Effective potential for natural spin orbitals

For the first time the explicit form of the effective nonlocal potential for the natural spin orbitals is derived and analyzed. It is shown that in the case of the degenerate one-electron reduced density matrix the potential is not unique. The knowledge of the effective potential allows one to establish one-electron equations for the natural spin orbitals that may be of great value for efficient density matrix functional theory calculations.     

Local approximation of the correlation energy functional in the density matrix functional theory

A local approximation formula of the correlation energy functional E(c) in terms of the first-order reduced density matrix (1-RDM) is presented. With the contracted Schr?dinger equation the principal dependence of E(c) on the natural occupation numbers n(i) is identified. Using the effective mass theory, E(c) is expressed as a functional of the local density and the local variable, J = SUM (i)[square root of (n(i)(1-n(i))] /phi(i)/(2), where phi(i) are the natural spin orbitals. This local approximation satisfies the homogeneous coordinate scaling relation, gives the exact result for a one-electron system, and is almost free from the exchange energy error. It reproduced about 90% of the correlation energies of atoms and molecules.     

Generalization of the variational principle and the Hohenberg and Kohn theorems for excited states of Fermion systems

Through the entanglement of a collection of K non-interacting replicas of a system of N interacting Fermions, and making use of the properties of reduced density matrices the variational principle and the theorems of Hohenberg and Kohn are generalized to excited states. The generalization of the variational principle makes use of the natural orbitals of an N-particle density matrix describing the state of lowest energy of the entangled state. The extension of the theorems of Hohenberg and Kohn is based on the ground-state formulation of density functional theory but with a new interpretation of the concept of a ground state: It is the state of lowest energy of a system of KN Fermions that is described in terms of the excited states of the N-particle interacting system. This straightforward implementation of the line of reasoning of ground-state density functional theory to a new domain leads to a unique and logically valid extension of the theory to excited states that allows the systematic treatment of all states in the spectrum of the Hamiltonian of an interacting system.     

Functional equations for path integrals

We consider the density matrices that arise in the statistical mechanics of the electron-phonon systems. In the path integral representation the phonon coordinates can be eliminated. This leads to an action that depends on pairs of points on a path, that depends explicitly on time differences, and that contains the phonon occupation numbers. The integral is reduced to a standard form by scaling to the thermal length. We use the technique of integration by parts and add specially chosen generating functionals to the action. We set down functional derivative equations for the source-dependent density matrix and for the mass operator. This allows us to develop a series of approximations for the operator in terms of exact propagators. The crudest approximation is a coherent potential approximation applicable at a general temperature.     

氢分子间色散相互作用能的自然轨道泛函

理论上对分子间色散相互作用能的精确计算一直是个难点问题.密度矩阵泛函基于非定域量一阶密度矩阵为基本变量,它与色散相互作用起源于电子间的非定域关联特性相吻合.论文以最简单的氢分子为研究对象,通过分析两相互平行的氢分子间色散相互作用能,构造出了该体系中色散相互作用能的自然轨道泛函.结果表明:描述该体系中色散相互作用能的自然轨道泛函形式为包含有4个轨道的非交换和库伦积分.该结果对发展色散相互作用能的密度矩阵泛函理论具有重要的参考价值.     

The problem of the universal density functional and the density matrix functional theory

The analysis in this paper shows that the Hohenberg-Kohn theorem is the constellation of two statements: (i) the mathematically rigorous Hohenberg-Kohn lemma, which demonstrates that the same ground-state density cannot correspond to two different potentials of an external field, and (ii) the hypothesis of the existence of the universal density functional. Based on the obtained explicit expression for the nonrel-ativistic particle energy in a local external field, we prove that the energy of the system of more than two non-interacting electrons cannot be a functional of the inhomogeneous density. This result is generalized to the system of interacting electrons. It means that the Hohenberg-Kohn lemma cannot provide justification of the universal density functional for fermions. At the same time, statements of the density functional theory remain valid when considering any number of noninteracting ground-state bosons due to the Bose condensation effect. In the framework of the density matrix functional theory, the hypothesis of the existence of the universal density matrix functional corresponds to the cases of noninteracting particles and to interaction in the Hartree-Fock approximation.     

