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Thermodynamic Perturbation Theory for Associating Fluids: Beyond First Order

Marshall, Bennett Davis
ENG
Relevância na Pesquisa
45.88%
Association interactions such as the hydrogen bond are a key component in many physical and biological systems. For this reason accurate theories are needed to describe both the thermodynamics and self – assembly of associating species. Applications of these theories range from those of industrial importance, such as equations of state for process simulations, to the realm of materials science where these theories can be used to predict how molecular structure determines the self – assembly of associating species into advanced supramolecular materials. Semi – empirical equations of state based on chemical or lattice theories do not contain the molecular level detail to make predictions on how molecular structure affects self – assembly of associating species. For this, one needs a theory whose starting point is the interaction potential between two associating species which includes this molecular level detail. Development of accurate molecular theories for associating fluids is hampered by the strength, directionality and limited valence of the association interaction. This has proven particularly true in the extension of Mayer’s cluster theory to these associating fluids. This problem was largely solved by Wertheim in the 1980’s who developed an exact cluster expansion using a multi – density formalism. Wertheim’s cluster theory incorporates the geometry of the association interaction at an early point in the derivation. This allowed Wertheim to develop the theory in such a way that accurate and simple approximation methods could be applied such as thermodynamic perturbation theory (TPT). When treated at first order in perturbation (TPT1)...

Relative perturbation theory for diagonally dominant matrices

Dailey, Megan; Martínez Dopico, Froilán C.; Ye, Qiang
Fonte: Society for Industrial and Applied Mathematics Publicador: Society for Industrial and Applied Mathematics
Tipo: info:eu-repo/semantics/publishedVersion; info:eu-repo/semantics/article
Publicado em /10/2014 ENG
Relevância na Pesquisa
86.08%
In this paper, strong relative perturbation bounds are developed for a number of linear algebra problems involving diagonally dominant matrices. The key point is to parameterize diagonally dominant matrices using their off-diagonal entries and diagonally dominant parts and to consider small relative componentwise perturbations of these parameters. This allows us to obtain new relative perturbation bounds for the inverse, the solution to linear systems, the symmetric indefinite eigenvalue problem, the singular value problem, and the nonsymmetric eigenvalue problem. These bounds are much stronger than traditional perturbation results, since they are independent of either the standard condition number or the magnitude of eigenvalues/singular values. Together with previously derived perturbation bounds for the LDU factorization and the symmetric positive definite eigenvalue problem, this paper presents a complete and detailed account of relative structured perturbation theory for diagonally dominant matrices.; This research was partially supported by the Ministerio de Economía y Competitividad of Spain under grant MTM2012-32542.

A new perturbation bound for the LDU factorization of diagonally dominant matrices

Dailey, Megan; Martínez Dopico, Froilán C.; Ye, Qiang
Fonte: Society for Industrial and Applied Mathematics Publicador: Society for Industrial and Applied Mathematics
Tipo: info:eu-repo/semantics/publishedVersion; info:eu-repo/semantics/article
Publicado em /07/2014 ENG
Relevância na Pesquisa
55.9%
This work introduces a new perturbation bound for the L factor of the LDU factorization of (row) diagonally dominant matrices computed via the column diagonal dominance pivoting strategy. This strategy yields L and U factors which are always well-conditioned and, so, the LDU factorization is guaranteed to be a rank-revealing decomposition. The new bound together with those for the D and U factors in [F. M. Dopico and P. Koev, Numer. Math., 119 (2011), pp. 337– 371] establish that if diagonally dominant matrices are parameterized via their diagonally dominant parts and off-diagonal entries, then tiny relative componentwise perturbations of these parameters produce tiny relative normwise variations of L and U and tiny relative entrywise variations of D when column diagonal dominance pivoting is used. These results will allow us to prove in a follow-up work that such perturbations also lead to strong perturbation bounds for many other problems involving diagonally dominant matrices.; Research supported in part by Ministerio de Economía y Competitividad of Spain under grant MTM2012-32542.

