Fluctuation Approximation Research Articles

Dispersion and Damping of Phononic Excitations in Fermi Superfluid Gases in 2D

We calculate the sound velocity and the damping rate of the collective excitations of a 2D fermionic superfluid in a non-perturbative manner. Specifically, we focus on the Anderson–Bogoliubov excitations in the BEC-BCS crossover regime, as these modes have a sound-like dispersion at low momenta. The calculation is performed within the path-integral formalism and the Gaussian pair fluctuation approximation. From the action functional, we obtain the propagator of the collective excitations and determine their dispersion relation by locating the poles of this propagator. We find that there is only one kind of collective excitation, which is stable at T = 0 and has a sound velocity of v F / 2 for all binding energies, i.e., throughout the BEC-BCS crossover. As the temperature is raised, the sound velocity decreases and the damping rate shows a non-monotonous behavior: after an initial increase, close to the critical temperature T C the damping rate decreases again. In general, higher binding energies provide higher damping rates. Finally, we calculate the response functions and propose that they can be used as another way to determine the sound velocity.

Large-eddy simulation of a bluff-body stabilised nonpremixed flame with radiation heat transfer

Turbulence-radiation interactions are studied in this work for large-eddy simulations (LES) of an artificially scaled configuration based on the Sydney bluff-body burner. This investigation is performed by applying the combustion model flamelet generated manifolds, and the transported PDF Eulerian stochastic field method is employed to account for turbulence-chemistry interaction. The radiative transfer equation is solved with the finite volume method, while the gas radiative properties are calculated using the non-gray weighted-sum-of-gray-gases (WSGG) model. For the solution of the energy conservation equation in LES, the filtered radiative source term, which is the difference between the filtered absorption term and the filtered emission term, is required. The absorption term is modelled with the optically thin fluctuation approximation and the emission term is computed by either omitting or considering the subgrid-scale contribution. The results indicate that the difference between the emission term calculated with these two procedures is significant only in the regions where the emission term is relatively small. Moreover, no relevant differences in the profiles of mean temperature computed for those two cases were found. These results suggest that the subgrid-scale contribution may be neglected for LES investigation of the considered configuration.

Pressure effects on radiative heat transfer in sooting turbulent diffusion flames

This article investigates the effects of increasing pressure up to 4 atm on radiative heat transfer in momentum-driven methane turbulent jet flames by using well-established chemical mechanism, combustion, soot production and radiation models. A transported PDF method is used to close properly the soot-production turbulence interaction and the emission Turbulence Radiation Interaction (TRI). A Narrow-Band CK (NBCK) model is used as the gas radiative property model. The absorption TRI is neglected based on the Optically-Thin Fluctuation Approximation (OTFA). In accordance with a previous study dealing with non-sooting hydrogen flames (Nmira et al., JQSRT 220 (2018) 172–179), the 3-atm and 4-atm flames are designed from the atmospheric flame by using a Froude modeling approach that allows to preserve the flame/flow structure as the pressure is increased and hence to isolate the pressure effects on soot production, radiative heat transfer, and TRI. The effects of increasing pressure on radiant fraction result from two competing mechanisms: i) an increase in soot emission that tends to increase the radiant fraction and ii) a reduction in flame transparency that tends to reduce it. For the present flames, the first mechanism dominates the second, resulting in an increased radiant fraction with increasing the pressure. The TRI effects on flame radiative loss are also governed by competing mechanisms. The enhancement mechanism is due to gas emission TRI and temperature self-correlation effects on soot emission whereas the reduction mechanism is caused by the negative correlation between soot volume fraction and temperature. The former dominates whereas the latter becomes increasingly important with increasing the pressure. This limits the increase in the global radiative loss due to TRI as the pressure is increased. In addition, numerical simulations show that the TRI effects can reduce the local radiative loss in regions of high soot concentration of the 4 atm flame.

