Stretching Semiflexible Polymer Chains: Evidence for the Importance of Excluded Volume Effects from Monte Carlo Simulation

Semiflexible macromolecules in dilute solution under very good solvent conditions are modeled by self-avoiding walks on the simple cubic lattice ($d=3$ dimensions) and square lattice ($d=2$ dimensions), varying chain stiffness by an energy penalty $\epsilon_b$ for chain bending. In the absence of excluded volume interactions, the persistence length $\ell_p$ of the polymers would then simply be $\ell_p=\ell_b(2d-2)^{-1}q_b^{-1}$ with $q_b= \exp(-\epsilon_b/k_BT)$, the bond length $\ell_b$ being the lattice spacing, and $k_BT$ is the thermal energy. Using Monte Carlo simulations applying the pruned-enriched Rosenbluth method (PERM), both $q_b$ and the chain length $N$ are varied over a wide range $(0.005 \leq q_b \leq 1, \; N \leq 50000$), and also a stretching force $f$ is applied to one chain end (fixing the other end at the origin). In the absence of this force, in $d=2$ a single crossover from rod-like behavior (for contour lengths less than $\ell_p$) to swollen coils occurs, invalidating the Kratky-Porod model, while in $d=3$ a double crossover occurs, from rods to Gaussian coils (as implied by the Kratky-Porod model) and then to coils that are swollen due to the excluded volume interaction. If the stretching force is applied, excluded volume interactions matter for the force versus extension relation irrespective of chain stiffness in $d=2$, while theories based on the Kratky-Porod model are found to work in $d=3$ for stiff chains in an intermediate regime of chain extensions. While for $q_b \ll 1$ in this model a persistence length can be estimated from the initial decay of bond-orientational correlations, it is argued that this is not possible for more complex wormlike chains (e.g. bottle-brush polymers). Consequences for the proper interpretation of experiments are briefly discussed.Comment: 23 pages, 17 figures, 2 tables, to be published in J. Chem. Phys. (2011

Chiral transition in a magnetic field and at finite baryon density

We consider the quark-meson model with two quark flavors in a constant external magnetic field $B$ at finite temperature $T$ and finite baryon chemical potential $\mu_B$. We calculate the full renormalized effective potential to one-loop order in perturbation theory. We study the system in the large-$N_c$ limit, where we treat the bosonic modes at tree level. It is shown that the system exhibits dynamical chiral symmetry breaking, i. e. that an arbitrarily weak magnetic field breaks chiral symmetry dynamically, in agreement with earlier calculations using the NJL model. We study the influence on the phase transition of the fermionic vacuum fluctuations. For strong magnetic fields, $|qB|\sim5m_{\pi}^2$ and in the chiral limit, the transition is first order in the entire $\mu_B-T$ plane if vacuum fluctuations are not included and second order if they are included. At the physical point, the transition is a crossover for $\mu_B=0$ with and without vacuum fluctuations.Comment: 11 pages. 5figs. V2: fixed a few typos and added refs. Submitted to PRD. V3: Added refs and substantial revision of tex

Chiral perturbation theory in a magnetic background - finite-temperature effects

We consider chiral perturbation theory for SU(2) at finite temperature $T$ in a constant magnetic background $B$. We compute the thermal mass of the pions and the pion decay constant to leading order in chiral perturbation theory in the presence of the magnetic field. The magnetic field gives rise to a splitting between $M_{\pi^0}$ and $M_{\pi^{\pm}}$ as well as between $F_{\pi^0}$ and $F_{\pi^{\pm}}$. We also calculate the free energy and the quark condensate to next-to-leading order in chiral perturbation theory. Both the pion decay constants and the quark condensate are decreasing slower as a function of temperature as compared to the case with vanishing magnetic field. The latter result suggests that the critical temperature $T_c$ for the chiral transition is larger in the presence of a constant magnetic field. The increase of $T_c$ as a function of $B$ is in agreement with most model calculations but in disagreement with recent lattice calculations.Comment: 24 pages and 9 fig

Solving Witten's string field theory using the butterfly state

We solve the equation of motion of Witten's cubic open string field theory in a series expansion using the regulated butterfly state. The expansion parameter is given by the regularization parameter of the butterfly state, which can be taken to be arbitrarily small. Unlike the case of level truncation, the equation of motion can be solved for an arbitrary component of the Fock space up to a positive power of the expansion parameter. The energy density of the solution is well-defined and remains finite even in the singular butterfly limit, and it gives approximately 68% of the D25-brane tension for the solution at the leading order. Moreover, it simultaneously solves the equation of motion of vacuum string field theory, providing support for the conjecture at this order. We further improve our ansatz by taking into account next-to-leading terms, and find two numerical solutions which give approximately 88% and 109%, respectively, of the D25-brane tension for the energy density. These values are interestingly close to those by level truncation at level 2 without gauge fixing studied by Rastelli and Zwiebach and by Ellwood and Taylor.Comment: 38 pages, no figures, LaTeX2e; v2: the footnote on hep-th/0302151 changed and moved to the introduction; v3: minor typos corrected, published versio

Consistency Relations in Effective Field Theory

The consistency relations in large scale structure relate the lower-order correlation functions with their higher-order counterparts. They are direct outcome of the underlying symmetries of a dynamical system and can be tested using data from future surveys such as Euclid. Using techniques from standard perturbation theory (SPT), previous studies of consistency relation have concentrated on continuity-momentum (Euler)-Poisson system of an ideal fluid. We investigate the consistency relations in effective field theory (EFT) which adjusts the SPT predictions to account for the departure from the ideal fluid description on small scales. We provide detailed results for the 3D density contrast $\delta$ as well as the {\em scaled} divergence of velocity $\bar\theta$. Assuming a $\Lambda$CDM background cosmology, we find the correction to SPT results becomes important at $k \gtrsim 0.05 \rm h/Mpc$ and that the suppression from EFT to SPT results that scales as square of the wave number $k$, can reach $40\%$ of the total at $k \approx 0.25\rm h/Mpc$ at $z=0$. We have also investigated whether effective field theory corrections to models of primordial non-Gaussianity can alter the squeezed limit behaviour, finding the results to be rather insensitive to these counterterms. In addition, we present the EFT corrections to the squeezed limit of the bispectrum in redshift space which may be of interest for tests of theories of modified gravity.Comment: 23 pages + bibliography, 6 figures. Minor changes to match version accepted for publication by JCA

The Equivalence Postulate of Quantum Mechanics: Main Theorems

We consider the two main theorems in the derivation of the Quantum Hamilton--Jacobi Equation from the Equivalence Postulate (EP) of quantum mechanics. The first one concerns a basic cocycle condition, which holds in any dimension with Euclidean or Minkowski metrics and implies a global conformal symmetry underlying the Quantum Hamilton--Jacobi Equation. In one dimension such a condition fixes the Schwarzian equation. The second theorem concerns energy quantization which follows rigorously from consistency of the equivalence postulate.Comment: 30 pages. Standard LaTe