1,322 research outputs found
Modelling two-dimensional Crystals with Defects under Stress: Superelongation of Carbon Nanotubes at high Temperatures
We calculate analytically the phase diagram of a two-dimensional square
crystal and its wrapped version with defects under external homogeneous stress
as a function of temperature using a simple elastic lattice model that allows
for defect formation. The temperature dependence turns out to be very weak. The
results are relevant for recent stress experiments on carbon nanotubes. Under
increasing stress, we find a crossover regime which we identify with a cracking
transition that is almost independent of temperature. Furthermore, we find an
almost stress-independent melting point. In addition, we derive an enhanced
ductility with relative strains before cracking between 200-400%, in agreement
with carbon nanotube experiments. The specific values depend on the Poisson
ratio and the angle between the external force and the crystal axes. We give
arguments that the results for carbon nanotubes are not much different to the
wrapped square crystal.Comment: 12 pages, 6 eps figures, section VI added discussing the
modifications of our model when applied to tube
Vortex Origin of Tricritical Point in Ginzburg-Landau Theory
Motivated by recent experimental progress in the critical regime of
high- superconductors we show how the tricritical point in a
superconductor can be derived from the Ginzburg-Landau theory as a consequence
of vortex fluctuations. Our derivation explains why usual renormalization group
arguments always produce a first-order transition, in contrast to experimental
evidence and Monte Carlo simulations.Comment: 4 pages,1 figur
Decrumpling membranes by quantum effects
The phase diagram of an incompressible fluid membrane subject to quantum and
thermal fluctuations is calculated exactly in a large number of dimensions of
configuration space. At zero temperature, a crumpling transition is found at a
critical bending rigidity . For membranes of fixed lateral
size, a crumpling transition occurs at nonzero temperatures in an auxiliary
mean field approximation. As the lateral size L of the membrane becomes large,
the flat regime shrinks with .Comment: 9 pages, 4 figure
Recursive Graphical Construction for Feynman Diagrams of Quantum Electrodynamics
We present a method for a recursive graphical construction of Feynman
diagrams with their correct multiplicities in quantum electrodynamics. The
method is first applied to find all diagrams contributing to the vacuum energy
from which all n-point functions are derived by functional differentiation with
respect to electron and photon propagators, and to the interaction. Basis for
our construction is a functional differential equation obeyed by the vacuum
energy when considered as a functional of the free propagators and the
interaction. Our method does not employ external sources in contrast to
traditional approaches.Comment: Author Information under
http://www.physik.fu-berlin.de/~kleinert/institution.html Latest update of
paper also at http://www.physik.fu-berlin.de/~kleinert/29
Critical dynamics, duality, and the exact dynamic exponent in extreme type II superconductors
The critical dynamics of superconductors is studied using renormalization
group and duality arguments. We show that in extreme type II superconductors
the dynamic critical exponent is given exactly by . This result does not
rely on the widely used models of critical dynamics. Instead, it is shown that
follows from the duality between the extreme type II superconductor and
a model with a critically fluctuating gauge field. Our result is in agreement
with Monte Carlo simulations.Comment: 7 pages, no figures; version accepted for publication in PR
Perturbation Theory for Path Integrals of Stiff Polymers
The wormlike chain model of stiff polymers is a nonlinear -model in
one spacetime dimension in which the ends are fluctuating freely. This causes
important differences with respect to the presently available theory which
exists only for periodic and Dirichlet boundary conditions. We modify this
theory appropriately and show how to perform a systematic large-stiffness
expansions for all physically interesting quantities in powers of ,
where is the length and the persistence length of the polymer. This
requires special procedures for regularizing highly divergent Feynman integrals
which we have developed in previous work. We show that by adding to the
unperturbed action a correction term , we can calculate
all Feynman diagrams with Green functions satisfying Neumann boundary
conditions. Our expansions yield, order by order, properly normalized
end-to-end distribution function in arbitrary dimensions , its even and odd
moments, and the two-point correlation function
Critical Exponents from Five-Loop Strong-Coupling phi^4-Theory in 4- epsilon Dimensions
With the help of strong-coupling theory, we calculate the critical exponents
of O(N)-symmetric phi^4-theories in 4- epsilon dimensions up to five loops with
an accuracy comparable to that achieved by Borel-type resummation methods.Comment: Author Information under
http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of
paper also at http://www.physik.fu-berlin.de/~kleinert/29
Nonperturbative Effects on T_c of Interacting Bose Gases in Power-Law Traps
The critical temperature T_c of an interacting Bose gas trapped in a general
power-law potential V(x)=\sum_i U_i|x_i|^{p_i} is calculated with the help of
variational perturbation theory. It is shown that the interaction-induced shift
in T_c fulfills the relation (T_c-T_c^0)/T_c^0= D_1(eta)a + D'(eta)a^{2 eta}+
O(a^2) with T_c^0 the critical temperature of the trapped ideal gas, a the
s-wave scattering length divided by the thermal wavelength at T_c, and
eta=1/2+\sum_i 1/p_i the potential-shape parameter. The terms D_1(eta)a and
D'(eta) a^{2 eta} describe the leading-order perturbative and nonperturbative
contributions to the critical temperature, respectively. This result
quantitatively shows how an increasingly inhomogeneous potential suppresses the
influence of critical fluctuations. The appearance of the a^{2 eta}
contribution is qualitatively explained in terms of the Ginzburg criterion.Comment: Author Information under
http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of
paper (including all PS fonts) at
http://www.physik.fu-berlin.de/~kleinert/35
Criterion for Dominance of Directional over Size Fluctuations in Destroying Order
For systems exhibiting a second-order phase transition with a spontaneously
broken continuous O(N)-symmetry at low temperature, we give a criterion for
judging at which temperature T_K long-range directional fluctuations of the
order field destroy the order when approaching the critical temperature from
below. The temperature T_K lies always significantly below the famous Ginzburg
temperature T_G at which size fluctuations of finite range in the order field
become important.Comment: Author Information under
http://www.physik.fu-berlin.de/~kleinert/institution.html . Latest update of
paper also at http://www.physik.fu-berlin.de/~kleinert/re3.html#29
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