Combined error estimates for local fluctuations of SPDEs

In this work, we study the numerical approximation of local fluctuations of certain classes of parabolic stochastic partial differential equations (SPDEs). Our focus is on effects for small spatially correlated noise on a time scale before large deviation effects have occurred. In particular, we are interested in the local directions of the noise described by a covariance operator. We introduce a new strategy and prove a Combined ERror EStimate (CERES) for the five main errors: the spatial discretization error, the local linearization error, the noise truncation error, the local relaxation error to steady state, and the approximation error via an iterative low-rank matrix algorithm. In summary, we obtain one CERES describing, apart from modelling of the original equations and standard round-off, all sources of error for a local fluctuation analysis of an SPDE in one estimate. To prove our results, we rely on a combination of methods from optimal Galerkin approximation of SPDEs, covariance moment estimates, analytical techniques for Lyapunov equations, iterative numerical schemes for low-rank solution of Lyapunov equations, and working with related spectral norms for different classes of operators.

Электронное строение и оптическое поглощение фуллеренов как сильно коррелированных систем на примере молекулы C-=SUB=-96-=/SUB=-(C-=SUB=-2-=/SUB=-)

Taking into account the intrasite Coulomb interaction with the parameter U ~ 10 eV in the approximation of static fluctuations, the energy spectrum of the isomer N 181 (C2) of the C96 fullerene is calculated, based on which its optical absorption spectrum is modeled. The obtained curve of the optical absorption spectrum at a good qualitative level coincides with the experimental curve. The same curve obtained in the framework of the traditional model without taking into account the intranode Coulomb interaction differs significantly from the experimental curve. Keywords: fullerene, energy spectrum, optical absorption spectrum, π electron, Hubbard subband, optical transitions.

Энергетический спектр и спектр оптического поглощения фуллерена C-=SUB=-24-=/SUB=- в модели Хаббарда

Anticommutator Green’s functions and energy spectra of fullerene C24 with the D6, D6d, and Oh symmetry groups have been obtained in an analytical form within the Hubbard model and static fluctuation approximation. The energy states have been classified using the methods of group theory, and the allowed transitions in the energy spectra of fullerene C24 with the D6, D6d, and Oh symmetry groups have been determined.

Энергетический спектр и спектр оптического поглощения фуллерена С-=SUB=-28-=/SUB=- в модели Хаббарда

Anticommutator Green’s functions and energy spectra of fullerene C28 and endofullerene Zr@C28 with the Td symmetry groups have been obtained in an analytical form within the Hubbard model and static fluctuation approxima-tion. The energy states have been classified using the methods of group theory, and the allowed transitions in the energy spectra of fullerene C28 and endofull-erene Zr@C28 with the Td symmetry groups have been determined.

Phononic collective excitations in superfluid Fermi gases at nonzero temperatures

We study the phononic collective modes of the pairing field $\Delta$ and their corresponding signature in both the order-parameter and density response functions for a superfluid Fermi gas at all temperatures below $T_c$ in the collisionless regime. The spectra of collective modes are calculated within the Gaussian Pair Fluctuation approximation. We deal with the coupling of these modes to the fermionic continuum of quasiparticle-quasihole excitations by performing a non-perturbative analytic continuation of the pairing field propagator. At low temperature, we recover the known exponential temperature dependence of the damping rate and velocity shift of the Anderson-Bogoliubov branch. In the vicinity of $T_c$, we find analytically a weakly-damped collective mode whose velocity vanishes with a critical exponent of $1/2$, and whose quality factor diverges logarithmically with $T_c-T$, thereby clarifying an existing debate in the literature (Andrianov et al. Th. Math. Phys. 28, 829, Ohashi et al. J. Phys. Jap. 66, 2437). A transition between these two phononic branches is visible at intermediary temperatures, particularly in the BCS limit where the phase-phase response function displays two maxima.

The Energy Spectrum and the Optical Absorption Spectrum of С36 Fullerene Within the Hubbard Model

Using the Hubbard model in an approximation of static fluctuations, analytical relations of anticommutator Green’s functions and energy spectra of С36 fullerene and La@C36 endohedral fullerene with the D6h symmetry groups are obtained. Using the group theory methods, a classification of the energy states is performed and the allowed transitions in the energy spectra of the С36 and La@C36 molecules are determined.

