Torque equations for spin and orbital angular momenta of radiation fields and Faraday effect

The spin angular momentum S of light has never been linked to the Faraday rotation of light traveling in an optically active medium possessing a rotational invariance of a crystal, because there was no helicity term associated with the phase shift in the previous torque equation for S. In order to relate the change in S with time to the Faraday rotation, therefore, we derived an exact torque equation for S. As a result, a magnetic helicity term appeared in a new torque equation for S, so that one-half of the phase shift derived from the helicity term was equivalent to the Faraday rotation angle. However, the orbital angular momentum L had no relation to the Faraday rotation. It was thus clarified that the change in S with time is related to the Faraday rotation angle of light traveling in an optically active medium, owing to the appearance of the helicity term without a rotational invariance around the optical axis. It was also demonstrated theoretically that the Faraday rotation is accompanied by a torque acting on the crystal so that the total angular momentum of light and matter is conserved.     

New Developments in the Eight Vertex Model II. Chains of Odd Length

We study the transfer matrix of the 8 vertex model with an odd number of lattice sites N. For systems at the root of unity pointsη=mK/L with m odd the transfer matrix is known to satisfy the famous ‘‘TQ’’ equation where Q(υ) is a specifically known matrix. We demonstrate that the location of the zeroes of this Q(υ) matrix is qualitatively different from the case of evenN and in particular they satisfy a previously unknown equation which is more general than what is often called ‘‘Bethe’s equation.’’ For the case of even m where no Q(υ) matrix is known we demonstrate that there are many states which are not obtained from the formalism of the SOS model but which do satisfy the TQ equation. The ground state for the particular case of η=2K/3 and N odd is investigated in detail.     

Scalar mesons and glueball in a quark model allowing for gluon anomalies

This paper is a sequel of a previous one (Scalar mesons in a chiral quark model with glueball, Eur. Phys. J. A 8, 567 (2000)) where an attempt to construct an effective U(3)×U(3)-symmetric meson Lagrangian with a scalar glueball was made. The glueball was introduced by using the dilaton model on the base of scale invariance. The scale invariance breaking because of current quark masses and the scale anomaly of QCD, reproduced by the dilaton potential, was taken into account. However, in the previous paper, the scale invariance breaking because of the terms like h _φφ² and h _σ , where φ and are the pseudoscalar and scalar isosinglets, was not taken into account. These terms are produced by the part of the 't Hooft interaction that is connected with gluon anomalies. Allowing for the scale invariance breaking by these terms has a decisive effect on the quarkonium-glueball mixing and noticeably changes the widths of glueball strong decays. Taking account of this additional source of the scale invariance breaking and its implications are the subject of the present work. It is also shown that in the decay of a glueball into four pions, the channel with two ρ-resonances dominates. Received: 11 January 2001 / Accepted: 25 January 2001     

Theoretical study of the A 3 0 + ← X 1 0 + and B 3 1 ← X 1 0 + transitions in the Cd-rare gas van der Waals molecules

Excitation spectra arising from A ³ 0 ⁺ ← X ¹ 0 ⁺ and B ³ 1 ← X ¹ 0 ⁺ electronic transitions in the Cd-rare gas (RG) van der Waals molecules are calculated using newly obtained theoretical potential curves for these species. In the molecular structure calculations, Cd²⁰⁺ and RG⁸⁺ cores are simulated by energy-consistent pseudopotentials which also account for scalar-relativistic effects and spin-orbit (SO) interaction within the valence shell. Potential energies in the Λ S coupling scheme have been obtained by means of ab initio complete-active-space multiconfiguration self consistent-field (CASSCF)/complete-active-space multireference second-order perturbation theory (CASPT2) calculations with a total 28 correlated electrons, while the SO matrix has been computed in a reduced CI space restricted to the CASSCF level. The final Ω potential curves are obtained by diagonalization of the modified SO matrix (its diagonal elements before diagonalization substituted for the corresponding CASPT2 eigen-energies). The spectroscopic parameters for the ground and several excited states of the Cd-RG complexes deduced from the calculated potential curves are in quite reasonable agreement with available experimental data. In addition, the radial Schr?dinger equation for nuclear motion was solved numerically with the calculated potentials to evaluate the corresponding vibrational levels and radial wavefunctions. The latter have been used in the calculation of the appropriate Franck-Condon factors to yield information on relative intensities of the vibrational bands of the Cd-RG complexes. The theoretical vibrational progressions are discussed in the context of experimental spectra. Received 10 August 2000 and Received in final form 7 November 2000     

