18 research outputs found
Quantum Cosmology
We give an introduction into quantum cosmology with emphasis on its
conceptual parts. After a general motivation we review the formalism of
canonical quantum gravity on which discussions of quantum cosmology are usually
based. We then present the minisuperspace Wheeler--DeWitt equation and
elaborate on the problem of time, the imposition of boundary conditions, the
semiclassical approximation, the origin of irreversibility, and singularity
avoidance. Restriction is made to quantum geometrodynamics; loop quantum
gravity and string theory are discussed in other contributions to this volume.Comment: 29 pages, 9 figures, contribution to "Beyond the Big Bang", ed. by R.
Vaas (Springer 2008); typos corrected, reference adde
Density matrix embedding theory for interacting electron-phonon systems
We describe the extension of the density matrix embedding theory (DMET)
framework to coupled interacting fermion-boson systems. This provides a
frequency-independent, entanglement embedding formalism to treat bulk
fermion-boson problems. We illustrate the concepts within the context of the
one-dimensional Hubbard-Holstein model, where the phonon bath states are
obtained from the Schmidt decomposition of a self-consistently adjusted
coherent state. We benchmark our results against accurate density matrix
renormalization group calculations
A radiation-like era before inflation
We show that the semiclassical approximation to the Wheeler-DeWitt equation
for the minisuperspace of a minimally coupled scalar field in the spatially
flat de Sitter Universe prompts the existence of an initial power-law evolution
driven by non-adiabatic terms from the gravitational wavefunction which act
like radiation. This simple model hence describes the onset of inflation from a
previous radiation-like expansion during which the cosmological constant is
already present but subleading.Comment: LaTeX, 8 pages, no figures; final version to be published in JCA
Hints of (trans-Planckian) asymptotic freedom in semiclassical cosmology
We employ the semiclassical approximation to the Wheeler-DeWitt equation in
the spatially flat de Sitter Universe to investigate the dynamics of a
minimally coupled scalar field near the Planck scale. We find that, contrary to
naive intuition, the effects of quantum gravitational fluctuations become
negligible and the scalar field states asymptotically approach plane-waves at
very early times. These states can then be used as initial conditions for the
quantum states of matter to show that each mode essentially originated in the
minimum energy vacuum. Although the full quantum dynamics cannot be solved
exactly for the case at hand, our results can be considered as supporting the
general idea of asymptotic safety in quantum gravity.Comment: 11 pages, 2 figures; replaced to match content of published versio
One-electron contributions to the g-tensor for second-order DouglasâKrollâHess theory
The electric g-tensor is a central quantity for the interpretation of electron paramagnetic resonance spectra. In this paper, a detailed derivation of the 1-electron contributions to the g-tensor is presented in the framework of linear response theory and the second-order DouglasâKrollâHess (DKH) transformation. Importantly, the DKH transformation in the presence of a magnetic field is not unique. Whether or not the magnetic field is included in the required Foldy-Wouthuysen transformation, different transformation matrices and, consequently, Hamiltonians result. In this paper, a detailed comparison of both approaches is presented, paying particular attention to the mathematical properties of the resulting Hamiltonians. In contrast to previous studies that address the g-tensor in the framework of DKH theory, the resulting terms are compared to those of the conventional Pauli theory and are given a physical interpretation. Based on these mathematical and physical arguments, we establish that the proper DKH transformation for systems with constant magnetic fields is based on a gauge-invariant Foldy-Wouthuysen transformation, i.e., a Foldy-Wouthuysen transformation including the magnetic field. Calculations using density functional theory (DFT) are carried out on a set of heavy, diatomic molecules, and a set of transition-metal complexes. Based on these calculations, the performance of the relativistic calculation with and without inclusion of picture-change effects is compared. Additionally, the g-tensor is calculated for the Lanthanide dihydrides. Together with the results from the other two molecular test sets, these calculations serve to quantify the magnitude of picture-change effects and elucidate trends across the periodic table
Derivation and assessment of relativistic hyperfine-coupling tensors on the basis of orbital-optimized second-order MĂžllerâPlesset perturbation theory and the second-order DouglasâKrollâHess transformation