Double Well Potential: Perturbation Theory, Tunneling, WKB (beyond instantons)

Turbiner, Alexander V
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
55.77%
A simple approximate solution for the quantum-mechanical quartic oscillator $V= m^2 x^2+g x^4$ in the double-well regime $m^2<0$ at arbitrary $g \geq 0$ is presented. It is based on a combining of perturbation theory near true minima of the potential, semi-classical approximation at large distances and a description of tunneling under the barrier. It provides 9-10 significant digits in energies and gives for wavefunctions the relative deviation in real $x$-space less than $\lesssim 10^{-3}$.; Comment: 13 pages, invited talk at "Crossing the boundaries: Gauge dynamics at strong coupling (Shifmania)", Minneapolis, May 14-17, 2009

A study of relative velocity statistics in Lagrangian perturbation theory with PINOCCHIO

Heisenberg, Lavinia; Schaefer, Bjoern Malte; Bartelmann, Matthias
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
45.95%
Subject of this paper is a detailed analysis of the PINOCCHIO algorithm for studying the relative velocity statistics of merging haloes in Lagrangian perturbation theory. Given a cosmological background model, a power spectrum of fluctuations as well as a Gaussian linear density contrast field $\delta_{\rm l}$ is generated on a cubic grid, which is then smoothed repeatedly with Gaussian filters. For each Lagrangian particle at position $\bmath{q}$ and each smoothing radius $R$, the collapse time, the velocities and ellipsoidal truncation are computed using Lagrangian Perturbation Theory. The collapsed medium is then fragmented into isolated objects by an algorithm designed to mimic the accretion and merger events of hierarchical collapse. Directly after the fragmentation process the mass function, merger histories of haloes and the statistics of the relative velocities at merging are evaluated. We reimplemented the algorithm in C++, recovered the mass function and optimised the construction of halo merging histories. Comparing our results with the output of the Millennium simulation suggests that PINOCCHIO is well suited for studying relative velocities of merging haloes and is able to reproduce the pairwise velocity distribution.; Comment: 10 pages...

Spectral density of the Hermitean Wilson Dirac operator: a NLO computation in chiral perturbation theory

Necco, S.; Shindler, A.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
45.79%
We compute the lattice spacing corrections to the spectral density of the Hermitean Wilson Dirac operator using Wilson Chiral Perturbation Theory at NLO. We consider a regime where the quark mass $m$ and the lattice spacing $a$ obey the relative power counting $m\sim a \Lambda_{\rm QCD}^2$: in this situation discretisation effects can be treated as perturbation of the continuum behaviour. While this framework fails to describe lattice spectral density close to the threshold, it allows nevertheless to investigate important properties of the spectrum of the Wilson Dirac operator. We discuss the range of validity of our results and the possible implications in understanding the phase diagram of Wilson fermions.; Comment: 27 pages, 4 figures; few typos corrected, added footnote, published version

High-Order Corrections to the Lipatov Asymptotics in the \phi^4 Theory

Lobaskin, D. A.; Suslov, I. M.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
45.8%
High orders in perturbation theory can be calculated by the Lipatov method. For most field theories, the Lipatov asymptotics has the functional form c a^N \Gamma(N+b) (N is the order of perturbation theory); relative corrections to this asymptotics have the form of a power series in 1/N. The coefficients of high order terms of this series can be calculated using a procedure analogous to the Lipatov approach and are determined by the second instanton in the considered field theory. These coefficients are calculated quantitatively for the n-component \phi^4 theory under the assumption that the second instanton is (i) a combination of two elementary instantons and (ii) a spherically asymmetric localized function. The technique of two-instanton calculations is developed, as well as the method for integrating over rotations of an asymmetric instanton in the coordinate state.; Comment: 20 pages, PDF

2-Nucleon 1-Loop Corrections to Pion Double Charge Exchange within Heavy Baryon Chiral Perturbation Theory

Misra, A.; Koltun, D. S.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
55.77%
One-loop corrections at the two-nucleon level to Pion Double Charge exchange (DCX) scattering off a nuclear target at threshold, are calculated within the framework of Heavy Baryon Chiral Perturbation Theory (HBChPT). An estimate for the (2-nucleon) 1-loop correction is obtained in the static limit and using an impulse approximation. We find a small (1.6%) increase relative to the leading order tree graphs.; Comment: 30 pages, RevTex, 5 tables, 5 ps figures; estimate of single-nucleon 1-loop corrections to the pi-pi, pi-N, 3pi-N vertices included in Section VI; references added; clarifying remarks regarding notations and new results related to 1-loop integrals included; discussion on Weinberg's power counting rule expanded; this revised version to appear in PRC