Bose condensation and spontaneous breaking of the uniformity of time

The spontaneous breaking of gauge invariance accompanying Bose condensation in mesoscopic systems corresponds to thermodynamically equilibrium ground states with nonintegral average particle number and results in a spontaneous breaking of the uniformity of time. In Fermi systems, the breaking of gauge invariance can be also accompanied by spontaneous breaking of invariances with respect to spatial rotations by an angle of 2π and double time reversal. Possible experiments are discussed. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 12, 963–969 (25 June 1996)     

Boundary critical behaviour of two-dimensional random Potts models

Using extensive Monte Carlo simulations, transfer matrix techniques and conformal invariance, ferromagnetic random q-state Potts models for are studied in the vicinity of the critical temperature. In particular the surface and bulk magnetization exponents and are found monotonically increasing with q. At the critical temperature, different moments (n) of the magnetization profiles are calculated which are all found to accurately follow predictions of conformal invariance. The critical correlation functions show multifractal behaviour, the decay exponents of the different moments both in the volume and at the surface, are n-dependent. Received 4 June 1999     

Phase transition in the Blume-Capel model with second neighbour interaction

A two dimensional antiferromagnetic spin-1 Ising model with negative next- nearest neighbour interaction (J ₂ <0) and under an external magnetic field is investigated by two methods: The mean-field theory and Finite-Size-Scaling based on transfer matrix (TMFSS) calculations. The ground state diagrams exhibit several new phases including frustrated ones. At finite temperature we obtain by these two methods quite rich phase diagrams, with several multicritical points. While Mean field approximation yields phase diagrams which are sometimes even qualitatively incorrect, accurate results are obtained from transfer matrix finite size scaling calculations. For a certain range of interaction parameters, the model is shown to violate the ordinary universality hypothesis. Received: 3 November 1997 / Revised: 31 March 1998 / Accepted: 7 April 1998     

Quantum field theory of phase transitions in Fermi systems

The theory of fermion phase transitions is reviewed from a unified field theoretic standpoint, based on the diagrammatic perturbation expansion of a generalized matrix propagator. Transitions from a normal to a condensed phase are characterized by the spontaneous appearance of long-range order and (in the presence of a suitable infinitesimal external field) broken symmetry. This is illustrated by the ferromagnetic, solid, superconducting and spindensity wave ground states. The phenomenon is explained qualitatively as caused by the creation of a long-range internal field, F, due to the interactions between particles. This field establishes long-range order in the system, and is in turn itself established by the long-range order, in a self-consistent fashion. The mechanism here is expressed quantitatively in terms of a self-consistent Dyson equation relating a generalized matrix propagator, G, to a proper self-energy matrix, Σ. The off-diagonal elements of G describe ‘anomalous’ propagation processes which are characteristic for the condensed phase, and they yield directly the long-range order parameters. The Σ-matrix is just the potential of the internal field. The method is illustrated by applying it to the ferromagnetic phase of a system with δ-function interaction between particles. Finally, the technique is used to derive the vertex part equation for the transition point.     

Nonlocal potential and optical properties of solids

Summary The theory of the RPA optical response of a solid has been generalized in order to take into account also the possible presence of spatially nonlocal potentials in the Hamiltonian. Explicit expressions for first- and second-order susceptibilities are given in the new framework. The expressions obtained depend on the matrix elements of operators of the form of a commutator of a component of the position operatorr and an operator that commutes with the lattice translations. The problem of the evaluation of these matrix elements is solved in a simple manner by introducing an auxiliary, periodic position operator,XXXr. In such a way a general formulation is obtained that preserves the gauge invariance. As an application of the new theory, the second harmonic generation (SHG) from a semiconductor in a simple two-band model has been studied. The differences between our correct gauge-invariant results and those obtained in the usual local approximation is an indication of a slow convergence of the expressions obtained in the local approximation.     

