Self-consistent Field Approximation Research Articles

Genesis of electroweak and dark matter scales from a bilinear scalar condensate

The condensation of scalar bilinear in a classically scale invariant strongly interacting hidden sector is used to generate the electroweak scale, where the excitation of the condensate is identified as dark matter. We formulate an effective theory for the condensation of the scalar bilinear and find in the self-consistent mean field approximation that the dark matter mass is of $O(1)$ TeV with the spin-independent elastic cross section off the nucleon slightly below the LUX upper bound.

Postquench dynamics and prethermalization in a resonant Bose gas

We explore the dynamics of a resonant Bose gas following its quench to a strongly interacting regime near a Feshbach resonance. For such deep quenches, we utilize a self-consistent dynamic field approximation and find that after an initial regime of many-body Rabi-like oscillations between the condensate and finite-momentum quasiparticle pairs, at long times, the gas reaches a pre-thermalized nonequilibrium steady state. We explore the resulting state through its broad stationary momentum distribution function, that exhibits a power-law high momentum tail. We study the dynamics and steady-state form of the associated enhanced depletion, quench-rate dependent excitation energy, Tan's contact, structure function and radio frequency spectroscopy. We find these predictions to be in a qualitative agreement with recent experiments.

Optical bistability in a nonlinear-shell-coated metallic nanoparticle.

We provide a self-consistent mean field approximation in the framework of Mie scattering theory to study the optical bistability of a metallic nanoparticle coated with a nonlinear shell. We demonstrate that the nanoparticle coated with a weakly nonlinear shell exhibits optical bistability in a broad range of incident optical intensity. This optical bistability critically relies on the geometry of the shell-coated nanoparticle, especially the fractional volume of the metallic core. The incident wavelength can also affect the optical bistability. Through an optimization-like process, we find a design with broader bistable region and lower threshold field by adjusting the size of the nonlinear shell, the fractional volume of the metallic core, and the incident wavelength. These results may find potential applications in optical bistable devices such as all-optical switches, optical transistors and optical memories.

Dust trap formation in a non-self-sustained discharge with external gas ionization

Results from numerical studies of a non-self-sustained gas discharge containing micrometer dust grains are presented. The non-self-sustained discharge (NSSD) was controlled by a stationary fast electron beam. The numerical model of an NSSD is based on the diffusion drift approximation for electrons and ions and self-consistently takes into account the influence of the dust component on the electron and ion densities. The dust component is described by the balance equation for the number of dust grains and the equation of motion for dust grains with allowance for the Stokes force, gravity force, and electric force in the cathode sheath. The interaction between dust grains is described in the self-consistent field approximation. The height of dust grain levitation over the cathode is determined and compared with experimental results. It is established that, at a given gas ionization rate and given applied voltage, there is a critical dust grain size above which the levitation condition in the cathode sheath cannot be satisfied. Simulations performed for the dust component consisting of dust grains of two different sizes shows that such grains levitate at different heights, i.e., size separation of dust drains levitating in the cathode sheath of an NSSD takes place.

Thermostating extended Lagrangian Born-Oppenheimer molecular dynamics.

Extended Lagrangian Born-Oppenheimer molecular dynamics is developed and analyzed for applications in canonical (NVT) simulations. Three different approaches are considered: the Nosé and Andersen thermostats and Langevin dynamics. We have tested the temperature distribution under different conditions of self-consistent field (SCF) convergence and time step and compared the results to analytical predictions. We find that the simulations based on the extended Lagrangian Born-Oppenheimer framework provide accurate canonical distributions even under approximate SCF convergence, often requiring only a single diagonalization per time step, whereas regular Born-Oppenheimer formulations exhibit unphysical fluctuations unless a sufficiently high degree of convergence is reached at each time step. The thermostated extended Lagrangian framework thus offers an accurate approach to sample processes in the canonical ensemble at a fraction of the computational cost of regular Born-Oppenheimer molecular dynamics simulations.