Structure of the two-neutrino double-$\beta$ decay matrix elements within perturbation theory

Stefanik, Dusan; Simkovic, Fedor; Faessler, Amand
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
55.77%
The two-neutrino double-$\beta$ Gamow-Teller and Fermi transitions are studied within an exactly solvable model, which allows a violation of both spin-isospin SU(4) and isospin SU(2) symmetries, and is expressed with generators of the SO(8) group. It is found that this model reproduces the main features of realistic calculation within the quasiparticle random-phase approximation with isospin symmetry restoration concerning the dependence of the two-neutrino double-$\beta$ decay matrix elements on isovector and isoscalar particle-particle interactions. By using perturbation theory an explicit dependence of the two-neutrino double-$\beta$ decay matrix elements on the like-nucleon pairing, particle-particle T=0 and T=1, and particle-hole proton-neutron interactions is obtained. It is found that double-$\beta$ decay matrix elements do not depend on the mean field part of Hamiltonian and that they are governed by a weak violation of both SU(2) and SU(4) symmetries by the particle-particle interaction of Hamiltonian. It is pointed out that there is a dominance of two-neutrino double-$\beta$ decay transition through a single state of intermediate nucleus. The energy position of this state relative to energies of initial and final ground states is given by a combination of strengths of residual interactions. Further...

Structure of Infrared Singularities of Gauge-Theory Amplitudes at Three and Four Loops

Ahrens, Valentin; Neubert, Matthias; Vernazza, Leonardo
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
45.79%
The infrared divergences of massless n-parton scattering amplitudes can be derived from the anomalous dimension of n-jet operators in soft-collinear effective theory. Up to three-loop order, the latter has been shown to have a very simple structure: it contains pairwise color-dipole interactions among the external partons, governed by the cusp anomalous dimension and a logarithm of the kinematic invariants s_{ij}, plus a possible three-loop correlation involving four particles, which is described by a yet unknown function of conformal cross ratios of kinematic invariants. This function is constrained by two-particle collinear limits and by the known behavior of amplitudes in the high-energy limit. We construct a class of relatively simple functions satisfying these constraints. We also extend the analysis to four-loop order, finding that three additional four-particle correlations and a single five-particle correlation appear, which again are governed by functions of conformal cross ratios. Our results suggest that the dipole conjecture, which states that only two-particle color-dipole correlations appear in the anomalous dimension, may need to be generalized. We present a weaker form of the conjecture, stating that to all orders in perturbation theory corrections to the dipole formula are governed by functions of conformal cross ratios...

The Effective Field Theory of Dark Matter and Structure Formation: Semi-Analytical Results

Hertzberg, Mark P.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
45.81%
Complimenting recent work on the effective field theory of cosmological large scale structures, here we present detailed approximate analytical results and further pedagogical understanding of the method. We start from the collisionless Boltzmann equation and integrate out short modes of a dark matter/dark energy dominated universe (LambdaCDM) whose matter is comprised of massive particles as used in cosmological simulations. This establishes a long distance effective fluid, valid for length scales larger than the non-linear scale ~ 10 Mpc, and provides the complete description of large scale structure formation. Extracting the time dependence, we derive recursion relations that encode the perturbative solution. This is exact for the matter dominated era and quite accurate in LambdaCDM also. The effective fluid is characterized by physical parameters, including sound speed and viscosity. These two fluid parameters play a degenerate role with each other and lead to a relative correction from standard perturbation theory of the form ~ 10^{-6}c^2k^2/H^2. Starting from the linear theory, we calculate corrections to cosmological observables, such as the baryon-acoustic-oscillation peak, which we compute semi-analytically at one-loop order. Due to the non-zero fluid parameters...

