Transformation of the effective rotational Hamiltonian of nonrigid X 2 Y molecules

The transformation of the effective rotational Hamiltonian H of nonrigid X ₂ Y molecules to the form having a minimum number of diagonals in the basis of rotational functions of a symmetric top is discussed. Such a transformation is a generalization of the reduction transformation performed for the polynomial effective Hamiltonian H. It is shown that in the general case the transformation substantially changes the form of the initial Hamiltonian, which restricts the region of applicability (J<J*) of the reduced Hamiltonian represented in a class of elementary functions in terms of angular momentum operators. The values of the rotational quantum number J* are estimated for the (000) ground and (010) vibrational states of the H₂O molecule.     

Effective chiral lagrangians with baryons—the mass splitting of the spin 1/2 parity partners

There are two inequivalent spin 1/2 baryon field operators that can be constructed directly out of three quark field operators. These are associated with a pair of parity partners. Their chiral transformation properties yield some unexpected results. In particular.U(1) axial transformations can mix the two operators. With these chiral transformation properties the spin 1/2 baryon parity partners are incorporated in an effective chiral lagrangian together with the spin 0 meson fields. The mass splitting of these parity partners is then found to be related to their coupling to the flavour singlet pseudoscalar, $$M_ - - M_ + \simeq F_\pi g_{\mathop {flavour}\limits_{singlet} N_ - N_ + } $$ The further selection rule, in the exact chiral limit, $$g_{\pi N_ + N_ - } = 0$$ is also found. Using these results, and their extension to the non-chiral limit, the enhancement of the decay ofN _? intoN ₊ η, as opposed toN ₊ π, is elucidated even though it is suppressed by phase space. Two flavours is given principle consideration although three flavours is also briefly discussed.     

Effective Hamiltonian for degenerate vibrational states in symmetric top molecules

A mixed matrix-operator form of the effective rotational Hamiltonian has been discussed for the degenerate vibrational states of symmetric top molecules. In this scheme, a rotational contact transformation can be applied to the effective Hamiltonian such that the operators of the “2, +2,” “2, −2,” and “2, −1” l-type interactions as well as the operators of the Δk = ±3 and ±4 interactions are eliminated from the first-order terms of the expansion of the rotational Hamiltonian in terms of the small parameter λ. The results have been used to discuss the correlation between various interaction parameters in the effective rotational Hamiltonian for the doubly degenerate fundamental vibrational levels of semirigid symmetric top molecules. For example, for C_3v or D₃ molecules, the parameter of the “2, −1” interaction is correlated with other parameters and cannot be determined separately by fitting the experimental data (unless there are certain accidental resonances between vibrational-rotational levels).     

Topologically non-trivial chiral transformations

The role of chiral transformations in effective theories modeling Quantum Chromo Dynamics is reviewed. In the context of the Nambu-Jona-Lasinio model the hidden gauge and massive Yang-Mills approaches to vector mesons are linked by a special chiral transformation which removes the chiral field from the scalar-pseudoscalar sector. The chirally rotated axial vector meson field (à _μ ) transforms homogeneously under flavor rotations and may thus be dropped without violating chiral symmetry. The fermion determinant for static meson field configurations is computed by summing the discretized eigenvalues of the Dirac Hamiltonian. It is discussed how the local chiral transformation loses its unitary character in a finite model space. This technical issue proves to be crucial for the construction of the soliton within the Nambu-Jona-Lasinio model when the chirally rotated axial vector field is neglected. In the background of this soliton the valence quark is strongly bound, and its eigenenergy turns out to be negative. This important feature, which usually is generated by non-vanishing axial vector profiles, is thus maintained by the simplificationà _μ = 0.     

Unitary renormalization of the Lee model Y4

The Lee model Y₄ is renormalized by unitary transformation. A norm convergent (in each sector) sequence of unitary dressing transformations, which transform a sequence of renormalized cut-off Hamiltonians to a sequence of operators converging strongly on a dense set of states, is defined. The self-adjointness and semiboundedness (in each sector) of the renormalized Hamiltonian are proved.     

Application of the Bogolyubov inequality to the calculation of thermodynamic functions of triatomic molecules

The Bogolyubov inequality is used in the calculation of the vibrational part of of thermodynamic functions of triatomic molecules where the vibrations are anharmonic. By variation of parameters in the approximate Hamiltonian, we obtain the best agreement between the free energy of the system based on the approximate Hamiltonian, and the exact free energy-of the system. The method is applied to the calculation of the thermodynamic functions for H₂O and C₃.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 3–6, January 1983.     

用变分法讨论超导体隧道体系的近似哈密顿量

我们推广了Боголюбов等人的变分近似方法用来处理超导体隧道体系问题,发现Cohen等人假设的模拟哈密顿量在变分法近似下到一级是成立的。Prange对这个问题的处理是不恰当的。 关键词：     

Optimal oscillation-center transformations

Systems with Hamiltonians of the form H₀(p) + H₁(q,p,t) are considered. A variational principle is proposed for defining that canonical transformation, continuously connected with the identity transformation, which minimizes the residual, coordinate-dependent part of the new Hamiltonian. The principle is based on minimization of the mean square generalized force over phase space and time. The transformation reduces to the action-angle transformation in that part of the phase space of an integrable system where the orbit topology is that of the unperturbed system, or on primary KAM surfaces. General arguments in favour of this definition are given, based on Galilean invariance, decay of the Fourier spectrum, and its ability to include external fields or inhomogeneous systems. The optimal oscillation-center transformation for the physical pendulum (or particle in a sinusoidal potential) is constructed analytically. A modified principle for relativistic systems is presented in an appendix.     

