2,917 research outputs found
Variational theory for a single polyelectrolyte chain revisited
We reconsider the electrostatic contribution to the persistence length,
, of a single, infinitely long charged polymer in the presence of
screening. A Gaussian variational method is employed, taking as the
only variational parameter. For weakly charged and flexible chains, crumpling
occurs at small length scales because conformational fluctuations overcome
electrostatic repulsion. The electrostatic persistence length depends on the
square of the screening length, , as first argued by
Khokhlov and Khachaturian by applying the Odijk-Skolnick-Fixman (OSF) theory to
a string of crumpled blobs. We compare our approach to previous theoretical
works (including variational formulations) and show that the result
found by several authors comes from the improper use of
a cutoff at small length scales. For highly charged and stiff chains, crumpling
does not occur; here we recover the OSF result and validate the perturbative
calculation for slightly bent rods.Comment: 11 pages, 6 figure
Persistence length of a polyelectrolyte in salty water: a Monte-Carlo study
We address the long standing problem of the dependence of the electrostatic
persistence length of a flexible polyelectrolyte (PE) on the screening
length of the solution within the linear Debye-Huckel theory. The
standard Odijk, Skolnick and Fixman (OSF) theory suggests ,
while some variational theories and computer simulations suggest . In this paper, we use Monte-Carlo simulations to study the conformation
of a simple polyelectrolyte. Using four times longer PEs than in previous
simulations and refined methods for the treatment of the simulation data, we
show that the results are consistent with the OSF dependence . The linear charge density of the PE which enters in the coefficient of
this dependence is properly renormalized to take into account local
fluctuations.Comment: 7 pages, 6 figures. Various corrections in text and reference
Novel Quantum States of the Rational Calogero Models Without the Confining Interaction
We show that the N-particle A_{N-1} and B_N rational Calogero models without
the harmonic interaction admit a new class of bound and scattering states.
These states owe their existence to the self-adjoint extensions of the
corresponding Hamiltonians, labelled by a real parameter z. It is shown that
the new states appear for all values of N and for specific ranges of the
coupling constants. Moreover, they are shown to exist even in the excited
sectors of the Calogero models. The self-adjoint extension generically breaks
the classical scaling symmetry, leading to quantum mechanical scaling anomaly.
The scaling symmetry can however be restored for certain values of the
parameter z. We also generalize these results for many particle systems with
classically scale invariant long range interactions in arbitrary dimensions.Comment: Latex file, 21 pages; minor changes in text, some references added,
to appear in Nucl. Phys.
Vacuum orbit and spontaneous symmetry breaking in hyperbolic sigma models
We present a detailed study of quantized noncompact, nonlinear SO(1,N)
sigma-models in arbitrary space-time dimensions D \geq 2, with the focus on
issues of spontaneous symmetry breaking of boost and rotation elements of the
symmetry group. The models are defined on a lattice both in terms of a transfer
matrix and by an appropriately gauge-fixed Euclidean functional integral. The
main results in all dimensions \geq 2 are: (i) On a finite lattice the systems
have infinitely many nonnormalizable ground states transforming irreducibly
under a nontrivial representation of SO(1,N); (ii) the SO(1,N) symmetry is
spontaneously broken. For D =2 this shows that the systems evade the
Mermin-Wagner theorem. In this case in addition: (iii) Ward identities for the
Noether currents are derived to verify numerically the absence of explicit
symmetry breaking; (iv) numerical results are presented for the two-point
functions of the spin field and the Noether current as well as a new order
parameter; (v) in a large N saddle-point analysis the dynamically generated
squared mass is found to be negative and of order 1/(V \ln V) in the volume,
the 0-component of the spin field diverges as \sqrt{\ln V}, while SO(1,N)
invariant quantities remain finite.Comment: 60 pages, 12 Figures, AMS-Latex; v2: results on vacuum orbit and
spontaneous symmetry breaking extended to all dimension
Massive stars as thermonuclear reactors and their explosions following core collapse
Nuclear reactions transform atomic nuclei inside stars. This is the process
of stellar nucleosynthesis. The basic concepts of determining nuclear reaction
rates inside stars are reviewed. How stars manage to burn their fuel so slowly
most of the time are also considered. Stellar thermonuclear reactions involving
protons in hydrostatic burning are discussed first. Then I discuss triple alpha
reactions in the helium burning stage. Carbon and oxygen survive in red giant
stars because of the nuclear structure of oxygen and neon. Further nuclear
burning of carbon, neon, oxygen and silicon in quiescent conditions are
discussed next. In the subsequent core-collapse phase, neutronization due to
electron capture from the top of the Fermi sea in a degenerate core takes
place. The expected signal of neutrinos from a nearby supernova is calculated.
The supernova often explodes inside a dense circumstellar medium, which is
established due to the progenitor star losing its outermost envelope in a
stellar wind or mass transfer in a binary system. The nature of the
circumstellar medium and the ejecta of the supernova and their dynamics are
revealed by observations in the optical, IR, radio, and X-ray bands, and I
discuss some of these observations and their interpretations.Comment: To be published in " Principles and Perspectives in Cosmochemistry"
Lecture Notes on Kodai School on Synthesis of Elements in Stars; ed. by Aruna
Goswami & Eswar Reddy, Springer Verlag, 2009. Contains 21 figure
Single-Particle Green Functions in Exactly Solvable Models of Bose and Fermi Liquids
Based on a class of exactly solvable models of interacting bose and fermi
liquids, we compute the single-particle propagators of these systems exactly
for all wavelengths and energies and in any number of spatial dimensions. The
field operators are expressed in terms of bose fields that correspond to
displacements of the condensate in the bose case and displacements of the fermi
sea in the fermi case.
Unlike some of the previous attempts, the present attempt reduces the answer
for the spectral function in any dimension in both fermi and bose systems to
quadratures.
It is shown that when only the lowest order sea-displacement terms are
included, the random phase approximation in its many guises is recovered in the
fermi case, and Bogoliubov's theory in the bose case. The momentum distribution
is evaluated using two different approaches, exact diagonalisation and the
equation of motion approach.
The novelty being of course, the exact computation of single-particle
properties including short wavelength behaviour.Comment: Latest version to be published in Phys. Rev. B. enlarged to around 40
page
- …