Jahn-Teller distortions of icosahedral complexes

Classification of the stable symmetries of Jahn-Teller systems ofI _h parent group is elaborated for triply, fourfold and fivefold degenerate electronic states with integer spin and for fourfold and sixfold degenerate ones with non-integer spin. The results produced by the epikernel principle and by the method of step-by-step descent in symmetry connected with degenerate states splitting are compared. The results obtained on the basis of epikernel principle are incomplete and may even be incorrect.     

Field Theory Describing Arbitrary Two-Body Scattering Amplitude as a Born Term

We propose in this paper the local relativistic quantum field-theoretic formulation of the most general isobar model, with unstable two-particle isobars having arbitrary mass and spin spectrum. Such infinite family of isobars is described by infinite-component field operator with its components given by symmetric, traceless and divergenceless field operators ϕu₁…uI (x;s), where I describes spin (I = 0, 1, 2…) and the continuous parameter S the spectrum of asymptotic masses. The asymptotic free states defined by generalized LSZ limits of ϕu₁…uI (x;s), can be described by means of stable multiparticle states. In such a field theory one can choose the parameters in such a way that already a Born term describes an arbitrarily chosen two-body scattering amplitude. As an example we present the generalization of Van Hove model of Reggeons to the case of complex Regge trajectory, describing Regge family of resonances on the second sheet. Finally the correspondence with conventional theory is discussed. It is shown that the Feynman diagrams in local field-theoretic isobar model can be interpreted in the framework of non local theory describing in some approximation an equivalent interaction between stable decay products.     

Spin eigenfunctions and operators for the Dn groups

An automated procedure for determining symmetry-adapted spin eigenfunctions is developed for the D_n symmetry groups with n equivalent spins for arbitrary size of I and for n=3,…,6. These eigenfunctions are also eigenfunctions of the vector sum of the n equivalent nuclear spins. Generalized hyperfine spin operators are developed that have real matrix elements and that exploit the full symmetry. These spin operators can be combined with operators for other spins and molecular rotation using only real arithmetic.     

Using resonance Raman cross‐section data to estimate the spin‐state populations of cytochromes P450

The cytochromes P450 (CYPs) are heme proteins responsible for the oxidation of xenobiotics and pharmaceuticals and the biosynthesis of essential steroid products. In all cases, substrate binding initiates the enzymatic cycle, converting ferric low‐spin to high‐spin state, with the efficiency of the conversion varying widely for different substrates, so documentation of this conversion for a given substrate is an important objective. Resonance Raman (rR) spectroscopy can effectively yield distinctive frequencies for the ν₃ ‘spin state marker’ bands. Here, employing a reference cytochrome P450 (CYP101), the intensities of the ν₃ modes (I_LS) and (I_HS) relative to an internal standard (sodium sulfate) yield relative populations for the two spin states; i.e., a value of 1.24 was determined for the ratio of the relative cross sections for the ν₃ modes. The use of this value was then shown to permit a reliable calculation of relative populations of the two spin states from rR spectra of several other CYPs P450. The importance of this work is that, using this information, it is now possible to conveniently document by rR the spin state population without conducting separate experiments requiring different analytical methods, instrumentation, and additional sample. Copyright © 2013 John Wiley & Sons, Ltd.     

Spin Squeezing of Arbitrary Superposition of Two Three-Qubit <Emphasis Type="Italic">W</Emphasis> States

We investigate the spin squeezing in a arbitrary superposition of two three-qubit W states. It is shown that the mean spin direction is determined by the superposition coefficients and the relative phase; while the length of mean spin and the spin squeezing parameter are only determined by the superposition coefficients. It is also shown that there is squeezing in the n ₂ direction and there is no squeezing in the n ₁ direction.     

The Pauli Exclusion Principle. Can It Be Proved?

The modern state of the Pauli exclusion principle studies is discussed. The Pauli exclusion principle can be considered from two viewpoints. On the one hand, it asserts that particles with half-integer spin (fermions) are described by antisymmetric wave functions, and particles with integer spin (bosons) are described by symmetric wave functions. This is a so-called spin-statistics connection. The reasons why the spin-statistics connection exists are still unknown, see discussion in text. On the other hand, according to the Pauli exclusion principle, the permutation symmetry of the total wave functions can be only of two types: symmetric or antisymmetric, all other types of permutation symmetry are forbidden; although the solutions of the Schrödinger equation may belong to any representation of the permutation group, including the multi-dimensional ones. It is demonstrated that the proofs of the Pauli exclusion principle in some textbooks on quantum mechanics are incorrect and, in general, the indistinguishability principle is insensitive to the permutation symmetry of the wave function and cannot be used as a criterion for the verification of the Pauli exclusion principle. Heuristic arguments are given in favor that the existence in nature only the one-dimensional permutation representations (symmetric and antisymmetric) are not accidental. As follows from the analysis of possible scenarios, the permission of multi-dimensional representations of the permutation group leads to contradictions with the concept of particle identity and their independence. Thus, the prohibition of the degenerate permutation states by the Pauli exclusion principle follows from the general physical assumptions underlying quantum theory.     

