Stretching Homopolymers

Force induced stretching of polymers is important in a variety of contexts. We have used theory and simulations to describe the response of homopolymers, with $N$ monomers, to force ($f$) in good and poor solvents. In good solvents and for {{sufficiently large}} $N$ we show, in accord with scaling predictions, that the mean extension along the $f$ axis $\sim f$ for small $f$, and $\sim f^{{2/3}}$ (the Pincus regime) for intermediate values of $f$. The theoretical predictions for \la Z\ra as a function of $f$ are in excellent agreement with simulations for N=100 and 1600. However, even with N=1600, the expected Pincus regime is not observed due to the the breakdown of the assumptions in the blob picture for finite $N$. {{We predict the Pincus scaling in a good solvent will be observed for $N\gtrsim 10^5$}}. The force-dependent structure factors for a polymer in a poor solvent show that there are a hierarchy of structures, depending on the nature of the solvent. For a weakly hydrophobic polymer, various structures (ideal conformations, self-avoiding chains, globules, and rods) emerge on distinct length scales as $f$ is varied. A strongly hydrophobic polymer remains globular as long as $f$ is less than a critical value $f_c$. Above $f_c$, an abrupt first order transition to a rod-like structure occurs. Our predictions can be tested using single molecule experiments.Comment: 24 pages, 7 figure

Green Function of the Sutherland Model with SU(2) internal symmetry

We obtain the hole propagator of the Sutherland model with SU(2) internal symmetry for coupling parameter $\beta=1$, which is the simplest nontrivial case. One created hole with spin down breaks into two quasiholes with spin down and one quasihole with spin up. While these elementary excitations are energetically free, the form factor reflects their anyonic character. The expression for arbitrary integer $\beta$ is conjectured.Comment: 13pages, Revtex, one ps figur

Foreword

This work reports on the performances of ohmic contacts fabricated on highly p-type doped 4H-SiC epitaxial layer selectively grown by vapor-liquid-solid transport. Due to the very high doping level obtained, the contacts have an ohmic behavior even without any annealing process. Upon variation of annealing temperatures, it was shown that both 500 and 800 °C annealing temperature lead to a minimum value of the Specific Contact Resistance (SCR) down to 1.3×10−6 Ω⋅cm2. However, a large variation of the minimum SCR values has been observed (up to 4×10−4 Ω⋅cm2). Possible sources of this fluctuation have been also discussed in this paper

Spin-Charge Separation at Finite Temperature in the Supersymmetric t-J Model with Long-Range Interactions

Thermodynamics is derived rigorously for the 1D supersymmetric {\it t-J} model and its SU($K,1$) generalization with inverse-square exchange. The system at low temperature is described in terms of spinons, antispinons, holons and antiholons obeying fractional statistics. They are all free and make the spin susceptibility independent of electron density, and the charge susceptibility independent of magnetization. Thermal spin excitations responsible for the entropy of the SU($K,1$) model are ascribed to free para-fermions of order $K-1$.Comment: 10 pages, REVTE

On Models with Inverse-Square Exchange

A one-dimensional quantum N-body system of either fermions or bosons with $SU(n)$ colors interacting via inverse-square exchange is presented in this article. A class of eigenstates of both the continuum and lattice version of the model Hamiltonians is constructed in terms of the Jastrow-product type wave function. The class of states we construct in this paper corresponds to the ground state and the low energy excitations of the model that can be described by the effective harmonic fluid Hamiltonian. By expanding the energy about the ground state we find the harmonic fluid parameters (i.e. the charge, spin velocities, etc.), explicitly. The correlation exponent and the compressibility of are also found. As expected the general harmonic relation(i.e. $v_S=(v_Nv_J)^{1/2}$) is satisfied among the charge and spin velocities.Comment: 26 page

Exact dynamical structure factor of the degenerate Haldane-Shastry model

The dynamical structure factor $S(q,\omega)$ of the K-component (K = 2,3,4) spin chain with the 1/r^2 exchange is derived exactly at zero temperature for arbitrary size of the system. The result is interpreted in terms of a free quasi-particle picture which is generalization of the spinon picture in the SU(2) case; the excited states consist of K quasi-particles each of which is characterized by a set of K-1 quantum numbers. Divergent singularities of $S(q,\omega)$ at the spectral edges are derived analytically. The analytic result is checked numerically for finite systems.Comment: 4 pages, 1 figure, accepted for publication in Phys. Rev. Let

Spectral projections and resolvent bounds for partially elliptic quadratic differential operators

We study resolvents and spectral projections for quadratic differential operators under an assumption of partial ellipticity. We establish exponential-type resolvent bounds for these operators, including Kramers-Fokker-Planck operators with quadratic potentials. For the norms of spectral projections for these operators, we obtain complete asymptotic expansions in dimension one, and for arbitrary dimension, we obtain exponential upper bounds and the rate of exponential growth in a generic situation. We furthermore obtain a complete characterization of those operators with orthogonal spectral projections onto the ground state.Comment: 60 pages, 3 figures. J. Pseudo-Differ. Oper. Appl., to appear. Revised according to referee report, including minor changes to Corollary 1.8. The final publication will be available at link.springer.co

Electron Addition Spectrum in the Supersymmetric t-J Model with Inverse-Square Interaction

The electron addition spectrum A^+(k,omega) is obtained analytically for the one-dimensional (1D) supersymmetric t-J model with 1/r^2 interaction. The result is obtained first for a small-sized system and its validity is checked against the numerical calculation. Then the general expression is found which is valid for arbitrary size of the system. The thermodynamic limit of A^+(k,omega) has a simple analytic form with contributions from one spinon, one holon and one antiholon all of which obey fractional statistics. The upper edge of A^+(k,omega) in the (k,omega) plane includes a delta-function peak which reduces to that of the single-electron band in the low-density limit.Comment: 5 pages, 1 figure, accepted for publication in Phys. Rev. Let