An Analogue of Holstein-Primakoff and Dyson Realizations for Lie Superalgebras. The Lie superalgebra sl(1/n)

An analogue of the Holstein-Primakoff and of the Dyson realization for the Lie superalgebra $sl(1/n)$ is written down. The expressions are formally the same as for the Lie algebra $sl(n+1)$, however in the latter the Bose operators have to be replaced with Fermi operators.Comment: TeX, 6 page

Transport Properties of Solitons

We calculate in this article the transport coefficients which characterize the dynamics of solitons in quantum field theory using the methods of dissipative quantum systems. We show how the damping and diffusion coefficients of soliton-like excitations can be calculated using the integral functional formalism. The model obtained in this article has new features which cannot be obtained in the standard models of dissipation in quantum mechanics.Comment: 16 Pages, RevTeX, Preprint UIU

Polaron Effective Mass, Band Distortion, and Self-Trapping in the Holstein Molecular Crystal Model

We present polaron effective masses and selected polaron band structures of the Holstein molecular crystal model in 1-D as computed by the Global-Local variational method over a wide range of parameters. These results are augmented and supported by leading orders of both weak- and strong-coupling perturbation theory. The description of the polaron effective mass and polaron band distortion that emerges from this work is comprehensive, spanning weak, intermediate, and strong electron-phonon coupling, and non-adiabatic, weakly adiabatic, and strongly adiabatic regimes. Using the effective mass as the primary criterion, the self-trapping transition is precisely defined and located. Using related band-shape criteria at the Brillouin zone edge, the onset of band narrowing is also precisely defined and located. These two lines divide the polaron parameter space into three regimes of distinct polaron structure, essentially constituting a polaron phase diagram. Though the self-trapping transition is thusly shown to be a broad and smooth phenomenon at finite parameter values, consistency with notion of self-trapping as a critical phenomenon in the adiabatic limit is demonstrated. Generalizations to higher dimensions are considered, and resolutions of apparent conflicts with well-known expectations of adiabatic theory are suggested.Comment: 28 pages, 15 figure

A liquid helium target system for a measurement of parity violation in neutron spin rotation

A liquid helium target system was designed and built to perform a precision measurement of the parity-violating neutron spin rotation in helium due to the nucleon-nucleon weak interaction. The measurement employed a beam of low energy neutrons that passed through a crossed neutron polarizer--analyzer pair with the liquid helium target system located between them. Changes between the target states generated differences in the beam transmission through the polarizer--analyzer pair. The amount of parity-violating spin rotation was determined from the measured beam transmission asymmetries. The expected parity-violating spin rotation of order $10^{-6}$ rad placed severe constraints on the target design. In particular, isolation of the parity-odd component of the spin rotation from a much larger background rotation caused by magnetic fields required that a nonmagnetic cryostat and target system be supported inside the magnetic shielding, while allowing nonmagnetic motion of liquid helium between separated target chambers. This paper provides a detailed description of the design, function, and performance of the liquid helium target system.Comment: V2: 29 pages, 14 figues, submitted to Nucl. Instrum. Meth. B. Revised to address reviewer comment

Calculation of excited polaron states in the Holstein model

An exact diagonalization technique is used to investigate the low-lying excited polaron states in the Holstein model for the infinite one-dimensional lattice. For moderate values of the adiabatic ratio, a new and comprehensive picture, involving three excited (coherent) polaron bands below the phonon threshold, is obtained. The coherent contribution of the excited states to both the single-electron spectral density and the optical conductivity is evaluated and, due to the invariance of the Hamiltonian under the space inversion, the two are shown to contain complementary information about the single-electron system at zero temperature. The chosen method reveals the connection between the excited bands and the renormalized local phonon excitations of the adiabatic theory, as well as the regime of parameters for which the electron self-energy has notable non-local contributions. Finally, it is shown that the hybridization of two polaron states allows a simple description of the ground and first excited state in the crossover regime.Comment: 12 pages, 9 figures, submitted to PR

Finite 3π3\pi Cut Approximation for the πNNˉ\pi N\bar{N} Form Factor

Assuming the length of the $3\pi$ cut to be finite and approximating the integrated amplitude by a constant, we derive an expression for the $\pi N\bar{N}$ form factor which is very close to that given by a simple pole. The specific predictions of the obtained form factor for the region of small momentum transfer are discussed along the lines of the Goldberger-Treiman relation.Comment: 17 pages, Late

Metal-insulator transition in the one-dimensional Holstein model at half filling

We study the one-dimensional Holstein model with spin-1/2 electrons at half-filling. Ground state properties are calculated for long chains with great accuracy using the density matrix renormalization group method and extrapolated to the thermodynamic limit. We show that for small electron-phonon coupling or large phonon frequency, the insulating Peierls ground state predicted by mean-field theory is destroyed by quantum lattice fluctuations and that the system remains in a metallic phase with a non-degenerate ground state and power-law electronic and phononic correlations. When the electron-phonon coupling becomes large or the phonon frequency small, the system undergoes a transition to an insulating Peierls phase with a two-fold degenerate ground state, long-range charge-density-wave order, a dimerized lattice structure, and a gap in the electronic excitation spectrum.Comment: 6 pages (LaTex), 10 eps figure

Self-trapping transition for nonlinear impurities embedded in a Cayley tree

The self-trapping transition due to a single and a dimer nonlinear impurity embedded in a Cayley tree is studied. In particular, the effect of a perfectly nonlinear Cayley tree is considered. A sharp self-trapping transition is observed in each case. It is also observed that the transition is much sharper compared to the case of one-dimensional lattices. For each system, the critical values of $\chi$ for the self-trapping transitions are found to obey a power-law behavior as a function of the connectivity $K$ of the Cayley tree.Comment: 6 pages, 7 fig

Aspects of radiative K^+_e3 decays

We re-investigate the radiative charged kaon decay K+- --> pi0 e+- nu_e gamma in chiral perturbation theory, merging the chiral expansion with Low's theorem. We thoroughly analyze the precision of the predicted branching ratio relative to the non-radiative decay channel. Structure dependent terms and their impact on differential decay distributions are investigated in detail, and the possibility to see effects of the chiral anomaly in this decay channel is emphasized.Comment: 15 pages, 6 figure

The quark loop calculation of the gamma -> 3 pi form factor

The presently experimentally interesting form factor for the anomalous process gamma -> pi^+ pi^0 pi^- is calculated as the quark "box"-amplitude where the intermediate fermion loop is the one of constituent quarks with the pseudoscalar coupling to pions. This also corresponds to the form factor, in the lowest order in pion interactions, of the sigma-model and of the chiral quark model. We give the analytic expression for the form factor in terms of an expansion in the pion momenta up to the order O(p^8) relative to the soft point result, and also perform its exact numerical evaluation. We compare our predictions with those of the vector meson dominance and chiral perturbation theory, as well as with the scarce data available so far.Comment: revtex, 12 pages including 3 eps figure