Self-Consistent Equations in the Ising Model of a Dilute Magnet

We have found the percolation thresholds for the Ising model of a dilute magnet and have constructed the dependences of the magnetization on the impurity concentration at zero temperature in different variants of the self-consistent field approximation.

Statistical model for nanoparticles formation: Self-consistent field approximation

In this paper, we propose a statistical model for the formation of metal nanoparticles in a homogeneous infinite medium. The Ising-like Hamiltonian of a system is analysed using the self-consistent field approximation for the lattice-gas model. Exclusively direct atom–atom interactions are considered. A special role of surface atoms and their interaction with the external medium are discussed in detail. The grand thermodynamic potential of a system is calculated and other thermodynamic functions are obtained. A consistent set of equations is found for describing both the radii of nanoparticles and their density (occupation number). The essential role of the medium nonhomogeneity in the process of nanoparticles arising is proved. The temperature dependence for the radii of the formed gold nanoparticles is estimated and the variance of their sizes is calculated.

Weakly Relativistic Quantum Effects in a Two-Dimensional Electron Gas: Dispersion of Langmuir Waves

537.611.43.: 530.145 A weakly-relativistic quantum-hydrodynamic model for charged spinless particles applied to low-dimensional systems is described in detail. The equations are constructed in the self-consistent field approximation. The Darwin term, the current-current interaction, and the weakly relativistic correction to the kinetic energy, all described by the Breit Hamiltonian, are considered together with the Coulomb interaction. The contributions of the described effects and also of relativistic-temperature effects to the dispersion of the Langmuir waves in a two-dimensional electron gas are calculated. A comparison with the corresponding formula for a threedimensional system of particles is presented.

Kinetic equation in the self-consistent field approximation for the number density of filaments forming in the propagation of femtosecond laser radiation

The general form of the kinetic equation for the filament number density with allowance for effects of their creation and decay is formulated—a nonlinear diffusion equation. The equation includes phenomenological parameters obtained by direct numerical simulation of the propagation of a high-power femtosecond laser pulse based on the stationary nonlinear Schrobinger equation for a number of limiting special cases.

Ising model of a dilute ferromagnet in the self-consistent field approximation

The method of averaging over the exchange interaction fields has been considered as applied to clusters of one and two magnetic atoms in the Ising model of a dilute ferromagnet, and a variant of fixed-scale group renormalization on the basis of this method has been constructed. It has been shown that the approximation obtained makes it possible to distinguish models with the site and bond dilutions.

Polaronic effects on the collective excitation in a GaAs parabolic quantum wire

In this paper, the plasmon-longitudinal optical (LO) phonon interaction effects on the intrasubband structure factor, on the pair correlation function and on the intrasubband plasmon energy associated with the lowest subband in a GaAs parabolic quantum well wire (QWW) are investigated by varying the subband separation energy and the electronic density. The calculations are performed using the self-consistent field approximation, which includes the local-field correction within the Singwi, Tosi, Land and Sjölander (STLS) theory, at zero temperature and assuming a three-subband model where only the first subband is occupied by electrons. The theoretical results obtained via STLS theory are compared with the random phase approximation (RPA) approach results, in order to emphasize the importance of the local field corrections (LFC) for the calculation of the collective excitations in quasi-one-dimensional systems.

Maxwell-Wagner-Sillars effects on the thermal-transport properties of polymer-dispersed liquid crystals.

We present the depolarization field effects (Maxwell-Wagner-Sillars effect) for the thermal transport properties of polymer dispersed liquid crystal composites under a frequency-dependent electric field. The experiments were conducted on polystyrene/4-Cyano-4'-pentylbiphenyl (PS/5CB) PDLCs of 73 vol.% and 85 vol.% liquid crystal (LC) concentrations. A self-consistent field approximation model is used to deduce the electrical properties of polymer and LC materials as well as the threshold electric field. Electric field-varying (at constant frequency) experiments were also conducted to calculate the interfacial thermal resistance between the LC droplets and polymer matrix as well as to find the elastic constant of LCs in droplet form.

