Lattice theory of ultrafast excitonic and charge-transfer dynamics in DNA

We propose a lattice fermion model suitable for studying the ultrafast photoexcitation dynamics of ordered chains of deoxyribonucleic acid (DNA) polymers. The model includes both parallel (intrachain) and perpendicular (cross-chain) terms as well as diagonal cross-chain terms coupling neighboring bases. The general form of our Hamiltonian is borrowed from lattice fermion models of quantum chromodynamics. The band structure for this model can be determined analytically, and we use this as a basis for computing the singly excited states of the poly(dA)poly(dT) DNA duplex using configuration interaction singles. Parameters for the model are taken from various literature sources and our own ab initio calculations. Results indicate that the excited states consist of a low energy band of dark charge-separated states followed by separate bands of delocalized excitonic states which have weak mixing between the thymidine and adenosine sides of the DNA chain. We then propose a lattice exciton model based upon the transition dipole-dipole couplings between bases and compare the analytical results for the survival probability of an initially localized exciton to exact numerical results. The results herein underscore the competing role of excitonic and charge-transfer dynamics in these systems.     

重费米子化合物LiV2 O4电子结构的第一性原理研究

用第一性原理的FP-LMTO能带计算方法研究了重费米子化合物LiV2O4的电子结构.结果表明:费米面附近的导带是由V原子的3d电子形成的宽度为2.5eV的窄能带,是3d态在立方晶体场中具有t2g对称性的子带;它与O的2p轨道构成的能带有近1.9eV的能隙.计算得出的费米能处电子态密度和线性电子比热系数分别是11.1 states/eV f.u.和26.7 mJ/molK2.费米面处的能带色散具有电子型和空穴型两种,呈现出一种复杂的费米面结构.LSDA以及LDA+GGA计算表明, LiV2O4有一个磁矩为每个钒原子1.13μB,总能比LDA基态低约148 meV/f.u.的铁磁性基态.由目前的能带结构计算的结果无法确定这一类Kondo体系的局域磁矩的来源,表明这一化合物中的重费米子行为可能有别于在含有4f和5f稀土的重费米子合金中观察到的局域磁矩与传导电子的交换作用机制,其中存在量子相变的可能.     

Phenomenological trends for heavy fermi liquids and narrow-band metals II: Practical estimates of electronic heat capacity and magnetic susceptibility

Quantitative techniques for evaluating magnetic and calorimetric parameters of narrow-band and heavy fermion metals are discussed. The behavior of the electronic heat capacity at temperatures near a transition to magnetic order is emphasized. The discussion illustrates the methods used in establishing a previously published correlation between the electronic heat capacity and magnetic susceptibility of heavy Fermi liquids and their low temperature ground states.     

Heavy fermion behavior in Cu3Au-structure compounds: CePb3 and U(In,Sn)3

The recent discovery of anomalous properties associated with extremely narrow f-band character in the electronic density of states in the vicinity of the Fermi energy has stimulated considerable interest in these systems. Some particularly exciting recent discoveries have emerged from studies of the magnetic and electronic properties of cerium- and uranium-based Cu₃Au intermetallic compounds which form with group IIIB and group IVB elements. It has been reported that CePb₃ is a heavy fermion antiferromagnetic system with a Néel temperature of 1.1K. In addition, this system displays field-induced superconductivity for magnetic fields greater than 15 T and temperatures below 0.5K. Studies of (Ce,La)Pb₃ clearly indicate that the heavy fermion behavior reported for this system is primarily a reflection of single-ion Kondo behavior. In addition, studies of U(In,Sn)₃ and Ce(In,Sn)₃ explicitly indicate that the heavy fermion and mixed-valent behavior reported for these systems are a result of a similar hybridization-driven mechanism. The CeX₃ and UX₃ systems where X is a group IIIB or group IVB element display many of the features of current interest to magnetic moment formation and allow a unique opportunity to study these phenomena systematically.     

A theoretical estimate for quasihomopolar singlet levels in long polyenes with a spin model hamiltonian

A spin model hamiltonian is employed to estimate the energy levels of quasihomopolar singlet states in long polyenes. To this end, the singlet excitation energies of the alternating spin chain are calculated as functions of γ and N using the Hartree-Fock method developed based on the spinless fermion formalism. The result indicates that the excitation energies decrease monotonically with increasing chain length in accord with the known experimental results. Using the parameters J and γ empirically determined from the data on short polyenes, an estimation is given for the energy levels of the lowest-lying 2¹A_g states as well as those of the second ¹B_u quasihomopolar states in long polyenes. In particular, the 2¹A_g level in polyacetylene is predicted to be at 1.1 eV in good agreement with a recent photoluminescence result (1.19 eV).     