Utility of Galilean Symmetry in Light-Front Perturbation Theory: A Nontrivial Example in QCD

Harindranath, A.; Kundu, Rajen
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
45.78%
Investigations have revealed a very complex structure for the coefficient functions accompanying the divergences for individual time ($x^+$) ordered diagrams in light-front perturbation theory. No guidelines seem to be available to look for possible mistakes in the structure of these coefficient functions emerging at the end of a long and tedious calculation, in contrast to covariant field theory. Since, in light-front field theory, transverse boost generator is a kinematical operator which acts just as the two-dimensional Galilean boost generator in non-relativistic dynamics, it may provide some constraint on the resulting structures. In this work we investigate the utility of Galilean symmetry beyond tree level in the context of coupling constant renormalization in light-front QCD using the two-component formalism. We show that for each $x^+$ ordered diagram separately, underlying transverse boost symmetry fixes relative signs of terms in the coefficient functions accompanying the diverging logarithms. We also summarize the results leading to coupling constant renormalization for the most general kinematics.; Comment: RevTeX, five PostScript figures

Loop Corrections in Non-Linear Cosmological Perturbation Theory

Scoccimarro, Roman; Frieman, Joshua
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
45.87%
Using a diagrammatic approach to Eulerian perturbation theory, we analytically calculate the variance and skewness of the density and velocity divergence induced by gravitational evolution from Gaussian initial conditions, including corrections *beyond* leading order. Except for the power spectrum, previous calculations in cosmological perturbation theory have been confined to leading order (tree level)-we extend these to include loop corrections. For scale-free initial power spectra, the one-loop variance \sigma^2 = \sigma^2_l + 1.82 \sigma^4_l and the skewness S_3 = 34/7 + 9.8 \sigma^2_l, where \sigma_l is the rms fluctuation of the linear density field. We also compute loop corrections to the variance, skewness, and kurtosis for several non-linear approximation schemes, where the calculation can be easily generalized to 1-point cumulants of higher order and arbitrary number of loops. We find that the Zel'dovich approximation gives the best approximation to the loop corrections of exact perturbation theory, followed by the Linear Potential approximation (LPA) and the Frozen Flow approximation (FFA), in qualitative agreement with the relative behavior of tree-level results. In LPA and FFA, loop corrections are infrared divergent for spectral indices n < 0; this is related to the breaking of Galilean invariance in these schemes.; Comment: 53 pages...

Cosmological perturbation theory for baryons and dark matter I: one-loop corrections in the RPT framework

Somogyi, Gabor; Smith, Robert E.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
55.77%
We generalize the `renormalized' perturbation theory (RPT) formalism of Crocce & Scoccimarro (2006a) to deal with multiple fluids in the Universe and here we present calculations up to the one-loop level. We apply the approach to the non-linear evolution of baryon and cold dark matter (CDM) perturbations, evolving from distinct sets of initial conditions. In current models of structure formation, it is standard practice to treat baryons and CDM as an effective single component fluid. In this approximation, one uses a weighed sum of late-time baryon and CDM transfer functions to set initial conditions. Here, we explore whether this approach can be used for high precision work. We show that, even for a pure linear treatment, there is a large-scale scale-dependent bias between baryons and CDM for WMAP5 cosmology. This bias is >1% until the present day, when it is driven towards unity through gravitational relaxation. Using the RPT formalism we test this approximation in the non-linear regime, and show that the CDM power spectrum in the 2-component fluid differs from that obtained from a 1-component fluid by ~3% on scales of order k~0.05 h/Mpc at z=10, and by ~0.5% at z=0. However, for the case of baryons the situation is worse and we find that the power spectrum is suppressed by ~15% on scales k~0.05 h/Mpc at z=10...

Perturbation Theory for Spin Ladders Using Angular-Momentum Coupled Bases

Piekarewicz, J.; Shepard, J. R.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
55.77%
We compute bulk properties of Heisenberg spin-1/2 ladders using Rayleigh-Schr\"odinger perturbation theory in the rung and plaquette bases. We formulate a method to extract high-order perturbative coefficients in the bulk limit from solutions for relatively small finite clusters. For example, a perturbative calculation for an isotropic $2\times 12$ ladder yields an eleventh-order estimate of the ground-state energy per site that is within 0.02% of the density-matrix-renormalization-group (DMRG) value. Moreover, the method also enables a reliable estimate of the radius of convergence of the perturbative expansion. We find that for the rung basis the radius of convergence is $\lambda_c\simeq 0.8$, with $\lambda$ defining the ratio between the coupling along the chain relative to the coupling across the chain. In contrast, for the plaquette basis we estimate a radius of convergence of $\lambda_c\simeq 1.25$. Thus, we conclude that the plaquette basis offers the only currently available perturbative approach which can provide a reliable treatment of the physically interesting case of isotropic $(\lambda=1)$ spin ladders. We illustrate our methods by computing perturbative coefficients for the ground-state energy per site, the gap, and the one-magnon dispersion relation.; Comment: 22 pages. 9 figures