Spin Squeezing in Superpositions of GHZ State and W States

We investigate the spin squeezing in superpositions of a N-qubit GHZ state and two W states. The spin squeezing parameter is determined by the superposition coefficients and the relative phase. It is shown that there is squeezing in the n ₂ direction and there is no squeezing in the n ₁ direction. It is also shown that the state with more number of qubits has smaller spin squeezing parameter.     

Spin in kink-type field theories

This paper studies some classical three-dimensional field theories for which the ranges of the field variables are a 3-sphere, a 2-sphere, the symplectic group,Sp(n), the special orthogonal group,SO(3), and theS _4,1 space of general relativistic metrics. The main result is the proof that these theories admit half-odd-integer spin, so that the 1-kink states are classical analogs of fermion states.     

Quantum registers based on single NV + <Emphasis Type="Italic">n</Emphasis><Superscript>13</Superscript>C centers in diamond: II. Spin characteristics of registers and spectra of optically detected magnetic resonance

The spin Hamiltonian method in combination with ab initio calculations of the spin characteristics of quantum registers that include an electron spin S = 1 of a single NV center in the ground electronic state and nuclear spins I = 1/2 of several atoms ¹³C located at different lattice sites near the vacancy of the NV center is applied to find eigenvalues and eigenfunctions of spin systems NV + n ¹³C for cases where the lattice sites nearest to the vacancy of the NV center contain one, two, or three ¹³C nuclear spins, as well as for cases where ¹³C atoms are located at sites more distant from the vacancy. For these single spin NV + n ¹³C systems, the spectra of optically detected magnetic resonance (ODMR) are calculated, which agree well with available experimental data.     

Quantum registers based on single NV + <Emphasis Type="Italic">n</Emphasis><Superscript>13</Superscript>C centers in diamond: I. The spin Hamiltonian method

Details of the application of the spin Hamiltonian method for studying spin characteristics of a quantum register that includes an electron spin S = 1 of a single NV center in the ground electronic state and nuclear spins I = 1/2 of several isotopic atoms ¹³C located at different lattice sites near the vacancy of the NV center. Two methods of finding the hyperfine interaction tensors for these NV + n ¹³C spin systems are considered, one of which is based on the conventional electron spin resonance (ESR) method, while the other involves methods of quantum chemistry. The results of the latter method are compared with ESR data and with spectra of optically detected magnetic resonance (ODMR) and with the character of the modulation of the ODMR echo decay observed in single NV + n ¹³C systems. This comparison shows that the ab initio modeling of the spin characteristics of diamond nanoclusters containing NV centers makes it possible to obtain quantitative spin characteristics of the quantum registers under study.     

Properties of oligothiophene polycations

The different electronic states of trications and tetracations have been studied for oligomers made of n 3,4‐ethylenedioxythiophene units, where n ranges from 2 to 30. Results have been compared with those obtained for neutral, monodications and dications of the same n‐oligomers. For the longer oligomer (n ≥ 24) trications, the doublet and quartet states are isoenergetic, while the triplet and quintet states are isoenergetic for tetracations of the same length. Analysis of the geometry reveals three separated polarons for the doublet and quartet states of tricationic n‐oligomers, even though that of the former state has been attributed to a heavy spin contamination. In contrast, the structure of tetracations shows double bipolaron character for the singlet state and two polaron pairs for both the triplet and quintet states. Analyses of both charge and spin density distributions support the polaronic or bipolaronic behavior predicted by molecular geometry for the different electronic states. Results have been also used to evaluate the ionization potentials and the π‐π^* lowest transition energy of infinite polymer chains. Copyright © 2014 John Wiley & Sons, Ltd.     

Low-energy electronic spin excitations between filling factors ν=1 and studied by optically detected nuclear magnetic resonance

We report measurements of the spin relaxation time (T_1n) for nuclei in the potential well confining a high-mobility two-dimensional electron system at a single GaAs–GaAlAs heterojunction. At low temperatures nuclear spin relaxation is dominated by electron–nuclear spin scattering: we find that T_1n displays sharp maxima at incompressible states throughout the hierarchy of the fractional quantum Hall effect. This behaviour is consistent with the existence of low-energy spin excitations only where the electron system is compressible. Our measurements also provide evidence for a gap in the spin excitation spectrum at .     