Quartic polynomial approximation for fluctuations of separation of trajectories in chaos and correlation dimension

We consider the cumulant generating function of the logarithm of the distance between two infinitesimally close trajectories of a chaotic system. Its long-time behavior is given by the generalized Lyapunov exponent providing the logarithmic growth rate of the kth moment of the distance. The Legendre transform of is a large deviations function that gives the probability of rare fluctuations where the logarithmic rate of change of the distance is much larger or much smaller than the mean rate defining the first Lyapunov exponent. The only non-trivial zero of is at minus the correlation dimension of the attractor which for incompressible flows reduces to the space dimension. We describe here general properties constraining the form of and the Gallavotti–Cohen type relations that hold when there is symmetry under time-reversal. This demands studying joint growth rates of infinitesimal distances and volumes. We demonstrate that quartic polynomial approximation for does not violate the Marcinkiewicz theorem on invalidity of polynomial form for the generating function. We propose that this quartic approximation will fit many experimental situations, not having the effective time-reversibility and the short correlation time properties of the quadratic Grassberger–Procaccia estimates. We take the existing for turbulent channel flow and demonstrate that the quartic fit is nearly perfect. The violation of time-reversibility for the Lagrangian trajectories of the incompressible Navier–Stokes (NS) turbulence below the viscous scale is considered. We demonstrate how the fit can be used for finding the correlation dimensions of strange attractors via easily measurable quantities. We provide a simple formula via the Lyapunov exponents, holding in quadratic approximation, and describe the construction of the quartic approximation. A different approximation scheme for finding the correlation dimension from expansion in the flow compressibility is also provided.

A microscopic study of spin-polarized 6Li atoms in highly elongated traps using the static fluctuation approximation (SFA)

The thermodynamic properties of spin-polarized 6Li atoms in highly elongated traps are studied within the Static Fluctuation Approximation. The chemical potential μ, energy per particle U/N, specific heat capacity CV/N, and the effective magnetic field h are determined as a function of temperature and potential strength (magnetic field B). We used the contact potential as the two-body interaction potential. For a repulsive interaction μ and U increase parabolically with B, while for an attractive interaction both increase monotonically with B until saturation at B larger than the resonance field. The effect of the two-body interaction on CV appears at temperatures comparable with the Fermi temperature. μ and U/N of the system were studied of different channels; It is found that these quantities are channel dependent, and the behavior of h at low temperature depends on the potential strength. Our results are consistent with that obtained by the mean-field Bogoliubov–de Gennes method.

Optical Absorption Spectrum of Metal–Nitride Complexes of С80 Fullerene as Strongly Correlated Systems

Within the framework of Hubbard’s model using an approximation of static fluctuations, the energy spectrum of the π-electron subsystem of an icosahedral C80 fullerene isomer is obtained. Based on the energy spectrum, an optical absorption spectrum of metal-nitride complexes M3N@C80 (M = Gd, Tm, Dy) is simulated. It is quite consistent with the respective experimental spectrum.

Theoretical study of electronic properties of gold fullerenes Au16–Au20

A theoretical study of gold fullerenes Au16–Au20 as strongly correlated electron systems is carried out within the framework of the Hubbard model in the approximation of static fluctuations. The Fourier transforms of anticommutator Green’s functions for electrons at different fullerene sites of gold atoms are obtained and energy spectra are constructed. The density of electron states, the graphical depiction of the equation for the chemical potential, thermodynamic averages characterizing electron transitions among adjacent sites and the description of the probabilities of detecting two electrons with oppositely oriented spin projections on a single site within nanosystems are presented and analyzed. The considered gold fullerenes are demonstrated to possess semiconductor properties.