Multi-reference vibration correlation methods

State-specific vibration correlation methods beyond the vibrational multi-configuration self-consistent field (VMCSCF) approximation have been developed, which allow for the accurate calculation of state energies for systems suffering from strong anharmonic resonances. Both variational multi-reference configuration interaction approaches and an implementation of approximate 2nd order vibrational multi-reference perturbation theory are presented. The variational approach can be significantly accelerated by a configuration selection scheme, which leads to negligible deviations in the final results. Relaxation effects due to the partitioning of the correlation space and the performance of a VMCSCF modal basis in contrast to a standard modal basis obtained from vibrational self-consistent field theory have been investigated in detail. Benchmark calculations based on high-level potentials are provided for the propargyl cation and cis-diazene.

Nonlinear susceptibilities of interacting polar molecules in the self-consistent field approximation.

The nonlinear stationary response of an assembly of long range interacting electric dipoles is calculated via Berne's nonlinear rotational diffusion equation [J. Chem. Phys. 62 1154 (1975)]. Analytical formulas are derived, showing that the behavior of ω and 3ω components of the nonlinear external field response spectra in such polar dielectrics strongly deviates from the Coffey-Paranjape formulas [Proc. R. Ir. Acad., Sect. A 78, 17 (1978)] as the long range dipole-dipole interactions increase, while the linear response remains qualitatively unaffected. By qualitatively comparing with recent experimental measurements on glycerol, it is further demonstrated that nonlinear dielectric response experiments provide a powerful tool for the characterization of short range intermolecular interactions in polar liquids.

Quantum Field Theory of Graphene with Dynamical Partial Symmetry Breaking

The quantum field theory approach has been proposed for the description of graphene electronic properties. It generalizes massless Dirac fermion model and is based on the Dirac-Hartree-Fock self-consistent field approximation and assumption on antiferromagnetic ordering of graphene lattice. The developed approach allows asymmetric charged carriers in single layer graphene with partially degenerated Dirac cones.

Metastable and spin-polarized states in electron systems with localized electron–electron interaction

We study the formation of spontaneous spin polarization in inhomogeneous electron systems with pair interaction localized in a small region that is not separated by a barrier from surrounding gas of non-interacting electrons. Such a system is interesting as a minimal model of a quantum point contact in which the electron–electron interaction is strong in a small constriction coupled to electron reservoirs without barriers. Based on the analysis of the grand potential within the self-consistent field approximation, we find that the formation of the polarized state strongly differs from the Bloch or Stoner transition in homogeneous interacting systems. The main difference is that a metastable state appears in the critical point in addition to the globally stable state, so that when the interaction parameter exceeds a critical value, two states coexist. One state has spin polarization and the other is unpolarized. Another feature is that the spin polarization increases continuously with the interaction parameter and has a square-root singularity in the critical point. We study the critical conditions and the grand potentials of the polarized and unpolarized states for one-dimensional and two-dimensional models in the case of extremely small size of the interaction region.

Assessment of charge-transfer excitations with time-dependent, range-separated density functional theory based on long-range MP2 and multiconfigurational self-consistent field wave functions

Charge transfer excitations can be described within Time-Dependent Density Functional Theory (TD-DFT), not only by means of the Coulomb Attenuated Method (CAM) but also with a combination of wave function theory and TD-DFT based on range separation. The latter approach enables a rigorous formulation of multi-determinantal TD-DFT schemes where excitation classes, which are absent in conventional TD-DFT spectra (like for example double excitations), can be addressed. This paper investigates the combination of both the long-range Multi-Configuration Self-Consistent Field (MCSCF) and Second Order Polarization Propagator Approximation (SOPPA) ansätze with a short-range DFT (srDFT) description. We find that the combinations of SOPPA or MCSCF with TD-DFT yield better results than could be expected from the pure wave function schemes. For the Time-Dependent MCSCF short-range DFT ansatz (TD-MC-srDFT) excitation energies calculated over a larger benchmark set of molecules with predominantly single reference character yield good agreement with their reference values, and are in general comparable to the CAM-B3LYP functional. The SOPPA-srDFT scheme is tested for a subset of molecules used for benchmarking TD-MC-srDFT and performs slightly better against the reference data for this small subset. Beyond the proof-of-principle calculations comprising the first part of this contribution, we additionally studied the low-lying singlet excited states (S1 and S2) of the retinal chromophore. The chromophore displays multireference character in the ground state and both excited states exhibit considerable double excitation character, which in turn cannot be described within standard TD-DFT, due to the adiabatic approximation. However, a TD-MC-srDFT approach can account for the multireference character, and excitation energies are obtained with accuracy comparable to CASPT2, although using a much smaller active space.

