Lower Ground-state Energy Research Articles

Spontaneous parity breaking in (2+1)-dimensional QED with a family of four-Fermi interactions.

We study the spontaneous breaking of parity in (2+1)-dimensional QED with a family of four-Fermi interactions parametrized by two integers N and M, where 0≤M≤N. In the context of the 1/N expansion, a parity-violating fermion mass can be generated dynamically, and parity violation is characterized by θ=1-2M/N. Calculating the vacuum energy densities to the next-to-leading order in 1/N we show that the theory with minimal parity violation has the lowest ground-state energy. The physical origin of this behavior is discussed

Shallow States of Donor Impurities at Defective Semiconductor Surfaces11The project supported by National Natural Science Foundation of China under grant No. 9687006-01.

Ground state energies for shallow states of donor impurities at certain idealized defective isotropic semiconductor surfaces are calculated variationally for GaAs surfaces with electrons confined within the semiconductor. Calculations show that impurity states with donor ions located at parts projecting out of surfaces have lower ground state energies than those with ions located at parts sunk into surfaces.

Effects of surface defects on the shallow states of donor impurities at semiconductor surfaces.

The ground-state energy for shallow states of donor impurities at certain idealized defective isotropic semiconductor surfaces is calculated variationally for a GaAs surface with the electron confined within the semiconductor. The calculation shows that the impurity state with the donor ion located at a part projecting out of the surface has a lower ground-state energy than that with the ion located at a part sunk into the surface. The results also show that the energy shift in the ground-state energy caused by the surface defects depends critically on the shape of the defects and that for some defects the energy shift and level spacing between the excited impurity states on a planar GaAs surface are of the same order of magnitude.

Phonon squeezed state in high-T c superconductors

We study the phonon states in high T c superconducting materials within a weak-coupling polaron model. It is confirmed that the squeezed state of phonons gives lower ground state energy of the whole system than the two-phonon coherent state and the displaced state proposed previously. We also examine a condition that the squeezed state occurs. It follows that the squeezed state can exist when the interband electron transfer is allowed in many-band system.

A Fulton–Gouterman approach to exciton localization and excitonic solitons

A one dimensional model for Frenkel excitons interacting with acoustical phonons is considered. The generalized Fulton–Gouterman transcription lays open a peculiar topological property which is very suggestive for variational calculations. A very simple Ansatz is shown to yield already lower groundstate energies than previous dressed exciton or soliton theories, containing both latter as special limits.

The ground-state energy of a two-level tunnelling unit in a phonon field

The ground-state energy of a truncated two-level localised tunnelling system coupled to a phonon field is studied within the framework of small-polaron theory by a variational calculation. In former similar calculations, even when treating the intermediate-coupling region and with finite-polaron bandwidth, a very large coupling-strength parameter was tacitly assumed in the variational procedure, while the ratio of the rigid-lattice tunnelling matrix element to the small-polaron binding energy was kept finite. The present calculation is extended to finite coupling strengths. This introduces dispersion in the lattice deformation parameters, leads to lower ground-state energy and produces weakest renormalisation of the tunnelling matrix element.

A new correlated ground state of the fractional quantised Hall effect

A new trial wavefunction for the fractional quantised Hall effect is shown to produce a lower ground-state energy than Laughlin's trial function (1983).

Collective excitations in the fractional quantum Hall effect of a multicomponent fermion system.

We derive the dispersion of the elementary excitations in a two-component integer and fractional quantum Hall effect. We consider the fully polarized ground state and show the existence of both a magnetoroton mode and a low-lying Goldstone mode (GM). For the unpolarized ground state we derive the dispersion for both a density-density mode and a spin-wave mode both going to a finite value at small momentum q. We examine the extension of the charge-density-wave (CDW)-like ground state and fluidlike Laughlin state to multicomponents. We show that the latter has the lowest ground-state energy with a polarized ground state at filling factor \ensuremath{\nu}=1, (1/3), and (1/5) and unpolarized at \ensuremath{\nu}=(2/5). Most important, the CDW predicts a polarized ground state at \ensuremath{\nu}=(2/5) and would, therefore, show dissipation via the GM channel contrary to the Laughlin-like ground states. We have, therefore, a new experimental possibility for selecting the correct ground state from many of the recent interesting suggestions.

The electroweak origin of biomolecular handedness

The parity-violating weak neutral current perturbation of the ground-state electronic energy has been calculated by ab initio methods for glycine over a range of chiral conformations, for L-alanine, L-α-aminopropionitrile, and for the peptide residue of polypeptides in the α-helix and the β-sheet conformation. It is found that L-alanine in its preferred conformation in aqueous solution and the L-peptides in the α-helix and the β-sheet conformation, have a lower ground-state energy than the corresponding D-enantiomers, because of the electroweak interaction. The enantiomer energy difference is small, of the order of 10 -14 J mol -1 , corresponding to an enantiomeric excess of 10 6 molecules of L-alanine or the L-peptide in one mole of the corresponding racemic mixture in thermodynamic equilibrium at ambient temperature. The significance of the energy difference between enantiomers arising from the electroweak interaction for the transition from racemic geochemistry to homochiral biochemistry in terrestrial evolution is discussed.