Thermodynamic properties of ferroics described by the transverse Ising model and their applications for CoNb2O6

The temperature and transverse field dependence of the entropy and the specific heat of ferroics in the quantum paramagnetic (QPa) state is investigated using the transverse Ising model (TIM) with different spin values within mean field and Gaussian spin fluctuation approximations. A maximum peak of the temperature dependence of the specific heat curves is enhanced in the QPa state due to spin fluctuations. This peak shifts to higher temperature region and its magnitude reduces with increasing transverse field. In addition, the temperature corresponding to this maximum depends linearly on the deviation of the transverse field from its critical value. The obtained specific heat qualitatively agrees with the experimental observation for the quasi-one-dimensional (1D) Ising ferromagnet CoNb2O6 in the QPa phase. It is also shown that the spin-1/2 three dimensional (3D) TIM clearly describes the specific heat of CoNb2O6 in the QPa states near the critical temperature. However, the spin-3/2 3D-TIM is more adequate than the spin-1/2 3D-TIM for describing the thermal behavior of CoNb2O6 in the QPa states at high fields and at elevated temperatures.

The activity coefficient within the solvation thermodynamics formalism: Fundamentals and applications to neutral solutes

The solvation thermodynamics is a molecular based statistical mechanics description of the solvation process, which provides a proper distinction from other processes that uniquely and unambiguously defines the solvation of any species in any environment. Because the activity coefficient involves the behavior of a given species in different environments, it is then related to the solvation process, which should be described within the solvation thermodynamics formalism. Indeed, the activity coefficient of a species i within an α phase, γi,αo,ρ, is expressed in terms of the binding energy of i to the α phase, Bi, α, and to the dilute-ideal phase, Bi, o. In addition to this molecular description, the activity coefficient can also be related to the Gibbs solvation energies of these two phases within the solvation thermodynamics formalism, which can provide, for instance, unique values of the activity coefficients from the experimental Gibbs solvation energies. The relevance and advantages of using the binding energy (or the coupling work of the solute with its surroundings) as the main molecular quantity for evaluating the activity coefficient is explored in detail. For instance, several cancellations occur when evaluating the binding energies, especially those related to the non-additive corrections (many-body effects), which can more promptly justify the use of the pairwise approximation. In addition, by partitioning the potential energy into two or more contributions, the activity coefficient can also be partitioned into these contributions, yielding exact expressions that are suitable for approximations and interpretations. In fact, a direct connection with perturbation theories can be established and new partitions can be proposed to explore recent approaches based on embedded quantum calculations of the potential energy in condensed phases. It has been shown that the approximation 〈e−βBi, α〉 ≅ e−β〈Bi, α〉, with β−1 = kBT, can be valid even when the condition 〈Bi, α〉 ≪ kBT is not satisfied, as long as the fluctuations, 〈(Bi, α − 〈Bi, α〉)2〉, and the higher order deviations of the binding energy, 〈(Bi, α − 〈Bi, α〉)n〉, (n ≥ 3), are negligible. This small fluctuations approximation (SFA) can rationalize and justify the good results obtained for systems with large binding energies. The SFA can also provide a new interpretation and insights for the activity coefficient. The partition of the potential energy into hard sphere (cavity) and attractive (non-cavity) contributions and the SFA were employed to obtain approximate expressions that allowed to explore the general behavior of the activity coefficient of neutral systems. For instance, the activity coefficient of strongly interacting large molecules (hard-spheres interacting by Lennard-Jones potential in an implicit solvent) tends to decrease with the increasing of the concentration of the solute, which is accentuated by the increase of the dielectric constant of the medium. In addition, the cavity contribution (modeled by hard-sphere mixtures of different sizes) to the activity coefficient is influenced by the relative sizes of the molecules and by the pure liquid densities. This contribution dominates the behavior of the activity coefficient with the concentration.