The accurate calculation of hyperfine-coupling tensors requires a good description of the electronic spin density, especially close to and at the nucleus. Thus, dynamic correlation as well as relativistic effects have to be included in the quantum-chemical calculation of this quantity. In this paper, orbital-optimized second-order MĂžllerâPlesset perturbation theory (MP2) is combined with the second-order DouglasâKrollâHess (DKH) transformation to yield an efficient and accurate ab initio method for the calculation of hyperfine couplings for larger molecules including heavy elements. Particular attention is paid to the derivation of the hyperfine-coupling tensor in the DKH framework. In the presence of a magnetic field, the DKH-transformation is not unique. Two different versions can be found in the literature. In this paper, a detailed derivation of one-electron contributions to the hyperfine-coupling tensor as they arise in linear-response theory is given for both DKH-transformations. It turns out that one of the two variants produces divergent hyperfine-coupling constants. The possibility to remove this divergence through a physically motivated finite-nucleus model taking into account the different extent of charge and magnetization distribution is discussed. Hyperfine-coupling values obtained at the orbital-optimized MP2 level with second-order DKH corrections for the non-divergent variant are presented. The influence of a Gaussian nucleus model is studied. The method is compared to four-component, high-accuracy calculations for a number of cations and atoms. Comparison to B3LYP and B2PLYP is made for a set of transition-metal complexes of moderate size
Natural triple excitations in local coupled cluster calculations with pair natural orbitals
In this work, the extension of the previously developed domain based local pair-natural orbital (DLPNO) based singles- and doubles coupled cluster (DLPNO-CCSD) method to perturbatively include connected triple excitations is reported. The development is based on the concept of triples-natural orbitals that span the joint space of the three pair natural orbital (PNO) spaces of the three electron pairs that are involved in the calculation of a given triple-excitation contribution. The truncation error is very smooth and can be significantly reduced through extrapolation to the zero threshold. However, the extrapolation procedure does not improve relative energies. The overall computational effort of the method is asymptotically linear with the system size O(N). Actual linear scaling has been confirmed in test calculations on alkane chains. The accuracy of the DLPNO-CCSD(T) approximation relative to semicanonical CCSD(T0) is comparable to the previously developed DLPNO-CCSD method relative to canonical CCSD. Relative energies are predicted with an average error of approximately 0.5 kcal/mol for a challenging test set of medium sized organic molecules. The triples correction typically adds 30%â50% to the overall computation time. Thus, very large systems can be treated on the basis of the current implementation. In addition to the linear C150H302 (452 atoms, >8800 basis functions) we demonstrate the first CCSD(T) level calculation on an entire protein, Crambin with 644 atoms, and more than 6400 basis functions
Magnetic properties of a Kramers doublet. An univocal bridge between experimental results and theoretical predictions
The magnetic response of a Kramers doublet is analyzed in a general case taking into account only the formal properties derived from time reversal operation. It leads to a definition of a matrix G (gyromagnetic matrix) whose expression depends on the chosen reference frame and on the Kramers conjugate basis used to describe the physical system. It is shown that there exists a reference frame and a suitable Kramers conjugate basis that gives a diagonal form for the G-matrix with all non-null elements having the same sign. A detailed procedure for obtaining this canonical expression of G is presented when the electronic structure of the KD is known regardless the level of the used theory. This procedure provides a univocal way to compare the theoretical predictions with the experimental results obtained from a complete set of magnetic experiments. In this way the problems arising from ambiguities in the g-tensor definition are overcome. This procedure is extended to find a spin-Hamiltonian suitable for describing the magnetic behavior of a pair of weakly coupled Kramers systems in the multispin scheme when the interaction between the two moieties as well as the individual Zeeman interaction are small enough as compared with ligand field splitting. Explicit relations between the physical interaction and the parameters of such a spin-Hamiltonian are also obtained.This work was supported by Spanish Ministry of Economy and Competitively (MINECO), Projects no. MAT2011-23861 to JIM and by ââGrupos de investigaciĂłnââ Program of the Aragon Autonomous
Government, refs. B18 and E33.Peer reviewe