Energy levels of 1s~2n d(n≤9)states for lithium-like ions

The full-core plus correlation method with multi-configuration interaction wave functions is extended to the calculation of the non-relativistic energies of 1s²nd (n ≤ 9) states for the lithium isoelectronic sequence from Z = 11 to 20. Relativistic and mass-polarization effects on the energy are calculated as the first-order perturbation correction. The quantum-electrodynamics correction is also included. The fine structure splittings are determined from the expectation values of spin—orbit and spin—other-orbit interaction operators in the Pauli—Breit approximation. Combining the term energies of lowly excited states obtained with the quantum defects calculated by the single channel quantum defect theory, each of which is a smooth function of energy and approximated by a weakly varying function of energy, the ion potentials of highly excited states (n ≤ 6) are obtained with the semi-empirical iteration method. The results are compared with experimental data in the literature and found to be closely consistent with the regularity.     

The group-theoretical structure of the atomic d shell and the energies of the corresponding terms

The icosahedral symmetry I?≈?A ₅ of the atomic d shell can arise from the symmetries of the five-dimensional d orbital space through the subgroup chain SO(5)???SO(3)???I or O(5)???S ₆???S ₅???I. In the latter case the symmetric group S ₅ can be generated from I?≈?A ₅ by addition of the period 4 kaleidoscope operator K, which mixes the d orbitals with m?=?±1 and those with m?=?±2. Furthermore, separation of the d ⁿ configurations into two sets according to the parity of n (even or odd) and the irreps of SO(5) is found to lead to new relationships between the multiplicities and seniorities of the corresponding terms. Thus the sums of the seniorities and multiplicities for even and odd n for a given irrep of SO(5) lead to a constant, namely 12. Furthermore, new pseudodegeneracies are found to arise when the energy expressions of pairs of otherwise equivalent terms with different seniorities for a given d ⁿ are adjusted to remove the radicals arising from solution of the quadratic secular equation. In addition to the well-known ²H/²P degeneracy for d³, ³F/³P degeneracies are found for d⁴ and a ²D/²S pseudodegeneracy is found for d⁵.     

Magnetic resonance in systems with equivalent spin-1/2 nuclides. Part 1

Electron paramagnetic resonance (EPR) spectra of S=1/2 systems XL(n) with n equivalent nuclei having spin I=1/2 have been simulated for microwave frequencies in the L-, X-, and W-bands. It has been shown that for n>2 nuclei, the EPR spectra have a more complicated form than anticipated from the usual oversimplified analysis, which predicts n+1 lines with intensity ratios given by the coefficients of the binomial expansion. For the XL(n) system with n=3, the EPR spectra in fact consist of six lines. The exact solution of the spin-hamiltonian for this case has been obtained, which gives four levels in zero magnetic field. For n>2 systems, the degeneracy of the energy levels cannot be completely removed by the Zeeman electronic and nuclear interactions. For n>4, certain spin states cannot occur, consistent with the (generalized) Pauli exclusion principle. Discussion of the underlying theory, invoking exchange degeneracy and the appropriate permutation group theory, is included in some detail. Analogous considerations hold for NMR spectroscopy of non-radicals.     

Noise in the Helical Edge Channel Anisotropically Coupled to a Local Spin

We calculate the frequency-dependent shot noise in the edge states of a two-dimensional topological insulator coupled to a magnetic impurity with spin S = 1/2 of arbitrary anisotropy. If the anisotropy is absent, the noise is purely thermal at low frequencies, but tends to the Poisson noise of the full current I at high frequencies. If the interaction only flips the impurity spin but conserves those of electrons, the noise at high voltages eV ≫ T is frequency-independent. Both the noise and the backscattering current I_bs saturate at voltageindependent values. Finally, if the Hamiltonian contains all types of non-spin-conserving scattering, the noise at high voltages becomes frequency-dependent again. At low frequencies, its ratio to 2eI_bs is larger than 1 and may reach 2 in the limit I_bs→0. At high frequencies, it tends to 1.

     

An Operator Method for the Addition of Two Angular Momenta by Symmetrizing the Product of n Spin Functions

A general expression of Clebsch-Gordan coefficients is derived by means of de Broglie-like méthode de fusion: the second angular momentum is added to the first in n steps of half each, the maximum symmetric composition of the n spin functions being taken into account explicitly. The procedure is operatorial. Group-theoretically speaking the irreducible representations of the direct product of two irreducible representations of the rotation group are realized via symmetric group S_n with the aid of projection operators (equivalent to Young's symmetrizers). The decomposition of the representations of S_n therein is performed inductively by utilizing the chain of subgroups: S_n ⊃ S_n−1 … ⊃ S₂ ⊃ S₁.