Density functional theory: Foundations reviewed

Guided by the above motto (quotation), we review a broad range of issues lying at the foundations of Density Functional Theory, DFT, a theory which is currently omnipresent in our everyday computational study of atoms and molecules, solids and nano-materials, and which lies at the heart of modern many-body computational technologies. The key goal is to demonstrate that there are definitely the ways to improve DFT. We start by considering DFT in the larger context provided by reduced density matrix theory (RDMT) and natural orbital functional theory (NOFT), and examine the implications that N$N$-representability conditions on the second-order reduced density matrix (2-RDM) have not only on RDMT and NOFT but, also, by extension, on the functionals of DFT. This examination is timely in view of the fact that necessary and sufficient N$N$-representability conditions on the 2-RDM have recently been attained.     

Replica Density Functional Study of One-Dimensional Hard Core Fluids in Porous Media

A binary quenched-annealed hard core mixture is considered in one dimension in order to model fluid adsorbates in narrow channels filled with a random matrix. Two different density functional approaches are employed to calculate adsorbate bulk properties and interface structure at matrix surfaces. The first approach uses Percus' functional for the annealed component and an explicit averaging over matrix configurations; this provides numerically exact results for the bulk partition coefficient and for inhomogeneous density profiles. The second approach is based on a quenched-annealed density functional whose results we find to approximate very well those of the former over the full range of possible densities. Furthermore we give a derivation of the underlying replica density functional theory.     

Density Matrix in Quantum Mechanics and Distinctness of Ensembles Having the Same Compressed Density Matrix

We clarify different definitions of the density matrix by proposing the use of different names, the full density matrix for a single-closed quantum system, the compressed density matrix for the averaged single molecule state from an ensemble of molecules, and the reduced density matrix for a part of an entangled quantum system, respectively. We show that ensembles with the same compressed density matrix can be physically distinguished by observing fluctuations of various observables. This is in contrast to a general belief that ensembles with the same compressed density matrix are identical. Explicit expression for the fluctuation of an observable in a specified ensemble is given. We have discussed the nature of nuclear magnetic resonance quantum computing. We show that the conclusion that there is no quantum entanglement in the current nuclear magnetic resonance quantum computing experiment is based on the unjustified belief that ensembles having the same compressed density matrix are identical physically. Related issues in quantum communication are also discussed.     

Testing one-body density functionals on a solvable model

There are several physically motivated density matrix functionals in the literature, built from the knowledge of the natural orbitals and the occupation numbers of the one-body reduced density matrix. With the help of the equivalent phase-space formalism, we thoroughly test some of the most popular of those functionals on a completely solvable model.     

The binatural orbitals of electronic transitions

The well-known natural orbitals are defined as eigenfunctions of a one-particle reduced density operator, and can be obtained from a computed density matrix by diagonalization. Similarly, in this article we define the binatural orbitals, which are obtained for a pair of wave functions by a singular value decomposition of a reduced transition density matrix. The pair of states would usually be eigenstates of the electronic Hamiltonian, and the binatural orbitals then serve as a useful tool for the analysis of the transition between these states. More generally, application to any two state functions gives important information as to how the two states differ. Some examples are shown.     

Exact density matrix of an oscillator-bath system: Alternative derivation

Starting from a total Lagrangian describing an oscillator-bath system, an alternative derivation of exact quantum propagator is presented. Having the quantum propagator, the exact density matrix, reduced density matrix of the main oscillator and thermal equilibrium fixed point are obtained. The modified quantum propagator is obtained in the generalised case where the main oscillator is under the influence of a classical external force. By introducing auxiliary classical external fields, the generalised quantum propagator or generating functional of position correlation functions is obtained.     

Quantum phase transitions and bipartite entanglement

We develop a general theory of the relation between quantum phase transitions (QPTs) characterized by nonanalyticities in the energy and bipartite entanglement. We derive a functional relation between the matrix elements of two-particle reduced density matrices and the eigenvalues of general two-body Hamiltonians of d-level systems. The ground state energy eigenvalue and its derivatives, whose nonanalyticity characterizes a QPT, are directly tied to bipartite entanglement measures. We show that first-order QPTs are signaled by density matrix elements themselves and second-order QPTs by the first derivative of density matrix elements. Our general conclusions are illustrated via several quantum spin models.     

