Local Field Correlation Functions Research Articles

Vibrational Dynamics of Pd-Ni-P Bulk Metallic Glasses: a Local Pseudopotential Study

In the present paper, Phonon modes and elastic constant of three different concentrations of PdxNi1-xP (Pd64Ni16P20, Pd40Ni40P20 and Pd16Ni64P20) bulk metallic glass are calculated using (1) Hubbard-Beeby (HB) and (2) Takeno-Goda (TG) approach along with our well established local model potential. The Hartree (H), Farid et al (F) and Sarkar et al (S) local field correlation functions (LFCF) are employed to examine the effect of the screening function on the collective dynamics of Pd-Ni-P bulk metallic glasses. Results are also reported for phonon dispersion curve, propagation elastic wave and elastic properties viz: bulk modulus BT, modulus of rigidity G, Poisson’s ratio ξ, Young’s modulus Y, Debye temperature ƟD. However, the calculated elastic constants results agree well with other theoretical and available experimental data.

Study of dynamical properties of Pd40Cu30Ni10P20 bulk metallic glass at various temperatures

Abstract In the present article, we study the dynamical properties such as velocity auto correlation function (VACF), power spectrum (PS) and mean square displacement (MSD) of Pd40Cu30N10P20 bulk metallic glass (BMG) computed using the local model potential approach at different temperatures i.e. 296 K, 573 K, 659 K 923 K, respectively. Such computations are performed with the static harmonic well approximation theory at various temperatures. The effective interatomic potential for aforementioned BMG is calculated using well established model pseudopotential of Jani et al. along with Farid et al. (F) local field correlation functions (LFCF) for studying the screening dependency on the aforesaid properties. It is observed that negative dip in the velocity auto correlation function decreases as the temperature increases and in results of the power spectrum, the peak is shifted towards lower ω observed as temperature increases. The obtained result of MSD concludes that the vibrating component in the atomic motion decreases as increases the temperatures. The velocity auto correlation function displays the transferability of the local pseudopotential in the present case of Pd-based BMG.

Toverline{T} deformation of correlation functions

We study the evolution of correlation functions of local fields in a two-dimensional quantum field theory under the lambda Toverline{T} deformation, suitably regularized. We show that this may be viewed in terms of the evolution of each field, with a Dirac-like string being attached at each infinitesimal step. The deformation then acts as a derivation on the whole operator algebra, satisfying the Leibniz rule. We derive an explicit equation which allows for the analysis of UV divergences, which may be absorbed into a non-local field renormalization to give correlation functions which are UV finite to all orders, satisfying a (deformed) operator product expansion and a Callan-Symanzik equation. We solve this in the case of a deformed CFT, showing that the Fourier-transformed renormalized two-point functions behave as k2∆+2λk2, where ∆ is their IR conformal dimension. We discuss in detail deformed Noether currents, including the energy-momentum tensor, and show that, although they also become non-local, when suitably improved they remain finite, conserved and satisfy the expected Ward identities. Finally, we discuss how the equivalence of the Toverline{T} deformation to a state-dependent coordinate transformation emerges in this picture.

Structural and Collective Dynamics of Bi50Zn50 of binary metallic glass

In the present paper, structural properties, collective dynamics and elastic properties have been studied of Bi50Zn50 liquid metallic glass at a wide range of temperatures. Ashcroft and Langreth binary structure factor have been used to study for static structure factor and pair correlation function for present alloy. The collective excitation has been studied for longitudinal and transverses phonon modes based on our well-established model potential along with Hubbard and Beeby (HB) approach. These frequencies are expressed in terms of many-body correlation functions of atoms as well as of interatomic potential. The important ingredients in the present study are the pair-potential and pair-correlation functions. The local field correlation functions due to Hartree (H) and Farid et al (F) are employed to investigate the influence of the screening effects on the vibrational dynamics of Bi50Zn50 liquid metallic glass. The results for bulk modulus (BT), modulus of rigidity (G), Poisson’s ratio (ξ), Young’s modulus (Y), Debye temperature (ƟD), the propagation velocity of elastic waves and dispersion curves are reported. Good agreement with the experiment is observed for the structure factors and elastic properties results are consistent and confirm the applicability of model potential and self-consistent phonon theory for such studies.

Branch point twist field correlators in the massive free Boson theory

Well-known measures of entanglement in one-dimensional many body quantum systems, such as the entanglement entropy and the logarithmic negativity, may be expressed in terms of the correlation functions of local fields known as branch point twist fields in a replica quantum field theory. In this “replica” approach the computation of measures of entanglement generally involves a mathematically non-trivial analytic continuation in the number of replicas. In this paper we consider two-point functions of twist fields and their analytic continuation in the 1+1 dimensional massive (non-compactified) free Boson theory. This is one of the few theories for which all matrix elements of twist fields are known so that we may hope to compute correlation functions very precisely. We study two particular two-point functions which are related to the logarithmic negativity of semi-infinite disjoint intervals and to the entanglement entropy of one interval. We show that our prescription for the analytic continuation yields results which are in full agreement with conformal field theory predictions in the short-distance limit. We provide numerical estimates of universal quantities and their ratios, both in the massless (twist field structure constants) and the massive (expectation values of twist fields) theory. We find that particular ratios are given by divergent form factor expansions. We propose such divergences stem from the presence of logarithmic factors in addition to the expected power-law behaviour of two-point functions at short-distances. Surprisingly, at criticality these corrections give rise to a log⁡(log⁡ℓ) correction to the entanglement entropy of one interval of length ℓ. This hitherto overlooked result is in agreement with results by Calabrese, Cardy and Tonni and has been independently derived by Blondeau-Fournier and Doyon [25].

