569 research outputs found
Ground State Wave Function of the Schr\"odinger Equation in a Time-Periodic Potential
Using a generalized transfer matrix method we exactly solve the Schr\"odinger
equation in a time periodic potential, with discretized Euclidean space-time.
The ground state wave function propagates in space and time with an oscillating
soliton-like wave packet and the wave front is wedge shaped. In a statistical
mechanics framework our solution represents the partition sum of a directed
polymer subjected to a potential layer with alternating (attractive and
repulsive) pinning centers.Comment: 11 Pages in LaTeX. A set of 2 PostScript figures available upon
request at [email protected] . Physical Review Letter
The dynamics of coset dimensional reduction
The evolution of multiple scalar fields in cosmology has been much studied,
particularly when the potential is formed from a series of exponentials. For a
certain subclass of such systems it is possible to get `assisted` behaviour,
where the presence of multiple terms in the potential effectively makes it
shallower than the individual terms indicate. It is also known that when
compactifying on coset spaces one can achieve a consistent truncation to an
effective theory which contains many exponential terms, however, if there are
too many exponentials then exact scaling solutions do not exist. In this paper
we study the potentials arising from such compactifications of eleven
dimensional supergravity and analyse the regions of parameter space which could
lead to scaling behaviour.Comment: 27 pages, 4 figures; added citation
Finite Temperature Depinning of a Flux Line from a Nonuniform Columnar Defect
A flux line in a Type-II superconductor with a single nonuniform columnar
defect is studied by a perturbative diagrammatic expansion around an annealed
approximation. The system undergoes a finite temperature depinning transition
for the (rather unphysical) on-the-average repulsive columnar defect, provided
that the fluctuations along the axis are sufficiently large to cause some
portions of the column to become attractive. The perturbative expansion is
convergent throughout the weak pinning regime and becomes exact as the
depinning transition is approached, providing an exact determination of the
depinning temperature and the divergence of the localization length.Comment: RevTeX, 4 pages, 3 EPS figures embedded with epsf.st
Before programs: The physical origination of multicellular forms
ABSTRACT By examining the formative role of physical processes in modern-day developmental systems, we infer that although such determinants are subject to constraints and rarely act in a “pure ” fashion, they are identical to processes generic to all viscoelastic, chemically excitable media, non-living as well as living. The processes considered are free diffusion, immiscible liquid behavior, oscillation and multistability of chemical state, reaction-diffusion coupling and mecha-nochemical responsivity. We suggest that such processes had freer reign at early stages in the history of multicellular life, when less evolution had occurred of genetic mechanisms for stabilization and entrenchment of functionally successful morphologies. From this we devise a hypothetical scenario for pattern formation and morphogenesis in the earliest metazoa. We show that the expected morphologies that would arise during this relatively unconstrained “physical” stage of evolution correspond to the hollow, multilayered and segmented morphotypes seen in the gastrulation stage embryos of modern-day metazoa as well as in Ediacaran fossil deposits of ~600 Ma. We suggest several ways in which organisms that were originally formed by predomi-nantly physical mechanisms could have evolved genetic mechanisms to perpetuate their mor-phologies
State Differentiation by Transient Truncation in Coupled Threshold Dynamics
Dynamics with a threshold input--output relation commonly exist in gene,
signal-transduction, and neural networks. Coupled dynamical systems of such
threshold elements are investigated, in an effort to find differentiation of
elements induced by the interaction. Through global diffusive coupling, novel
states are found to be generated that are not the original attractor of
single-element threshold dynamics, but are sustained through the interaction
with the elements located at the original attractor. This stabilization of the
novel state(s) is not related to symmetry breaking, but is explained as the
truncation of transient trajectories to the original attractor due to the
coupling. Single-element dynamics with winding transient trajectories located
at a low-dimensional manifold and having turning points are shown to be
essential to the generation of such novel state(s) in a coupled system.