Odderon and seven Pomerons: QCD Reggeon field theory from JIMWLK evolution

Kovner, Alex; Lublinsky, Michael
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
45.79%
We reinterpret the JIMWLK/KLWMIJ evolution equation as the QCD Reggeon field theory (RFT). The basic "quantum Reggeon field" in this theory is the unitary matrix $R$ which represents the single gluon scattering matrix. We discuss the peculiarities of the Hilbert space on which the RFT Hamiltonian acts. We develop a perturbative expansion in the RFT framework, and find several eigenstates of the zeroth order Hamiltonian. The zeroth order of this perturbation preserves the number of $s$ - channel gluons. The eigenstates have a natural interpretation in terms of the $t$ - channel exchanges. Studying the single $s$ - channel gluon sector we find the eigenstates which include the reggeized gluon and five other colored Reggeons. In the two ($s$ - channel) gluon sector we study only singlet color exchanges. We find five charge conjugation even states. The bound state of two reggeized gluons is the standard BFKL Pomeron. The intercepts of the other Pomerons in the large $N$ limit are $1+\omega_P=1+2\omega$ where $1+\omega$ is the intercept of the BFKL Pomeron, but their coupling in perturbation theory is suppressed by at least $1/N^2$ relative to the double BFKL Pomeron exchange. For the $[27,27]$ Pomeron we find $\omega_{[27,27]}=2\omega+O(1/N)>2\omega$. We also find three charge conjugation odd exchanges...

Characteristic Scales of Baryon Acoustic Oscillations from Perturbation Theory: Non-linearity and Redshift-Space Distortion Effects

Nishimichi, Takahiro; Ohmuro, Hiroshi; Nakamichi, Masashi; Taruya, Atsushi; Yahata, Kazuhiro; Shirata, Akihito; Saito, Shun; Nomura, Hidenori; Yamamoto, Kazuhiro; Suto, Yasushi
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
45.84%
An acoustic oscillation of the primeval photon-baryon fluid around the decoupling time imprints a characteristic scale in the galaxy distribution today, known as the baryon acoustic oscillation (BAO) scale. Several on-going and/or future galaxy surveys aim at detecting and precisely determining the BAO scale so as to trace the expansion history of the universe. We consider nonlinear and redshift-space distortion effects on the shifts of the BAO scale in $k$-space using perturbation theory. The resulting shifts are indeed sensitive to different choices of the definition of the BAO scale, which needs to be kept in mind in the data analysis. We present a toy model to explain the physical behavior of the shifts. We find that the BAO scale defined as in Percival et al. (2007) indeed shows very small shifts ($\lesssim$ 1%) relative to the prediction in {\it linear theory} in real space. The shifts can be predicted accurately for scales where the perturbation theory is reliable.; Comment: 21 pages, 9 figures, references and supplementary sections added, accepted for publication in PASJ

Peculiar Velocity, Cosmic Perturbation Theory and the CMB Anisotropy

Bruni, Marco; Lyth, David H.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
45.85%
This is a somewhat extended version of the original July 93 report. It is proved that the cosmological density perturbation is associated with a peculiar velocity field. This allows a simple formulation of cosmological perturbation theory, which works entirely with quasi-Newtonian fluid flow equations. As an illustration, the large scale cosmic microwave background anisotropy (Sachs-Wolfe effect) is calculated without any reference to the metric perturbation. In addition, assuming the usual adiabatic initial condition on the density perturbation, we show that the dipole of the anisotropy measures our peculiar velocity relative to the average peculiar velocity within the last scattering surface of the microwave background, thus defining its frame of reference.; Comment: 9 pages, REVTEX, LANCS 9321

The Continuum Version of \phi^4_{1+1}-theory in Light-Front Quantization

Grangé, Pierre; Ullrich, Peter; Werner, Ernst
Tipo: Artigo de Revista Científica