Study of phonon modes and elastic properties of Sc36Al24Co20Y20 and Gd36Al24Co20Y20 rare-earth bulk metallic glasses

A phonon modes and elastic properties of two different rare-earth based bulk metallic glasses Sc36Al24Co20Y20 and Gd36Al24Co20Y20 are computed using Hubbard-Beeby approach and our well established model potential. The local field correlation functions due to Hartree (H), Taylor (T), Ichimaru and Utsumi (IU), Farid et al (F) and Sarkar Sen et al (S) are employed to investigate the influence of the screening effects on the vibrational dynamics of Sc36Al24Co20Y20 and Gd36Al24Co20Y20 bulk metallic glasses. The results for bulk modulus BT, modulus of rigidity G, Poisson's ratio ξ, Young's modulus Y, Debye temperature ΘD, propagation velocity of elastic waves and dispersion curves are reported. The computed elastic properties are found to be in good agreement with experimental and other available data.

Collective Modes and Elastic Constants of Liquid Al83Cu17 Binary Alloy

The collective dynamics (longitudinal and transverse phonon modes) are studied for aluminum-copper (Al-Cu) binary alloy in terms of the eigen-frequencies of the localized collective excitations. The model pseudopotential formalism is employed using a self-consistent phonon scheme by involving multiple scattering and phonon eigen-frequencies. These frequencies are expressed in terms of many-body correlation functions of atoms as well as of interatomic potential. The important ingredients in the present study are the pair-potential and pair-correlation functions. The most recent and sparingly used local field correlation functions are employed to investigate the influence of the screening effects on the vibrational dynamics of non-crystalline Al83Cu17 binary alloy. The results for the elastic constants like bulk modulus BT, rigidity modulus G, Poisson's ratio ζ, Young's modulus Y, Debye temperature θD, propagation velocity of elastic waves and dispersion curves are reported based on the collective modes of this binary alloys. The present results are consistent and confirm the applicability of model potential and self-consistent phonon theory for such studies.

Study of collective dynamics of a non-crystalline aluminum–nickel binary alloy using pseudopotential theory

The phonon dynamics of a transition metal–aluminum alloy, i.e. the Al0.75Ni0.25 binary non-crystalline system, has been studied in terms of the eigenfrequencies of the localized collective excitations using model potential formalism. The self-consistent phonon scheme given by Takeno and Goda, involving multiple scattering and phonon eigenfrequencies that are expressed in terms of many-body correlation functions of atoms as well as of interatomic potential in the solids, has been used to generate the collective modes in the non-crystalline Al0.75Ni0.25 alloy. The pair potential is obtained in Wills Harrison (WH) form from the well-recognized model potential of Ashcroft as a test case. The local field correlation functions due to Hartree (H), Taylor (T), Ichimaru–Utsumi (IU), Sarkar et al (S) and Farid (F) are used to investigate the influence of the screening effects on the vibrational properties. Results for the bulk modulus BT are obtained using the aforesaid local field correction functions. The results for the Shear modulus (C′), deviation from Cauchy's relation, Poisson's ratio (σ), Young modulus (Y), propagation velocity of elastic waves and phonon dispersion curves using model potential are reported here and good agreement with available experimental results was achieved.

Static and vibrational properties of equiatomic Na-based binary alloys

The computations of the static and vibrational properties of four equiatomic Na-based binary alloys viz. Na 0.5Li 0.5, Na 0.5K 0.5, Na 0.5Rb 0.5 and Na 0.5Cs 0.5, to second order in local model potential is discussed in terms of real-space sum of Born von Karman central force constants. The local field correlation functions due to Hartree (H), Ichimaru–Utsumi (IU) and Sarkar et al. (S) are used to investigate the influence of the screening effects on the aforesaid properties. Results for the lattice constants C 11, C 12, C 44, C 12– C 44, C 12/ C 44 and bulk modulus B obtained using the H-local field correction function have higher values in comparison with the results obtained for the same properties using IU- and S-local field correction functions. The results for the Shear modulus ( C′), deviation from Cauchy's relation, Poisson's ratio σ, Young modulus Y, propagation velocity of elastic waves, phonon dispersion curves and degree of anisotropy A are highly appreciable for the four equiatomic Na-based binary alloys.

Time and Temperature Dependent Correlation Functions of the One-Dimensional Impenetrable Electron Gas

We consider the one-dimensional delta-interacting electron gas in the case of infinite repulsion. We use determinant representations to study the long time, large distance asymptotics of correlation functions of local fields in the gas phase. We derive differential equations which drive the correlation functions. Using a related Riemann–Hilbert problem we obtain formulae for the asymptotics of the correlation functions, which are valid at all finite temperatures. At low temperatures these formulae lead to explicit asymptotic expressions for the correlation functions, which describe power law behavior and exponential decay as functions of temperature, magnetic field and chemical potential.