Multiscale theory of collective and quasiparticle modes in quantum nanosystems

A quantum nanosystem (such as a quantum dot, nanowire, superconducting nanoparticle, or superfluid nanodroplet) involves widely separated characteristic lengths. These lengths range from the average nearest-neighbor distance between the constituent fermions or bosons, or the lattice spacing for a conducting metal, to the overall size of the quantum nanosystem (QN). This suggests the wave function has related distinct dependencies on the positions of the constituent fermions and bosons. We show how the separation of scales can be used to generate a multiscale perturbation scheme for solving the wave equation. Results for electrons or other fermions show that, to lowest order, the wave function factorizes into an antisymmetric (fermion) part and a symmetric (bosonlike) part. The former manifests the short-range/exclusion-principle behavior, while the latter corresponds to collective behaviors, such as plasmons, which have a boson character. When the constituents are bosons, multiscale analysis shows that, to lowest order, the wave function can also factorize into short- and long-scale parts. However, to ensure that the product wave function has overall symmetric particle label exchange behavior, there could, in principle, be states of the boson nanosystem where both the short- and long-scale factors are either boson- or fermionlike; the latter "dual fermion" states are, due to their exclusion-principle-like character, of high energy (i.e., single particle states cannot be multiply occupied). The multiscale perturbation analysis is used to argue for the existence of a coarse-grained wave equation for bosonlike collective behaviors. Quasiparticles, with effective mass and interactions, emerge naturally as consequences of the long-scale dynamics of the constituent particles. The multiscale framework holds promise for facilitating QN computer simulations and novel approximation schemes.     

Crossover from bosonic to fermionic features in composite boson systems

We study the quantum dynamics of conversion of composite bosons into fermionic fragment species with increasing densities of bound fermion pairs using the open quantum system approach. The Hilbert space of N-state-functions is decomposed into a composite boson subspace and an orthogonal fragment subspace of quasi-free fermions that enlarges as the composite boson constituents deviate from ideal boson commutation relations. The tunneling dynamics of coupled composite bosons states in confined systems is examined, and the appearance of exceptional points under experimentally testable conditions (densities, lattice temperatures) is highlighted. The theory is extended to examine the energy transfer between macroscopically coherent systems such as multichromophoric macromolecules in photosynthetic light harvesting complexes.     

Algebraic structure of fermion density matrices. II

The properties of the algebraic structure of fermion density matrices are studied. The algebraic structure of a density matrix leads to a more varied and detailed classification scheme than that offered by the usual shell structure approach. Investigation of the algebraic structure of fermion density matrices by the methods of algebraic topology leads to a classification scheme based on Betti numbers.     

Calculating electron binding energies for quadratic fermion Hamiltonian by virtue of the IEO method

In this work, we discuss how to use the invariant eigen‐operator (IEO) method to derive the electron binding energies for the quadratic fermion Hamiltonian. We find that the task of solving the energy gap of fermion Hamiltonian can be ascribed to simply solving a standard eigenvalue problem of a numerical matrix, which is determined by the parameters of the given Hamiltonian. The IEO method provides us with a new approach for solving quadratic Hamiltonians in a more convenient and concise way. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Spin-free quantum theory. XXV. The unitary-group formulation of fermion many-body theory

The fermion unitary group formulation (UGF ) of many-body theory is based on the unitary group U(2n) where n is the number of freeon orbitals. This formulation, which conserves particle-number but not spin, is isomorphic to the particle-number-conserving, second-quantized formulation (SQF ). In UGF we derive the familiar diagrammatic algorithm for matrix elements, M(Y) = (?1)^H+L where H and L denote the numbers of hole lines and loops in the diagram D(Y) of M(Y). The unitary group derivation is considerably simpler than is the conventional, second-quantized derivation that employs time-dependence, Wick's theorem, normal-order, and contractions. In neither fermion UGF nor SQF is spin conserved. We carry out in UGF the spin-projection (symmetry adaptation to SU (2)) of the fermion vectors and obtain with a spin-free Hamiltonian the same matrix elements as with the freeon UGF (part 24 of this series). The fermion unitary group formulation for a spin-free Hamiltonian should be regarded as an alternate path to spin-free quantum chemistry.     

Wave-mechanical theory of field ionization and field-ion energy distributions

Although field-ion energy distributions have been measured for many years, no theoretical treatment has ever been published that is strictly compatible with the axioms of quantum mechanics. This article shows how a fully wave-mechanical theory of field ionization and field-ion energy distributions can be constructed, based on the idea that surface field ionization is the fermion analogy for Dirac's treatment of photon emission. The theory is formal and suggests, as expected, that existing quasiclassical treatments are essentially satisfactory in normal circumstances.The discussion comprises of three main steps. The first is to clarify the various definitions of energy and potential used in field-ion theory, and to codify the corresponding energy diagrams. The second is to derive and expression for the rate-constant for transfer from one vibrational state to another. The third is to sum over initial states to derive a formal expression for the ion energy distribution. The article concludes by discussing the possible development of this theory.     

