Change In Occupation Number Research Articles

Three mode interaction noise in laser interferometer gravitational wave detectors

Triply resonant three mode interactions in long optical cavities have been shown to lead to enhanced scattering of carrier light by the ultrasonic acoustic modes of the test mass mirrors. At high optical power, this can lead to parametric instability (parametric gain ) for a few acoustic modes with strong spectral and spatial overlap. Numerous acoustic modes of the test masses are predicted to have . Experimental studies have shown that such modes also strongly scatter the carrier light, enabling very sensitive readout of the acoustic modes. The three-mode scattering from the thermal fluctuation of large population of ultrasonic modes would causes random changes in occupation number of the carrier light and cavity transverse optical modes. Because the thermal fluctuation time scale (set by the acoustic mode relaxation times) is typically a few seconds, the noise spectrum from thermally induced photon number fluctuations is strongly peaked at low frequency. The noise level depends on the acoustic mode structure and acoustic losses of the test masses, the transverse optical mode spectrum of the optical cavities and on the test mass temperature. We theoretically investigate the possible effect of this noise and show that in advanced detectors under construction three mode interaction noise is below the standard quantum limit, but could set limits on future low frequency detectors that aim to exceed the free mass standard quantum limit.

Stochastic-Shielding Approximation of Markov Chains and its Application to Efficiently Simulate Random Ion-Channel Gating

Markov chains provide realistic models of numerous stochastic processes in nature. We demonstrate that in any Markov chain, the change in occupation number in state A is correlated to the change in occupation number in state B if and only if A and B are directly connected. This implies that if we are only interested in state A, fluctuations in B may be replaced with their mean if state B is not directly connected to A, which shortens computing time considerably. We show the accuracy and efficacy of our approximation theoretically and in simulations of stochastic ion-channel gating in neurons.

Evolution of the clustering of photometrically selected SDSS galaxies

We measure the angular auto-correlation functions (w) of SDSS galaxies selected to have photometric redshifts 0.1 < z < 0.4 and absolute r-band magnitudes Mr < -21.2. We split these galaxies into five overlapping redshift shells of width 0.1 and measure w in each subsample in order to investigate the evolution of SDSS galaxies. We find that the bias increases substantially with redshift - much more so than one would expect for a passively evolving sample. We use halo-model analysis to determine the best-fit halo-occupation-distribution (HOD) for each subsample, and the best-fit models allow us to interpret the change in bias physically. In order to properly interpret our best-fit HODs, we convert each halo mass to its z = 0 passively evolved bias (bo), enabling a direct comparison of the best-fit HODs at different redshifts. We find that the minimum halo bo required to host a galaxy decreases as the redshift decreases, suggesting that galaxies with Mr < -21.2 are forming in halos at the low-mass end of the HODs over our redshift range. We use the best-fit HODs to determine the change in occupation number divided by the change in mass of halos with constant bo and we find a sharp peak at bo ~ 0.9 - corresponding to an average halo mass of ~ 10^12Msol/h. We thus present the following scenario: the bias of galaxies with Mr < -21.2 decreases as the Universe evolves because these galaxies form in halos of mass ~ 10^12Msol/h (independent of redshift), and the bias of these halos naturally decreases as the Universe evolves.

Variational, V-representable, and variable-occupation-number perturbation theories