Universality of this mechanism for the novel state generation and its relevance
to biological cell differentiation are briefly discussed.Comment: 8 pages. Phys. Rev. E. in pres
The Unusual Universality of Branching Interfaces in Random Media
We study the criticality of a Potts interface by introducing a {\it froth}
model which, unlike its SOS Ising counterpart, incorporates bubbles of
different phases. The interface is fractal at the phase transition of a pure
system. However, a position space approximation suggests that the probability
of loop formation vanishes marginally at a transition dominated by {\it strong
random bond disorder}. This implies a linear critical interface, and provides a
mechanism for the conjectured equivalence of critical random Potts and Ising
models.Comment: REVTEX, 13 pages, 3 Postscript figures appended using uufile
String Theory in the Penrose Limit of AdS_2 x S^2
The string theory in the Penrose limit of AdS_2 x S^2 is investigated. The
specific Penrose limit is the background known as the Nappi-Witten spacetime,
which is a plane-wave background with an axion field. The string theory on it
is given as the Wess-Zumino-Novikov-Witten (WZNW) model on non-semi-simple
group H_4. It is found that, in the past literature, an important type of
irreducible representations of the corresponding algebra, h_4, were missed. We
present this "new" representations, which have the type of continuous series
representations. All the three types of representations of the previous
literature can be obtained from the "new" representations by setting the
momenta in the theory to special values. Then we realized the affine currents
of the WZNW model in terms of four bosonic free fields and constructed the
spectrum of the theory by acting the negative frequency modes of free fields on
the ground level states in the h_4 continuous series representation. The
spectrum is shown to be free of ghosts, after the Virasoro constraints are
satisfied. In particular we argued that there is no need for constraining one
of the longitudinal momenta to have unitarity. The tachyon vertex operator,
that correspond to a particular state in the ground level of the string
spectrum, is constructed. The operator products of the vertex operator with the
currents and the energy-momentum tensor are shown to have the correct forms,
with the correct conformal weight of the vertex operator.Comment: 30 pages, Latex, no figure
New axially symmetric Yang-Mills-Higgs solutions with negative cosmological constant
We construct numerically new axially symmetric solutions of SU(2)
Yang-Mills-Higgs theory in anti-de Sitter spacetime. Two types of
finite energy, regular configurations are considered: multimonopole solutions
with magnetic charge and monopole-antimonopole pairs with zero net
magnetic charge. A somewhat detailed analysis of the boundary conditions for
axially symmetric solutions is presented. The properties of these solutions are
investigated, with a view to compare with those on a flat spacetime background.
The basic properties of the gravitating generalizations of these configurations
are also discussed.Comment: 18 pages, 7 figures; v2: typos correcte
Vortex solutions in the noncommutative torus
Vortex configurations in the two-dimensional torus are considered in
noncommutative space. We analyze the BPS equations of the Abelian Higgs model.
Numerical solutions are constructed for the self-dual and anti-self dual cases
by extending an algorithm originally developed for ordinary commutative space.
We work within the Fock space approach to noncommutative theories and the
Moyal-Weyl connection is used in the final stage to express the solutions in
configuration space.Comment: 18 pages, 5 figure
Non-locality and short-range wetting phenomena
We propose a non-local interfacial model for 3D short-range wetting at planar
and non-planar walls. The model is characterized by a binding potential
\emph{functional} depending only on the bulk Ornstein-Zernike correlation
function, which arises from different classes of tube-like fluctuations that
connect the interface and the substrate. The theory provides a physical
explanation for the origin of the effective position-dependent stiffness and
binding potential in approximate local theories, and also obeys the necessary
classical wedge covariance relationship between wetting and wedge filling.
Renormalization group and computer simulation studies reveal the strong
non-perturbative influence of non-locality at critical wetting, throwing light
on long-standing theoretical problems regarding the order of the phase
transition.Comment: 4 pages, 2 figures, accepted for publication in Phys. Rev. Let
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