Optical properties of the heavy fermion superconductor UBe13

We report on the optical properties of the heavy fermion superconductor UBe₁₃ from 0.050 to 2eV. The reflectance shows sharp structure at low frequencies superimposed on a smooth decrease down to 50% at 1.6eV. The ThBe₁₃ compound is shown for comparison as a non-heavy fermion system. Kramers-Kronig analysis of reflectance measurements yields sharp interband structure in UBe₁₃ in the 0.1 eV region. In the far IR, above 100 K, the material shows normal Drude behavior: the optical conductivity agrees well with the d.c. conductivity.     

Shell model calculations: An efficient new algorithm

We describe an efficient new algorithm which extends the range of feasible shell model calculations. This algorithm is applicable to single shell and multiple shell configurations, where two or more quantum numbers (e.g., L and S) are required to label the states within each shell. The algorithm proceeds by factoring the shell model Hilbert space into a product of subspaces, one for each angular momentum. N-particle wave functions are built up recursively from N – 1 particle wave functions. Three kinds of N – 1- to N-particle coefficients are required to carry out the construction of N-particle electron (or fermion) states from N – 1 particle states. These are (1) coefficients of fractional parentage (CFP s) within a single shell, (2) outerproduct isoscalar factors (OISF s) within a single angular momentum subspace, and (3) innerproduct isoscalar factors (IISF s) which describe how multishell states within the complementary angular momentum subspaces are combined to form totally antisymmetric wave functions. All three types of N – 1- to N-particle coefficients are generated recursively using a single powerful and efficient matrix diagonalization algorithm. Matrix elements of single particle creation and annihilation operators are expressed in terms of single particle CFP s, OISF s, and IISF s. We also describe an efficient algorithm for computing matrix elements of products of creation and anihilation operators by inserting and summing over complete sets of intermediate states. This is the Feynman-like sum over path overlaps procedure. Timing benchmarks are presented comparing the new Drexel University shell model (DUSM ) code with a state of the art shell model code.     

Expansion and completeness theorems for operator manifolds

Some expansion and completeness theorems for operator manifolds, which are currently being employed in propagator theory, are derived. It is shown that excitation or ionization operators satisfying the conditions Q|0〉 = |Λ〉 and Q_Λ|0〉 = 0 for general excited states |Λ〉 and reference state |0〉 may be expanded uniquely in particular sets of basis operators. These results are then used to discuss rigorous expressions for fermion propagators.     

Theoretical studies on cerium nickel aluminides: polar intermetallics with heavy fermion behavior

The electronic structures of Ce₄Ni₆Al₂₃, CeNiAl₄, CeNi₂Al₅, CeNiAl and CeNi₄Al have been calculated using the TB-LMTO-ASA (tight-binding, linear muffin-tin orbital, atomic-spheres approximation) approach to probe relationships between chemical bonding and physical properties in this series of intermetallic compounds. Analysis from crystal orbital Hamilton populations (COHP) reveal that the Al-rich compounds may be considered as “polar intermetallic” because the Fermi level coincides to the separation of bonding and antibonding states of the Ni-Al framework. On the other hand, although the densities of states (DOS) of CeNiAl suggest “polar intermetallic” behavior, the bonding is more complex. Finally, the Ni-rich example, CeNi₄Al, has significant Ni-3d character at the Fermi level. The results of these calculations are also discussed in connection with heavy fermion or possible valence fluctuation behavior observed for some of these intermetallic compounds: those showing exceptional properties also exhibit significant “lattice covalency” between Ce and the Ni-Al nets.     

Algebraic structure of fermion density matrices. I

In this paper we define the algebraic structure of a reduced fermion density matrix. We relate the algebraic structure to certain symmetry properties of the reduced density matrix.     

General Hartree-Fock solutions for a one dimensional δ-function gas

The one dimensional fermion gas with δ-function interactions is studied within the General Hartree-Fock (GHF) framework. Solutions of the eight Fukutome types are constructed by pairing and the corresponding gap equations are solved. The character of the solutions is studied as a function of the particle density.     

Heavy fermions and heavy atoms

The heavy fermion state is a recently discovered ground state for the electrons in some cerium and light actinide compounds at low temperatures. Their properties are briefly reviewed and the calculational problems they present are discussed.     

Information theory interpretation of the Pauli principle and Hund rule

Making use of different information measures, the Pauli exclusion principle and the first Hund rule were found to be related to a trend toward acquiring a maximum information content of the atoms and molecules, and more generally, for any fermion system. The bosons conversely always have a minimum (zero) information content with respect to the permutation symmetry of their wave functions. Some new interpretations of the Pauli principle are presented.     

Spin-free quantum chemistry. XXIV. Freeon many-body theory

We present the freeon, singlet, unitary group formulation of many-body theory as an alternative to the particle-number-conserving, spin-projected, fermion, second-quantized formulation. It is based on the generator-state-approach (GSA ) developed in part 23 of this series. We develop C1, perturbation, coupled-cluster, and random-phase theories.