Density-functional perturbation theory with variationally fitted Kohn-Sham (KS) potentials is described. Requiring the Fock matrix and density matrix to commute through each order of perturbation theory determines the off-diagonal elements of the density matrix, and thus the effect of changing occupation numbers in density-functional perturbation theory. At each order of perturbation theory, the change in occupation numbers at that order enters only the diagonal part of the density matrix. The theory contains no phases, and a limiting process relates the rest of the diagonal density matrix element, obtained from wave function perturbation theory, to the off-diagonal part, obtained by commutation. V-representable density-functional theory is most practical when the KS potential is expanded in a finite basis to create the Sambe-Felton (SF) potential of analytic density-functional theory. This reduces the dimensionality of perturbation theory from order N(2) in the orbital basis to order N in the SF basis. Computing the (occupied-virtual)(2), i.e., N(4), sum over states once at the end of a self-consistent-field molecular orbital calculation removes the orbitals from all higher orders of perturbation theory. The rank-N(2) iterative coupled-perturbed equations are replaced by rank-N matrix inversion, to fit variationally the perturbed SF potential at each order. As an example of the 2n+1 rule of perturbation theory, the variational, first-order potential is used to give precise second and third derivatives of the energy with respect to occupation number. The hardness and hyperhardness are computed for a standard set of molecules. Both are essentially independent of how the variational SF potential is constrained for four different constraint combinations. With variational fitting, the precision of derivatives and the fidelity of the fit to the SF potential are not related. Analytic derivatives are accurate to machine precision for any constraint and all fitting basis sets.

First-principles Wannier functions and effective lattice fermion models for narrow-band compounds

We propose a systematic procedure for constructing effective lattice fermion models for narrow-band compounds on the basis of first-principles electronic structure calculations. The method is illustrated for the series of transition-metal (TM) oxides: SrVO$_3$, YTiO$_3$, V$_2$O$_3$, and Y$_2$Mo$_2$O$_7$. It consists of three parts, starting from LDA. (i) construction of the kinetic energy Hamiltonian using downfolding method. (ii) solution of an inverse problem and construction of the Wannier functions (WFs) for the given kinetic energy Hamiltonian. (iii) calculation of screened Coulomb interactions in the basis of \textit{auxiliary} WFs, for which the kinetic-energy term is set to be zero. The last step is necessary in order to avoid the double counting of the kinetic-energy term, which is included explicitly into the model. The screened Coulomb interactions are calculated in a hybrid scheme. First, we evaluate the screening caused by the change of occupation numbers and the relaxation of the LMTO basis functions, using the conventional constraint-LDA approach, where all matrix elements of hybridization involving the TM $d$ orbitals are set to be zero. Then, we switch on the hybridization and evaluate the screening associated with the change of this hybridization in RPA. The second channel of screening is very important, and results in a relatively small value of the effective Coulomb interaction for isolated $t_{2g}$ bands. We discuss details of this screening and consider its band-filling dependence, frequency dependence, influence of the lattice distortion, proximity of other bands, and the dimensionality of the model Hamiltonian.

Study of the reactivity of radical-molecular addition reaction using density functional theory

The reactivity of radical-molecular addition reaction was studied in terms of density-functional theory (DFT) and Hartree-Fock theory (HFT). It was found that the DFT method can give more accurate estimated result than the HFT method. The reason might be that the energy of the highest occupied molecular orbital (HOMO) in DFT is not the ionization energy, but rather represents the change in the total energy with respect to the change in occupation number of electrons in the HOMO, consistent with the concept of the transition state. The energy of HOMO in HFT is the ionization energy, which may represent more properly the property of the products and reactants themselves.

Possibility of ripplon-induced weak localization

Ripplon-induced weak localization is proposed for electrons on a liquid-helium surface. Ripplon scattering is quasi-elastic, the ripplons are quasi-static relative to the electron velocity, and the relative change in occupation number of the ripplon state in a scattering event is small. Conditions for the observation of ripplon-induced weak localization are calculated.

Theory of theα−γPhase Transition in Metallic Cerium

A simple model for the $\ensuremath{\alpha}\ensuremath{-}\ensuremath{\gamma}$ phase transition in Ce is presented. It is based on the change of occupation number of the $f$ levels, which are assumed to be atomiclike in character, i.e., highly correlated and with a very narrow bandwidth. The change in occupation number is, as a function of temperature, caused by the short-range part of the electron-electron interaction. The theory allows for the existence of a critical point. With the assumption of a linear relationship between $f$-level occupation numbers and lattice constant, pressure-latticeconstant isotherms are calculated. Curves for the paramagnetic susceptibility as a function of pressure and temperature are also presented.