 pages, 3 figure
Hamiltonian Determination with Restricted Access in Transverse Field Ising Chain
We propose a method to evaluate parameters in the Hamiltonian of the Ising
chain under site-dependent transverse fields, with a proviso that we can
control and measure one of the edge spins only. We evaluate the eigenvalues of
the Hamiltonian and the time-evoultion operator exactly for a 3-spin chain,
from which we obtain the expectation values of of the first spin.
The parameters are found from the peak positions of the Fourier transform of
the expectation value. There are four assumptions in our method, which are mild
enough to be satisfied in many physical systems.Comment: 15pages, 4 figure
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