Ab initio Compton maps of small molecules

A closed form expression for the evaluation of directional Compton profiles (DCP) from the position space one-electron reduced density matrix expanded in Cartesian Gaussian basis functions is presented. The Compton map, i.e. a two-dimensional contour plot of the DCP function J(q) in a selected plane, is introduce as a convenient method for describing the DCP Examples of theoretical Compton maps are given for the hydrogen molecule ion (both ground and excited states), water, ammonia, ethylene and ¹A₁ methylene molecules in their ground states. Compton maps generated with Hartree-Fock, configuration interaction and density functional theory methods are compared.     

Some considerations on the restoration of Galilei invariance in the nuclear many-body problem

The effects of the restoration of Galilei invariance in the nuclear many-body problem on the energies of simple bound states are investigated. As examples we consider the oscillator ground states of ⁴He, ¹⁶O and ⁴⁰Ca as well as the various hole states with respect to these reference configurations. Density-independent as well as density-dependent interactions are studied. It turns out that the full restoration of Galilei-invariance yields considerable contributions on top of the trivial 1/A effect resulting from removing the center-of-momentum part of the Hamiltonian. Received: 20 February 2001 / Accepted: 10 May 2002     

On kaonic hydrogen. Phenomenological quantum field theoretic model revisited

We argue that due to isospin and U-spin invariance of strong low-energy interactions the S-wave scattering lengths a ⁰ ₀ and a ¹ ₀ of ˉN scattering with isospin I = 0 and I = 1 satisfy the low-energy theorem a ⁰ ₀ +3a ¹ ₀ = 0 valid to leading order in chiral expansion. In the model of strong low-energy ˉN interactions at threshold (Eur. Phys. J. A 21, 11 (2004)) we revisit the contribution of the Σ(1750) resonance, which does not saturate the low-energy theorem a ⁰ ₀ +3a ¹ ₀ = 0, and replace it by the baryon background with properties of an SU(3) octet. We calculate the S-wave scattering amplitudes of K^-N and K^-d scattering at threshold. We calculate the energy level displacements of the ground states of kaonic hydrogen and deuterium. The result obtained for kaonic hydrogen agrees well with recent experimental data by the DEAR Collaboration. We analyse the cross-sections for elastic and inelastic K^-p scattering for laboratory momenta 70MeV/c < p _K < 150MeV/c of the incident K^--meson. The theoretical results agree with the available experimental data within two standard deviations.     

Application of symmetry coupling coefficients in zero-field splitting of d5 ion complexes

Symmetry coupling coefficients and symmetry reduced matrix elements are used in calculating the minimum required matrix elements required to determine the analytical expressions for the three ⁶ A ₁ ground-state energy levels for a d⁵ ion in a weak crystal field of tetragonal symmetry. Expressions for the spin hamiltonian parameters a, D, F and G are derived, from which the effect of spin-orbit coupling and the tetragonal component of the crystal field are examined. The parameters describe the form of the hamiltonian and consequently the spin eigenfunctions and eigenvalues of the ground state where a is a measure of the isotropic component whereas D, F and G measure the tetragonal component of the interaction giving rise to the zero-field splitting. Some experimental results are examined.     

Mixed spin ladders with exotic ground states

We study the “mixed spin” isotropic ladder system having S=1 spins on one leg and S=1/2 spins on the other, with general-type exchange interactions between spins on neighboring rungs. A set of model Hamiltonians with exact ground states in the form of a certain matrix product wave function is obtained. We show that sufficiently strong frustration can lead to exotic singlet ground states with infinite (exponential) degeneracy. We also list a couple of rather simple models with nontrivial ground states, including a model with only bilinear exchange. Received: 2 December 1997 / Accepted: 28 January 1998     

Theoretical investigation of the ultrafast NeNePo spectroscopy of Au 4 and Ag 4 Clusters

Ultrafast ground state nuclear dynamics of Au₄ and Ag₄ is theoretically explored in the framework of negative ion - to neutral - to positive ion (NeNePo) pump-probe spectroscopy based on the ab initio Wigner distribution approach. This involves the preparation of a nonequilibrium neutral ensemble by pump induced photodetachment of a thermal anionic ground state distribution, gradient corrected DFT classical trajectory simulations “on the fly” on the neutral ground state, and detection of the relaxation process of the ensemble in the cationic ground state by a time-delayed probe pulse. In Au₄, the initially prepared linear structure is close to a local minimum of the neutral state giving rise to characteristic vibrations in the signals for probe wavelength near the initial Franck-Condon transition. A timescale of ∼1 ps for the structural relaxation towards the stable rhombic D_2h neutral isomer was determined by the increase of the signal for probe wavelength in vicinity of the vertical ionization energy of the rhombic structure. In contrast, the relaxation dynamics in Ag₄ is characterized by normal mode vibrations since both the initially prepared anionic ground state and the neutral ground state have rhombic minimum geometries. Thus, time-resolved oscillations of pump-probe signals are fingerprints of structural behaviour which can be used experimentally for the identification of particular isomers in the framework of NeNePo spectroscopy. Received 22 December 2000     