IBM: Discrete symmetry viewpoint

It is shown that the set of transformations of the s and d boson operators that maintain the IBM-like form of the Hamiltonian comprises a discrete point symmetry group D ₂′. The transformations manifest themselves as a parameter symmetry of the IBM-1 Hamiltonian. The transformations considered are also necessary for constructing the most general IBM-2 Hamiltonian. The properties of the potential energy surfaces arising in connection with these transformations are discussed.     

Tensorial development of the rovibronic Hamiltonian and dipole moment operators for XY3Z molecules with a degenerate electronic state: Preliminary application to the CH3O radical

We present a development of the Hamiltonian and transition moment operators of XY₃Z (C_3v) symmetric tops molecules in a degenerate electronic state with the aid of a tensorial formalism developed in a recent paper [A. El Hilali, V. Boudon, M. Loëte, J. Mol. Spectrosc. 239 (2006) 41-50]. Electronic operators are defined from group theory properties. They provide a new approach to build an effective rovibronic Hamiltonian as well as an effective dipole moment operator for rovibronic transition of XY₃Z molecules. This model is studied qualitatively thanks to the tensorial algebra properties. Expressions of the matrix elements are derived for these operators. A first simple application to the ground electronic state of CH₃O is proposed as an illustrative example.     

Parafermionic theory with the symmetry Z5

A parafermionic conformal theory with the symmetry Z₅ is constructed, based on the second solution of Fateev–Zamolodchikov for the corresponding parafermionic chiral algebra.The primary operators of the theory, which are the singlet, doublet 1, doublet 2, and disorder operators, are found to be accommodated by the weight lattice of the classical Lie algebra B₂. The finite Kac tables for unitary theories are defined and the formula for the conformal dimensions of primary operators is given.     

On the spectra of periodic waves for infinite-dimensional Hamiltonian systems

We consider the problem of determining the spectrum for the linearization of an infinite-dimensional Hamiltonian system about a spatially periodic traveling wave. By using a Bloch-wave decomposition, we recast the problem as determining the point spectra for a family of operators J_γL_γ, where J_γ is skew-symmetric with bounded inverse and L_γ is symmetric with compact inverse. Our main result relates the number of unstable eigenvalues of the operator J_γL_γ to the number of negative eigenvalues of the symmetric operator L_γ. The compactness of the resolvent operators allows us to greatly simplify the proofs, as compared to those where similar results are obtained for linearizations about localized waves. The theoretical results are general, and apply to a larger class of problems than those considered herein. The theory is applied to a study of the spectra associated with periodic and quasi-periodic solutions to the nonlinear Schrödinger equation, as well as periodic solutions to the generalized Korteweg-de Vries equation with power nonlinearity.     

Exchange interaction of weakly delocalized multielectron systems

The polar model of a metal developed by Bogolyubov [1] is extended to the case of a group of equivalent electrons on each of the atoms that form a crystal. A procedure is suggested for treating the second-quantized Hamiltonian that includes the interconfigurational interaction with the help of the double tensor operators W _q . The relationship between these operators and the unitary operators ^a , which act separately in the space of the spin and orbital functions, is pointed out. The conditions for the applicability of the Heisenberg model are analyzed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 80–87, May, 1973.In conclusion I wish to thank B. V. Karpenko for the statement of this problem and for numerous consultations and discussions.     

Possible relevance of lattice effects in high-T c superconductors

The relevance of the lattice-mediated superconducting pairing in a system of quasilocalized polarons dressed by local lattice deformations is considered. The spin correlations are taken into account using thet-J model expressed in terms of holon and spin operators. The Holstein-like Hamiltonian for holons with the transport term depending on spin correlations is transformed by the generalized Lang-Firsov transformation which implies the spread of the charge and the deformations to the nearest neighbours. The analytical formula for the superconducting transition temperatureT _c is deduced using the assumption of an extremely narrow polaron band. The hole-concentration dependence ofT _c and the isotope exponent are discussed using the classical approximation for incommensurate spiral spin correlations. This work was supported by the Grant Agency of the Czech Republic, project No. 202/96/0864.     

Relativistic Jahn–Teller Effect for Triplet States of Tetrahedral Molecular Complexes

A relativistic multimode Jahn?Teller effect for tetrahedral molecular complexes in a triplet electronic state is considered. The analysis is based on the symmetry properties of the electronic Hamiltonian and its generalized symmetry operators, acting on both the coordinates (spatial operations) and spins (matrix operations) of the electrons. As a result, a 9 × 9 vibronic matrix that includes the vibronic coupling constants of orbital and spin-orbital nature and depends on the five normal modes of t₂ and e symmetry has been obtained.     

Centrifugal distortion coefficients of asymmetric-top molecules: Reduction of the octic terms of the rotational Hamiltonian

The rotational Hamiltonian of an asymmetric-top molecule in its standard form, containing terms up to eighth degree in the components of the total angular momentum, is transformed by a unitary transformation with parameters S_pqr to a reduced Hamiltonian so as to avoid the indeterminacies inherent in fitting the complete Hamiltonian to observed energy levels. Expressions are given for the nine determinable combinations of octic constants Θ′_i (i = 1 to 9) which are invariant under the unitary transformation. A method of reduction suitable for energy calculations by matrix diagonalization is considered. The relations between the coefficients of the transformed Hamiltonian, for suitable choice of the parameters S_pqr, and those of the reduced Hamiltonian are given. This enables the determination of the nine octic constants Θ′_i in terms of the experimental constants.     

General solution of relativistic one-channel inverse scattering problem

We find explicitly in the p-representation the kernels of the logarithms of unitary operators transforming the free Hamiltonian into the general solution of the one-channel inverse scattering problem, when bound states are absent. Then we construct the transformation of the Hamiltonian adding to its spectrum the given set of bound states without changing the scattering operator. Other generators of the Poincaré group are constructed in a similar way. The proof of some relevant limits is given.