On the exact formulation of multi-configuration density-functional theory: electron density versus orbitals occupation

The exact formulation of multi-configuration density-functional theory is discussed in this work. As an alternative to range-separated methods, where electron correlation effects are split in the coordinate space, the combination of configuration interaction methods with orbital occupation functionals is explored at the formal level through the separation of correlation effects in the orbital space. When applied to model Hamiltonians, this approach leads to an exact site-occupation embedding theory (SOET). An adiabatic connection expression is derived for the complementary bath functional and a comparison with density matrix embedding theory is made. Illustrative results are given for the simple two-site Hubbard model. SOET is then applied to a quantum chemical Hamiltonian, thus leading to an exact complete active space site-occupation functional theory (CASSOFT) where active electrons are correlated explicitly within the CAS and the remaining contributions to the correlation energy are described with an orbital occupation functional. The computational implementation of SOET and CASSOFT as well as the development of approximate functionals are left for future work.     

Fluctuations of dielectric constant in a system of hard spheres

The correlation function for fluctuations of a dielectric constant in a latex-like suspension of spherical particles was calculated. An exact analytical expression was derived for the correlation function using the Percus-Yewick approximation for a system of hard spheres. The obtained results made it possible to calculate the indicatrix of single scattering, the extinction coefficient, and the transport mean path. It is shown that, starting with a volume content of about ten percent, the “gas” approximation becomes invalid, and optical parameters begin to depend on concentration in quite a complicated manner. In particular, the extinction length and the mean transport path, which are the basic parameters in describing the coherent effects in multiple scattering, vary nonmonotonically with concentration. It is found that there exists a range of sizes and concentrations of scattering particles in which an effect similar to the emergence of blue phase in liquid crystals can be observed.     

Analytical approach to the current correlation function in dissipative two-state systems

Using the spin-boson model with coupling to Ohmic bath, an analytical approach is developed to study the dynamics of the current correlation function in dissipative two-state systems with the view of understanding the effects of environment and tunneling on the coherent oscillation and the long-time decay of the current correlation function in these systems. An analytic expression of current correlation function is obtained and the results agree very well with that of numerical simulations.     

Analytical approach to the current correlation function in dissipative two-state systems

Using the spin-boson model with coupling to Ohmic bath, an analytical approach is developed to study the dynamics of the current correlation function in dissipative two-state systems with the view of understanding the effects of environment and tunneling on the coherent oscillation and the long-time decay of the current correlation function in these systems. An analytic expression of current correlation function is obtained and the results agree very well with that of numerical simulations.      

A sum rule for the transverse current correlation function in an electron liquid

An exact expression for the first frequency moment sum rule of the transverse current correlation function in an electron liquid is obtained and discussed.     

Temperature and bath size in exact diagonalization dynamical mean field theory

Dynamical mean field theory (DMFT), combined with finite-temperature exact diagonalization, is one of the methods used to describe electronic properties of strongly correlated materials. Because of the rapid growth of the Hilbert space, the size of the finite bath used to represent the infinite lattice is severely limited. In view of the increasing interest in the effect of multi-orbital and multi-site Coulomb correlations in transition metal oxides, high-T(c) cuprates, iron-based pnictides, organic crystals, etc, it is appropriate to explore the range of temperatures and bath sizes in which exact diagonalization provides accurate results for various system properties. On the one hand, the bath must be large enough to achieve a sufficiently dense level spacing, so that useful spectral information can be derived, especially close to the Fermi level. On the other hand, for an adequate projection of the lattice Green's function onto a finite bath, the choice of the temperature is crucial. The role of these two key ingredients in exact diagonalization DMFT is discussed for a wide variety of systems in order to establish the domain of applicability of this approach. Three criteria are used to illustrate the accuracy of the results: (i) the convergence of the self-energy with the bath size, (ii) the quality of the discretization of the bath Green's function, and (iii) comparisons with complementary results obtained via continuous-time quantum Monte Carlo DMFT. The materials comprise a variety of three-orbital and five-orbital systems, as well as single-band Hubbard models for two-dimensional triangular, square and honeycomb lattices, where non-local Coulomb correlations are important. The main conclusion from these examples is that a larger number of correlated orbitals or sites requires a smaller number of bath levels. Down to temperatures of 5-10?meV (for typical bandwidths W?≈?2?eV) two bath levels per correlated impurity orbital or site are usually adequate.     

Scattering response of a phonon damped harmonic oscillator

We calculate the response for scattering off a particle bound by an isotropic harmonic force and damped through hybridization with a phonon bath. An exact expression for the scattering response is studied numerically to provide a detailed picture of its dependence on wave vector, frequency, temperature and phonon hybridization strength.     

Exact multiple scattering of waves from random rough surfaces: Speckle contrast

An exact formula for the mean multiple scattered intensity is presented by using normal statistics, as well as a gaussian correlation function, for the random rough surface in the limit of large correlation distance, T → ∞. Comparisons with the Kirchoff-Beckman approximation are also done. Further, we obtain an exact expression for the speckle contrast which explains experimental data and draws conclusions on the physical properties of the surface.     

The Dynamical Evolution of Quantum Correlations in the Two Isolate Spin Particles Coupled to a Common Bath

We study the dynamical evolution of quantum correlations between two central spins independently coupled to a common bath, which are represented by quantum entanglement and quantum discord. According to the results of the exact solution, we show that quantum discord is more robust and includes richer correlation than quantum entanglement due to the nonvanishing quantum correlation in the region of entanglement death, i.e., the separable states maybe contain nonclassical correlations. We discuss the effects of the intrinsic properties of the bath on quantum correlation between the two central spins in the XY and XXZ model baths. At the low temperature, the central system can keep the good quantum correlation. With the more spin number in the bath, the dynamical evolution of quantum correlation can be bounded with the small oscillation and finally approaches a stable value. In addition, we find that the interaction between the central spins and the bath in the z direction has the significant effects on quantum correlation of the central spin system.     