Active-space N-representability constraints for variational two-particle reduced density matrix calculations

The ground-state energy of a system of fermions can be calculated by minimizing a linear functional of the two-particle reduced density matrix (2-RDM) if an accurate set of N-representability conditions is applied. In this Letter we introduce a class of linear N-representability conditions based on exact calculations on a reduced active space. Unlike wave-function-based approaches, the 2-RDM methodology allows us to combine information from calculations on different active spaces. By adding active-space constraints, we can iteratively improve our estimate for the ground-state energy. Applying our methodology to a 1D Hubbard model yields a significant improvement over traditional 2-positivity constraints with the same computational scaling.     

Remarks on the density functional approach to the inhomogeneous electron gas

The density functional approach is reformulated by using the most general form of the Hohenberg-Kohn theorem based on p-particle densities. Comparison with the reduced density matrix theory is made, exhibiting fully the p-particle hierarchy of both theories. Some advantages and drawbacks of the generalized density functional approach are discussed. The 1-particle spin-polarized case is presented to indicate the place of the usual DFA within the framework of the generalized theory.     

On the Decoherence of Macroscopic Bodies

We consider the field, either gravitational or electric, associated to a macroscopic source. Tracing over the field's degrees of freedom we show that the reduced density matrix diagonalizes on the position basis for macroscopic separations. The non diagonal reduced density matrix elements are quenched by a factor which is independent of the body being at rest or in motion. This may provide an explanation of the classical behavior of everyday objects not dissimilar to the one based on decoherence by environment. We discuss a few examples which indicate that the electric field even in the case of a totally neutral body is more effective, through a dipole contribution, than the gravitational field.     

Decoherence effects in case of molecular rotations in solids

A single XH₃ group interacting with an ensemble of lattice oscillators is considered using the Feynman-Vernon formalism. It is shown that the influence functional depends explicitly on the difference between winding numbers of the paths contributing to the path-integral expression for the reduced density matrix. However, the resulting interference is suppressed due to the presence of the Debye-Waller factor in the influence functional. The meaning of this result in connection with the topology of the XH₃ rotation angle is also discussed. Finally, the emergence of a gauge-like potential term describing one aspect of the XH₃-lattice interaction is indicated.     

Algorithm for solving the inverse vibronic problem on the basis of SVL fluorescence spectra

Computer methods whereby the inverse vibronic problem is solved on the basis of resonance fluorescence spectra with the use of modern quantum-mechanical methods for constructing structuraldynamic models of polyatomic molecules are discussed. An algorithm is proposed for solving the inverse vibronic problem according to resonance fluorescence spectra under laser excitation, and the corresponding calculation programs are constructed. The initial program data are acquired by means of an original software package which implements the scaling of quantum-mechanical force fields in two electronic states. The Duschinsky matrix and the initial matrix of shifts in normal coordinates caused by electron excitation are calculated in the Cartesian and natural vibrational coordinates. The program data are taken from quantum-molecular models based on calculations performed via ab initio modern quantum-mechanical methods and density functional theory. The algorithm is tested through the calculation of a model molecular system.     

A First Order Generalized Thomas-Fermi Approximation for the Electron Density in Inversion Layers

An operator evaluation of the one-particle density matrix of a degenerate system of independent particles in first order with respect to the gradient of the potential developed by Macke and Rennert yields an analytic expression for the particle density. This method is extended here to potentials with an infinite step and to finite temperatures – a situation which is characteristic for inversion electrons in MIS-systems. The resulting density can be expressed as the Airy transform of the zeroth order (local density approximation). The first order yields both the tunneling into the classically forbidden region and oscillations of the density near the step of the potential. The operator evaluation of the density matrix is shown to be equivalent to solving a Schrödinger like equation. The first order density yields results for the subband structure of (100)Si inversion and accumulation layers at OK in remarkable agreement to density functional calculations of Ando.