Single Molecule Quantum-Confined Stark Effect Measurements of Semiconductor Nanoparticles at Room Temperature

We measured the quantum-confined Stark effect (QCSE) of several types of fluorescent colloidal semiconductor quantum dots and nanorods at the single molecule level at room temperature. These measurements demonstrate the possible utility of these nanoparticles for local electric field (voltage) sensing on the nanoscale. Here we show that charge separation across one (or more) heterostructure interface(s) with type-II band alignment (and the associated induced dipole) is crucial for an enhanced QCSE. To further gain insight into the experimental results, we numerically solved the Schrödinger and Poisson equations under self-consistent field approximation, including dielectric inhomogeneities. Both calculations and experiments suggest that the degree of initial charge separation (and the associated exciton binding energy) determines the magnitude of the QCSE in these structures.

Can ORMAS be used for nonadiabatic coupling calculations? SiCH4 and butadiene contours

When appropriately used, the multiconfigurational self-consistent field (MCSCF) approximation is useful in discerning correct electronic structure results. However, with the increasing size of chemical systems of interest, MCSCF rapidly becomes unfeasible due to the requirement of larger active spaces, which lead to computationally unmanageable numbers of configurations. This situation is especially true for complete active space self-consistent field (CASSCF). In particular, reducing this computational expense by using restricted active spaces in solving for gradients and nonadiabatic couplings (NACs) during dynamics runs would save computer time. However, the validity of such restricted spaces is not well-known even for recovering the majority of the nondynamical correlation and inevitably varies between chemical systems across a range of nuclear geometries. As such, we use the recently implemented coupled perturbed–occupation restricted multiple active space (CP-ORMAS) equations (West et al., unpublished) to verify the accuracy of this approximation for gradients and NACs vectors around two specific conical intersection geometries for the silaethylene and butadiene systems. Overall, no excitations between appropriate subspaces show qualitatively reasonable results while single excitations significantly improve ORMAS results relative to the CASSCF level in these particular systems. However, single excitation schemes do not always lead to the correct orbital subspaces, and as a result, seemingly smooth potential energy surfaces (PES) do not always result in smooth analytical gradients and NACs. In addition, while some of the single excitation ORMAS and CASSCF schemes have improper orbitals rotate into the active space, the schemes without excitations (even with more subspaces) do not exhibit this behavior.

CORRELATED REDUCED TRANSFER MATRIX APPROACH FOR ISING MODEL

In this paper we present a simple approximate transfer matrix method for 2D and 3D hyper cubic nearest neighbor Ising models with various coordination number z to calculate the corresponding critical coupling strengths Kc. The critical coupling strengths of the Ising ferromagnets are obtained quite accurately by simple improvements over the self-consistent correlated field (SCCF) approximation. The important physical effect included in this work is some of the fluctuation effects of the systems by the help of a reduced transfer matrix method. When used in combination with the accuracy of the average magnetization obtained from the SCCF approximation, this reduced transfer matrix method leads to estimate of Kc more accurate than those obtained from the Bethe–Peierls–Weiss approximation and also SCCF approximation. Therefore, we believe that the approach we refer to as the correlated reduced transfer matrix method is potentially very useful scheme for obtaining approximate values of the critical coupling strengths of the Ising models with a mathematically easy meaner.