Effects of nearest and next-nearest neighbour interaction parameters on atomic correlation functions of stepped surfaces

We extend the range of the interaction between the surface scatterers to the next-nearest neighbours and thus treat the stepped surface as a second-order Markov chain. We employ two interaction parameters to describe the behaviour of the atomic pair correlation function for a two-level system and derive an exact expression for this function. This expression is then used to calculate the profile of the diffracted intensity. The effects of the interaction parameters on the intensity profiles as well as on the terrace width distributions are investigated in detail and compared to the molecular beam epitaxy measurement of Si on a Si(111) surface. The physical meaning of the interaction parameters is also interpreted in terms of the Ising model.     

Exact time correlation function for a nonlinearly coupled vibrational system

The time correlation function (t)=Re<[c(t), c (0)]>, which is related to the dipole spectrum and is the main focus of quantum molecular time scale generalized Langevin equation theory, is calculated for the Hamiltonian system in which a single oscillator is coupled by a nonlinear Davydov term to a chain of oscillators comprising a phonon heat bath. An exact expression for (t) is obtained. At long times we find that the time correlation function decays as a small power law atT=0K, but switches to exponential decay at higher temperature. This is a new result and bears on the long-standing issue of the existence of long-time tails.     

On the electronic contribution to the surface energy of metals

An expression for the exchange and correlation contributions to the surface energy of metals is derived using the dielectric formulation of the electron gas. The result which is obtained in the infinite barrier model for the surface is exact within the RPA and include the off-diagonal character of the response function.     

Quantum work fluctuation theorem: Nonergodic Brownian motion case

The work fluctuations of a quantum Brownian particle driven by an external force in a general nonergodic heat bath are studied under a general initial state. The exact analytical expression of the work probability distribution function is derived. Results show the existence of a quantum asymptotic fluctuation theorem, which is in general not a direct generalization of its classical counterpart. The form of this theorem is dependent on the structure of the heat bath and the specified initial condition.     

On one-eighth law in unforced two-dimensional turbulence

We critically revisit the various attempts to prove one-eighth law in two-dimensional (2D) turbulence and reconcile them. Herein, the one-eighth law has been proved for unforced 2D incompressible high Reynolds number turbulence. An exact expression of the time derivative of two-point second order velocity correlation function is also derived for the enstrophy cascade dominated regime.     

An approximate exchange-correlation hole density as a functional of the natural orbitals

The Fermi and Coulomb holes that can be used to describe the physics of electron correlation are calculated and analysed for a number of typical cases, ranging from prototype dynamical correlation to purely nondynamical correlation. Their behaviour as a function of the position of the reference electron and of the nuclear positions is exhibited. The notion that the hole can be written as the square of a hole amplitude, which is exactly true for the exchange hole, is generalized to the total holes, including the correlation part. An Ansatz is made for an approximate yet accurate expression for the hole amplitude in terms of the natural orbitals. employing the local (at the reference position) values of the natural orbitals and the density. This expression for the hole amplitude leads to an approximate two-electron density matrix that: (a) obeys correct permutation symmetry in the electron coordinates; (b) integrates to the exact one-matrix; and (c) yields exact correlation energies in the limiting cases of predominant dynamical correlation (high Z two-electron ions) and pure nondynamical correlation (dissociated H₂).     

Translationally Invariant Single Particle Picture of the Three-Nucleon System

An ansatz of a single particle picture, known for example from the shell model, has been used to construct a model wave function which is as close as possible to an exact three-body wave function. The exact wave function is obtained by solving the Faddeev equation with the Malfliet–Tjon potential. In order to judge the quality of the model wave function, we compare correlation functions of the model wave function and the exact solution. The correlation functions differ significantly at small distances but are close to each other for larger values of their arguments.     

Magnetic ordering in a random system of point Ising dipoles

An exact expression for the random magnetic field distribution function is obtained for a simple model of a random system of Ising magnetic dipoles. The magnetic phase diagram for such a system is deter-mined within the framework of the random mean field theory. The magnetic characteristics of individual phases of this system are described.     

A resonance effect of the atomic populations kinetics induced by a fluctuating plasma

The effect of fluctuations of the electron temperature on the population kinetics of a reduced atomic system is investigated in the case of a low density plasma, where the coronal approximation can be used. An exponential correlation function is assumed for the electron temperature fluctuations. A resonance of the average population as a function of the correlation time is observed and analyzed.     

Influence of Initial Correlations on Evolution of a Subsystem in a Heat Bath and Polaron Mobility

A regular approach to accounting for initial correlations, which allows to go beyond the unrealistic random phase (initial product state) approximation in deriving the evolution equations, is suggested. An exact homogeneous (time-convolution and time-convolutionless) equations for a relevant part of the two-time equilibrium correlation function for the dynamic variables of a subsystem interacting with a boson field (heat bath) are obtained. No conventional approximation like RPA or Bogoliubov’s principle of weakening of initial correlations is used. The obtained equations take into account the initial correlations in the kernel governing their evolution. The solution to these equations is found in the second order of the kernel expansion in the electron–phonon interaction, which demonstrates that generally the initial correlations influence the correlation function’s evolution in time. It is explicitly shown that this influence vanishes on a large timescale (actually at \(t\rightarrow \infty \)) and the evolution process enters an irreversible kinetic regime. The developed approach is applied to the Fröhlich polaron and the low-temperature polaron mobility (which was under a long-time debate) is found with a correction due to initial correlations.