Rotation of a self-bound many-body system

We discuss the rotational excitations of highly quantum many-body systems (for example, polyatomic molecules or microdroplets of helium). For a general system, the states F?, where and ? is a rotationally invariant ground or vibrational state, are shown to be eigenfunctions of L ² and L_z , with eigenvalues L(L+1)? ² and L? (for even L). These wavefunctions preserve the translational invariance and the permutation and inversion symmetries of the N-particle state ?. For harmonic pair interactions, the f = 1 wavefunctions are shown to be exact eigenstates of the N-body hamiltonian. For large N, the states F?(f=1) represent surface oscillations of the type first proposed by Bohr. An inequality for the rotational excitation energy is obtained variationally; it depends on two, three, and four-particle correlations. Other translationally invariant angular momentum eigenfunctions are also discussed.     

Atom in an elliptically polarized resonance field: Exact stationary solution

An analytical method is developed for finding the exact stationary solution for the density matrix of atoms in a monochromatic resonance field of arbitrary ellipticity and intensity. A solution for the transitions F _g=F → F _e=F+1 (F _g and F _e are the angular momenta of the ground and excited states) is obtained in an analytical invariant form. The properties of this solution are investigated. Pis'ma Zh. éksp. Teor. Fiz. 64, No. 1, 8–12 (10 July 1996)     

Density of states in random lattices with translational invariance

We propose a random matrix approach to describe vibrations in disordered systems. The dynamical matrix M is taken in the form M = AA ^T , where A is a real random matrix. It guaranties that M is a positive definite matrix. This is necessary for mechanical stability of the system. We built matrix A on a simple cubic lattice with translational invariance and interaction between nearest neighbors. It was found that for a certain type of disorder acoustical phonons cannot propagate through the lattice and the density of states g(ω) is not zero at ω = 0. The reason is a breakdown of affine assumptions and inapplicability of the macroscopic elasticity theory. Young modulus goes to zero in the thermodynamic limit. It reminds of some properties of a granular matter at the jamming transition point. Most of the vibrations are delocalized and similar to diffusons introduced by Allen, Feldman, et al., Phil. Mag. B 79, 1715 (1999). We show how one can gradually return rigidity and phonons back to the system increasing the width of the so-called phonon gap (the region where g(ω) ∝ ω²). Above the gap the reduced density of states g(ω)/ω² shows a well-defined Boson peak which is a typical feature of glasses. Phonons cease to exist above the Boson peak and diffusons are dominating. It is in excellent agreement with recent theoretical and experimental data.     

Pairing mechanism in the doped Hubbard antiferromagnet: the 4×4 model as a test case

We introduce a local formalism, in terms of eigenstates of number operators, having well defined point symmetry, to solve the Hubbard model at weak coupling on a N × N square lattice (for even N). The key concept is that of W = 0 states, that are the many-body eigenstates of the kinetic energy with vanishing Hubbard repulsion. At half filling, the wave function demonstrates an antiferromagnetic order, a lattice step translation being equivalent to a spin flip. Further, we state a general theorem which allows to find all the W = 0 pairs (two-body W = 0 singlet states). We show that, in special cases, this assigns the ground state symmetries at least in the weak coupling regime. The N = 4 case is discussed in detail. To study the doped half filled system, we enhance the group theory analysis of the 4×4 Hubbard model introducing an Optimal Group which explains all the degeneracies in the one-body and many-body spectra. We use the Optimal Group to predict the possible ground state symmetries of the 4×4 doped antiferromagnet by means of our general theorem and the results are in agreement with exact diagonalization data. Then we create W = 0 electron pairs over the antiferromagnetic state. We show analitycally that the effective interaction between the electrons of the pairs is attractive and forms bound states. Computing the corresponding binding energy we are able to definitely predict the exact ground state symmetry. Received 24 October 2000