Spin density wave selection in the one-dimensional Hubbard model

The Hartree-Fock ground state phase diagram of the one-dimensional Hubbard model is calculated, constrained to uniform phases, which have no charge density modulation. The allowed solutions are saturated ferromagnetism (FM), a spiral spin density wave (SSDW) and a double spin density wave} (DSDW). The DSDW phase comprises two canted interpenetrating antiferromagnetic sublattices. FM occurs for small filling, SSDW in most of the remainder of the phase diagram, and DSDW in a narrow tongue near quarter (and three-quarter) filling. Itinerant electrons lift the degeneracy with respect to canting angle in the DSDW. The Hartree-Fock states are metallic except at multiples of a quarter filling. Near half filling the uniform SSDW phase is unstable against phase separation into a half-filled antiferromagnetic phase and a hole-rich SSDW phase. The dependence of the ground state wave number on chemical potential is conjectured to be a staircase. Comparison is made with higher dimensional Hubbard models and the $J_{1}-J_{2}$ Heisenberg model.Comment: 15 pages LaTeX, 5 Postscript figures in uuencoded file. To appear in J Phys: Condensed Matter. Requires files ioplppt.sty, iopl10.sty, iopl12.sty (available at http://www.ioppublishing.com/Journals/texstyle.html

Phase-space path-integral calculation of the Wigner function

The Wigner function W(q,p) is formulated as a phase-space path integral, whereby its sign oscillations can be seen to follow from interference between the geometrical phases of the paths. The approach has similarities to the path-centroid method in the configuration-space path integral. Paths can be classified by the mid-point of their ends; short paths where the mid-point is close to (q,p) and which lie in regions of low energy (low P function of the Hamiltonian) will dominate, and the enclosed area will determine the sign of the Wigner function. As a demonstration, the method is applied to a sequence of density matrices interpolating between a Poissonian number distribution and a number state, each member of which can be represented exactly by a discretized path integral with a finite number of vertices. Saddle point evaluation of these integrals recovers (up to a constant factor) the WKB approximation to the Wigner function of a number state.Comment: 16 pages. Small number of typos corrected, including sign in eq A2

Exact Classical Effective Potential

A quantum spin system can be modelled by an equivalent classical system, with an effective Hamiltonian obtained by integrating all non-zero frequency modes out of the path integral. The effective Hamiltonian H_eff(S_i) derived from the coherent-state integral is highly singular: the quasiprobability density exp(-beta H_eff), a Wigner function, imposes quantisation through derivatives of delta functions. This quasiprobability is the distribution of the time-averaged lower symbol of the spin in the coherent-state integral. We relate the quantum Monte Carlo minus-sign problem to the non-positivity of this quasiprobability, both analytically and by Monte Carlo integration.Comment: 4 page

Supersonic airplane design optimization method for aerodynamic performance and low sonic boom

This paper presents a new methodology for the optimization of supersonic airplane designs to meet the dual design objectives of low sonic boom and high aerodynamic performance. Two sets of design parameters are used on an existing High Speed Civil Transport (HSCT) configuration to maximize the aerodynamic performance and minimize the sonic boom under the flight track. One set of the parameters perturbs the camber line of the wing sections to maximize the lift-over-drag ratio (L/D). A preliminary optimization run yielded a 3.75 percent improvement in L/D over a baseline low-boom configuration. The other set of parameters modifies the fuselage area to achieve a target F-function. Starting from an initial configuration with strong bow, wing, and tail shocks, a modified design with a flat-top signature is obtained. The methods presented can easily incorporate other design variables and objective functions. Extensions to the present capability in progress are described

Pseudogap in high-temperature superconductors from realistic Fr\"ohlich and Coulomb interactions

It has been recently shown that the competition between unscreened Coulomb and Fr\"{o}hlich electron-phonon interactions can be described in terms of a short-range spin exchange $J_p$ and an effective on-site interaction $\tilde{U}$ in the framework of the polaronic $t$-$J_p$-$\tilde{U}$ model. This model, that provides an explanation for high temperature superconductivity in terms of Bose-Einstein condensation (BEC) of small and light bipolarons, is now studied as a charged Bose-Fermi mixture. Within this approximation, we show that a gap between bipolaron and unpaired polaron bands results in a strong suppression of low-temperature spin susceptibility, specific heat and tunneling conductance, signaling the presence of normal state pseudogap without any assumptions on preexisting orders or broken symmetries in the normal state of the model.Comment: 5 pages, 5 figure

Coherent-state path integral calculation of the Wigner function

We consider a set of operators hat{x}=(hat{x}_1,..., hat{x}_N) with diagonal representatives P(n) in the space of generalized coherent states |n>; hat{x}=int dn P(n) |n>_L over polygonal paths with L vertices {n_1...L}. The distribution of the path centroid bar{P}=(1/L) sum_{i=1}^{L}P(n_i) tends to the Wigner function W(x), the joint distribution for the operators: W(x)=lim_{L->infinity} _{L}. This result is proved in the case where the Hamiltonian commutes with hat{x}. The Wigner function is non-positive if the dominant paths with path centroid in a certain region have Berry phases close to odd multiples of pi. For finite L the path centroid distribution is a Wigner function convolved with a Gaussian of variance inversely proportional to L. The results are illustrated by numerical calculations of the spin Wigner function from SU(2) coherent states. The relevance to the quantum Monte Carlo sign problem is also discussed

Time Discretization of Functional Integrals

Numerical evaluation of functional integrals usually involves a finite (L-slice) discretization of the imaginary-time axis. In the auxiliary-field method, the L-slice approximant to the density matrix can be evaluated as a function of inverse temperature at any finite L as $\rho_L(\beta)=[\rho_1(\beta/L)]^L$, if the density matrix $\rho_1(\beta)$ in the static approximation is known. We investigate the convergence of the partition function $Z_L(\beta)=Tr\rho_L(\beta)$, the internal energy and the density of states $g_L(E)$ (the inverse Laplace transform of $Z_L$), as $L\to\infty$. For the simple harmonic oscillator, $g_L(E)$ is a normalized truncated Fourier series for the exact density of states. When the auxiliary-field approach is applied to spin systems, approximants to the density of states and heat capacity can be negative. Approximants to the density matrix for a spin-1/2 dimer are found in closed form for all L by appending a self-interaction to the divergent Gaussian integral and analytically continuing to zero self-interaction. Because of this continuation, the coefficient of the singlet projector in the approximate density matrix can be negative. For a spin dimer, $Z_L$ is an even function of the coupling constant for L<3: ferromagnetic and antiferromagnetic coupling can be distinguished only for $L\ge 3$, where a Berry phase appears in the functional integral. At any non-zero temperature, the exact partition function is recovered as $L\to\infty$

Angular distribution of photoelectrons at 584A using polarized radiation

Photoelectron angular distributions for Ar, Xe, N2, O2, CO, CO2, and NH3 were obtained at 584 A by observing the photoelectrons at a fixed angle and simply rotating the plane of polarization of a highly polarized photon source. The radiation from a helium dc glow discharge source was polarized (84%) using a reflection type polarizer

Application of CFD to sonic boom near and mid flow-field prediction

A 3-D parabolized Navier-Stokes (PNS) code was used to calculate the supersonic overpressures from three different geometries at near- and mid-flow fields. Wind tunnel data is used for code validation. Comparison of the computed results with different grid refinements is shown. It is observed that a large number of grid points is needed to resolve the tail shock/expansion fan interaction. Therefore, an adaptive grid approach is employed to calculate the flow field. The agreement between the numerical results and the wind tunnel data confirms that computational fluid dynamics can be applied to the problem of sonic boom prediction