The parity-violating energy difference between enantiomeric molecules

The parity-violating weak neutral current perturbation of the groundstate electronic energy has been calculated, by ab initio methods, for the (S)-isomer of hydrogen peroxide, over a range of standard Gaussian basis sets. The STO-N-31G, but not the STO-NG, sets give energy shifts E pv which converge with increasing N towards the corresponding E pv value given by an extended basis. Calculations for α-amino acids, peptides, model helical systems, with the STO-6-31G basis, or with an analogous set for corre-sponding sulphur analogues, show that the E pv shift is sensitive in sign and magnitude to the molecular conformation generally. It is found that L-alanine and the L-peptides in the α-helix and the β-sheet conformation have a lower ground state energy than the corresponding D-enantiomers due to the WNC interaction. The energy shift E pv only approximates to an expected Z 5 proportionality, and it does not correlate consistently in sign with the handedness of a helical system.

Computational experiments on the lowest two electronic states of the N2H3 radical

The most accurate computational study to date of the hydrazyl radical N2H3 has resolved previous ambiguities in the lowest energy ground state conformation, showing it to have a nonplanar arrangement of the nuclei, derivable from a planar structure by depressing the NH2 group by approximately 28°. This structure is derived after complete geometry optimization using a ’’double zeta plus polarization’’ first-order configuration interaction wave function with 1771 configuration state functions. Other structures studied with this same wave function give the following information about the lowest two potential energy surfaces for this radical. The ground state inversion barrier about nitrogen is small, with a computed value of 0.5 kcal/mole. Rotation is shown to be the lowest energy path for interconversion between equivalent ground state structures; a rotational barrier of 24.9 kcal/mole being computed. An optimized structure for the alternative transition state, with a linear N–N–H arrangement, lies 51 kcal/mole above the lowest energy ground state structure. Vertical excitation requires 4.32 eV, to a point lying 2.95 eV above the minimum on the excited state surface. The f number for the transition is 0.0066. Nuclear relaxation following excitation changes the geometry to a symmetric perpendicular structure in which the NNH plane of symmetry bisects the NH2 group. The minimum on the second potential energy surface is shown to be a point of intersection for symmetric perpendicular 2A″ and 2A′ states.

A two-band Hubbard-model description of an almost mixed valence system: A new ground state for La

Though not quite a 'mixed valence' system, La shows anomalous properties (e.g. low melting and low Debye temperature, high superconducting transition temperature) which are thought to be due to the proximity of the atomic f-level to the Fermi level. To study the influence of the f-band on the ground state, a two-band Hubbard model is used and it is shown that an ansatz for the ground state, constructed by partially suppressing configurations where two d-electrons are on the same ion by allowing one of them to transfer to the f-level, gives a lower ground-state energy than the Hartree-Fock state.

The role of model systems in the few‐body reduction of the N‐fermion problem

AbstractThe problem of upper and lower ground state energy bounds for many‐fermion systems is considered from the viewpoint of reduced density matrices. Model density matrices are used for upper bounds to, first uncoupled, then coupled fermions. Model Hamiltonians are developed for lower bounds in corresponding fashion. Both mathematical and physical models are constructed for setting up universally valid inequalities on density matrices. These are joined by both inequalities and equalities in which the explicit form of the system at hand is used. A few illustrative examples are presented.

Ionization potentials of the N 2O molecule

Minimal basis STO, SCF and CI calculations have been made for the three lowest ionization potentials of NNO. Although lower ground state energies are obtained both in the CI and SCF calculations when identical Slater orbitals, centered on different nitrogen atoms, have different exponents, the computed ionization potentials become better as those exponents are made equal.

Density modulation and superconductivity in a system of fermions

An antisymmetrized product of periodic density modulated one particle functions is investigated as a trial wave function for different local twobody forces. The model is compared with a BCS ground state. For some potentials a lower ground state energy has been found for the density modulated state. In lowest order cluster expansion forces with a hard core have been examined. A liquid-solid transition is indicated for3He at a density near the experimental value.

Valency-bond studies of some conjugated hydrocarbons—II : Pentalene, and some preliminary results on heptalene

Valency-bond studies of the still unknown molecule pentalene C 8H 6 in which the molecular symmetry may be either D 2 h or C 2 h show that a more stable molecule (lower ground state energy) is found for the lower symmetry, and that marked alternation of bond lengths occurs. The corresponding Penney-Dirac bond orders have been determined. Preliminary results for heptalene forecast a similar conclusion.

Theory of Superconductivity

Recently Eliashberg derived the theory of superconductivity by the Green's function technique. The energy-gap equation was deduced by a self-consistent calculation. The result is similar to the integral equation of Bardeen, Cooper, and Schrieffer except that the effective electron interaction potential is different from the Bardeen-Pines potential as well as the Bogoliubov potential. The purpose of this paper is to discuss these differences. It shows that the "dangerous terms" in the Bogoliubov theory may be calculated in a different manner. The compensation of these dangerous terms leads to the result of Eliashberg. Therefore the self-consistent calculation of Eliashberg is but a different interpretation of the Bogoliubov's idea. However, it is argued that the most reliable way of treating the problem should be the variational method because it gives the lowest ground-state energy. This method gives all the results of Bogoliubov in the lowest order of approximation, but is free from arbitrary interpretations.