A rigorous description of the energy spectrum of the ammonia dimer. II. Taking into account the inversional motion

Using the group chain methods, a rigorous algebraic model for describing the energy spectrum of the ammonia dimer (NH₃)₂ is constructed with an allowance for both the most important torsional and exchange nonrigid motions and the inversional nonrigid motion also taken into account. The model is rigorous in the sense that its correctness is limited only by the correctness of the chosen symmetry of internal dynamics of the dimer.     

A rigorous description of the energy spectrum of the isopropanol molecule taking into account the internal rotation of hydroxyl

Using the methods of a group chain, a rigorous algebraic model is constructed to describe the energy spectrum of the isopropanol molecule (CH₃)₂CHOH with an allowance for the internal rotation of hydroxyl. The model is rigorous in the sense that its correctness is limited only by the correctness of a chosen symmetry of internal dynamics of the molecule.     

Rigorous description of an energy spectrum of the isopropanol molecule taking into account the internal rotation of methyl tops

By using the group chain methods, a rigorous algebraic model is constructed to describe the energy spectrum of the isopropanol molecule (CH₃)₂CHOH with an allowance for the internal motion of hydroxil and two identical methyl tops. The model is rigorous in the sense that its correctness is limited only by the correctness of a symmetry chosen to describe internal dynamics of the molecule.     

Possibilities of the observation of the discrete spectrum of the water dimer at equilibrium in millimeter-wave band

Attempts of experimental observations of the water dimer spectrum at equilibrium conditions have lasted for more than 40 years since the dimeric hypothesis for extra absorption, but have not yielded any positive confirmed result. In the present paper a new approach is considered: using a high-resolution millimeter-wave spectrum of the water dimer at equilibrium, calculated by a rigorous fully quantum method, we show the potential existence of discernible spectral series of discrete features of the water dimer, which correspond to J+1←J, K lines of E₁ symmetry, already observed in cold molecular beam experiments and having, therefore, well-defined positions. The intensity of spectral series and contrast to the remaining continuum-like spectrum of the dimer are calculated and compared with the monomer absorption. The suitability of two types of microwave spectrometers for observing these series is considered. The collisional line-width of millimeter lines of the dimer at equilibrium is estimated and the width of IR dimer bands is discussed. It is pointed out that the large width of IR dimer bands may pose difficulties for their reliable observation and conclusive separation from the rest of absorption in water vapor. This situation contrasts with the suggested approach of dimer detection in millimeter-waves.     

Description of the spectrum of the ethanol molecule with allowance for the torsional motions of its hydroxyl and methyl groups

On the basis of symmetry methods, a rigorous model is, for the first time, obtained for describing the spectrum of the ethanol molecule CH₃CH₂OH in a given vibronic state with allowance for the simultaneous torsional motion of the hydroxyl group OH and the methyl group CH₃.     

Description of the spectrum of the ethanol molecule with allowance for the mixing of its trans and gauche conformers

Based on symmetry methods, a rigorous model is, for the first time, obtained for describing the spectrum of the ethanol molecule CH₃CH₂OH in a given vibronic state with allowance for the mixing of its trans and gauche conformers due to the torsional motion of the hydroxyl group OH.     

Description of torsional motion in ionic complexes ArH<Stack><Subscript>3</Subscript><Superscript>+</Superscript></Stack> and ArD<Stack><Subscript>3</Subscript><Superscript>+</Superscript></Stack>

An algebraic model that describes the internal dynamics of the ionic complexes ArH₃⁺ and ArD₃⁺ in the ground electronic-vibrational state taking into account the torsional motion of the structure of identical hydrogen nuclei is constructed by symmetry-group chain methods. It is important that the correctness of this model is only limited by the correctness of the choice of geometric symmetry of the internal dynamics of the ionic complex.     

Internal dynamics of (H2O)2 and (D2O)2 dimers: II. Effective operators of physical quantities with account of inversion and exchange motions

Using the symmetry group chain methods, a model of the internal dynamics of (H₂O)₂ and (D₂O)₂ dimers that takes into account their real geometries and two nonrigid motions with the lowest energy barriers is constructed. The motions are the inversion motion (or the acceptor switching) and the exchange motion of the acceptor and donor via an intermediate trans configuration. The model rigorously describes the interactions of various motions and leads to a simple algebraic scheme of calculation of both the positions of the levels in the energy spectrum and the intensities of transitions between them. It is important that the correctness of the model is limited only by the trueness of the choice of the symmetry of the internal dynamics.     

Internal dynamics of (H<Subscript>2</Subscript>O)<Subscript>2</Subscript> and (D<Subscript>2</Subscript>O)<Subscript>2</Subscript> dimers: III. Description taking into account inversion,exchange and bifurcation motions

Using the symmetry group chain methods, the stationary states of (H₂O)₂ and (D₂O)₂ dimers that correspond to the lowest energy barriers of the inversion, exchange via an intermediate trans configuration, and bifurcation motions are classified taking into account the real geometries of the dimers. A model that rigorously describes the interactions of the motions and leads to a simple algebraic scheme for calculating of both the positions of the levels in the energy spectrum and the intensities of transitions between them is constructed. It is important that the correctness of the model is limited only by the trueness of the choice of symmetry of the internal dynamics.     