Study of turbulence-radiation interactions in large-eddy simulation of scaled Sandia flame D

The importance of the subgrid-scale contribution for computing the radiative source term in large-eddy simulations (LES) for the scaled Sandia flame D is studied in this work. This study is carried out by employing the flamelet generated manifolds approach as a combustion model in combination with the Eulerian stochastic field method to account for the turbulence-chemistry interaction. Furthermore, the finite volume method is employed to solve the radiative transfer equation with the non-grey weighted-sum-of-grey-gases (WSGG) model for the spectral resolution. In order to take thermal radiation into account in the LES context, the filtered radiative source term should be computed. The contribution of the resolved scales can be explicitly calculated, whereas the terms involving the subgrid-scale contributions are unclosed and require approximations. In this work, the optically thin fluctuation approximation is applied for modelling the filtered absorption term and different methods are used for computing the emission term, in which the subgrid-scales are either considered or omitted. The results show that the difference between the radiative source terms computed by accounting and by neglecting the subgrid-scale contribution is significant only in the regions where this term is small. Besides, no relevant differences are found in the profiles of mean temperature and CO2 species concentration calculated using those two different approaches. These results indicate that the subgrid-scale contribution may be neglected in the context of LES for the flame under consideration.

A microscopic study of spin-polarized asymmetric hot nuclear matter within the static fluctuation approximation (SFA)

In this work, the thermodynamic properties of spin-polarized asymmetric hot nuclear matter are studied within the Static Fluctuation Approximation (SFA). Specifically, the energy per unit volume, pressure, entropy per unit volume, and specific heat capacity are determined as functions of density up to 0.6 fm−3, and temperature up to 80 MeV. Also, the effects of the asymmetry and spin-polarization parameters on these quantities are explored. The main input in the formalism is the Urbana V14 nucleon–nucleon potential. It is found that these parameters have significant effects on the thermodynamic properties at high densities or low temperatures where quantum features become pronounced. As expected, the entropy results show that the system is more ordered when polarized or for large values of the asymmetry parameter. The quadratic dependence of the energy on the asymmetry and spin-polarization parameters is confirmed at different densities and temperatures. The results are compared to those obtained with different approaches, such as the lowest-order constrained variational method, the conventional variational method, and the relativistic mean-field approximation. It is found that the present results are consistent with those.

Influence of Deformation on the Energy and Optical Absorption Spectra of Fullerene C20 within the Hubbard Model

Abstract—Anticommutator Green’s functions and energy spectra of fullerene C20 with the Ih, D5d, and D3d symmetry groups have been obtained in an analytical form within the Hubbard model and static fluctuation approximation. The energy states have been classified using the methods of group theory, and the allowed transitions in the energy spectra of fullerene C20 with the Ih, D5d, and D3d symmetry groups have been determined. It is also shown how the energy levels of fullerene C20 with the Ih symmetry group are split with the symmetry reduction.

Electronic properties of gold nanotubes (5, 3) and (5, 0) in the Hubbard model in the static fluctuation approximation

A theoretical analysis of the electronic properties of single-walled gold nanotubes with chiralities (5, 3) and (5, 0) with the growth of nanotubes is presented. The results of the study of single-walled gold nanotubes with chiralities (5, 3) and (5, 0) were compared with the results obtained by X.P. Yang and J.M. Dong. The Hubbard model with a certain selection of model parameters allows us to explain the data obtained using the electron density functional theory. According to our results, only the semiconductor–metal transition occurs with the growth of gold nanotubes, and there are no semiconductor–metal–semiconductor–metal “oscillations”, which were indicated in the following work: X.P. Yang and J.M. Dong, Phys. Rev. B 71, 233403 (2005).

Влияние деформации на энергетический спектр и спектр оптического поглощения фуллерена C-=SUB=-20-=/SUB=- в модели Хаббарда

Abstract —Anticommutator Green’s functions and energy spectra of fullerene C_20 with the I _ h , D _5 d , and D _3 d symmetry groups have been obtained in an analytical form within the Hubbard model and static fluctuation approximation. The energy states have been classified using the methods of group theory, and the allowed transitions in the energy spectra of fullerene C_20 with the I _ h , D _5 d , and D _3 d symmetry groups have been determined. It is also shown how the energy levels of fullerene C_20 with the I _ h symmetry group are split with the symmetry reduction.