Description of the torsional motion in the isotopically asymmetric ionic complexes ArH<Subscript>2</Subscript>D<Superscript>+</Superscript> and ArD<Subscript>2</Subscript>H<Superscript>+</Superscript>

The internal dynamics of the isotopically asymmetric ionic complexes ArH₂D⁺ and ArD₂H⁺ is considered to be a distorted dynamics of the isotopically symmetric ArH₃⁺ complex. By using the group chain methods, a rigorous algebraic model is constructed to describe the spectrum of the asymmetric complexes with an allowance for the torsional motion of the structure of hydrogen nuclei. The model is based on the geometrical group of symmetry of internal dynamics of the isotopically symmetric ionic complex, which is used here as a noninvariant group.     

Geometry of the internal dynamics of the 12C13CH 3 + carbocation

The internal dynamics of the ¹²C¹³CH₃⁺ isotopomer of the simplest carbocation is considered to be a distorted dynamics of its symmetric C₂H₃⁺ isotopomer. By using the group-chain methods and assuming quite naturally that the carbocation equilibrium structures continue to be planar and the nonrigid motion occurring between them is retained upon this isotopic substitution, a simple algebraic model is constructed to describe the spectrum of the ¹²C¹³CH₃⁺ isotopomer. The correctness of the model is limited only by that of the adopted geometrical symmetry of internal dynamics of the C₂H₃⁺ isotopomer.     

Bose-Einstein Condensation and Spontaneous Symmetry Breaking

After recalling briefly the connection between spontaneous symmetry breaking and off-diagonal long-range order for models of magnets a general proof of spontaneous breaking of gauge symmetry as a consequence of Bose-Einstein condensation is presented. The proof is based on a rigorous validation of Bogoliubov's c-number substitution for the k = 0 mode operator α₀.     

Hidden symmetry breaking and the Haldane phase inS=1 quantum spin chains

We study the phase diagram ofS=1 antiferromagnetic chains with particular emphasis on the Haldane phase. The hidden symmetry breaking measured by the string order parameter of den Nijs and Rommelse can be transformed into an explicit breaking of aZ ₂×Z ₂ symmetry by a nonlocal unitary transformation of the chain. For a particular class of Hamiltonians which includes the usual Heisenberg Hamiltonian, we prove that the usual Néel order parameter is always less than or equal to the string order parameter. We give a general treatment of rigorous perturbation theory for the ground state of quantum spin systems which are small perturbations of diagonal Hamiltonians. We then extend this rigorous perturbation theory to a class of diagonally dominant Hamiltonians. Using this theory we prove the existence of the Haldane phase in an open subset of the parameter space of a particular class of Hamiltonians by showing that the string order parameter does not vanish and the hiddenZ ₂×Z ₂ symmetry is completely broken. While this open subset does not include the usual Heisenberg Hamiltonian, it does include models other than VBS models.     

Spontaneous symmetry breakings in Z2 gauge theories for doped quantum dimer and eight-vertex models

Behavior of doped fermions in Z₂ gauge theories for the quantum dimer and eight-vertex models is studied. Fermions carry charge and spin degrees of freedom. In the confinement phase of the Z₂ gauge theories, these internal symmetries are spontaneously broken and a superconducting or Neél state appears. On the other hand in the deconfinement-topologically ordered state, all symmetries are respected. From the view point of the quantum dimer and eight-vertex models, this result indicates interplay of the phase structure of the doped fermions and background configuration of the dimer or the eight-vertex groundstate. At the quantum phase transitions in these systems, structure of the doped fermions groundstate and also that of the background dimer or eight-vertex groundstate both change. Translational symmetry breaking induces a superconducting or antiferromagnetic state of the doped fermions.     

General refinement strategy for magnetic structures using spherical neutron polarimetry and representation analysis

Spherical neutron polarimetry (SNP) is a powerful technique for the determination of magnetic structures which may otherwise be intractable. The complexity of the neutron scattering process and the large number of different possible trial structures typically leads to refinements based on a simple trial and error generation of possible models and a possible failure to explore valid possible models. The combination of the model symmetry types determined from representational analysis and reverse-Monte Carlo refinement creates a generalized refinement strategy for SNP data that allows refinement in terms of symmetry adapted modes built up from the basis vectors that describe the orientations of the magnetic moments on the different magnetic sites, and those of the different domains that are possible in a sample: spin (S)-domains and K-domains. This methodology typically leads to a large reduction in the number of refined parameters as well as the rigorous inclusion of any symmetry related domains. In combination with reverse-Monte Carlo refinement algorithms a general strategy for refining complex magnetic structures can be created. We present an example of a frustrated magnetic structure that have been determined using this approach Er₂Ti₂O₇.