Coherent State Method Research Articles

Nonlinear excitations in 1D ferromagnetic spin chains with anisotropic interactions

Abstract Nonlinear solitary-like and periodic-like excitations in a spin chain with a biquadratic anisotropic exchange interaction are investigated using coherent-state method combined with the Holstein–Primakoff bosonic representation of the spin operators. Using the idea of the shallow water wave approximation it has been shown that the modified terms of nonlinear Schrodinger equation are strongly restricted by the relation between the continuum approximation and the semi classical approximation. These relations may lead to three classes of the nonlinear Schrodinger equations. We derive solitary as well as the periodic solutions for each type of nonlinear Schrodinger-like equation for such a ferromagnetic chain.

Calculation of the multimode Franck–Condon factors based on the coherent state method

The equivalence of two ways for the calculation of overlap integrals, i.e. the Sharp–Rosenstock generating function method and the Doktorov coherent state method, has been proved. On the basis of the generating function of the overlap integrals, a new closed form expression for the Franck–Condon integrals for overlap multidimensional harmonic oscillators has been exactly derived. In addition, some useful analytical expressions for the calculations of the multimode Franck–Condon factors have been given.

Necessary and sufficient conditions for non-perturbative equivalences of largeNcorbifold gauge theories

Large N coherent state methods are used to study the relation between U(N) gauge theories containing adjoint representation matter fields and their orbifold projections. The classical dynamical systems which reproduce the large N limits of the quantum dynamics in parent and daughter orbifold theories are compared. We demonstrate that the large N dynamics of the parent theory, restricted to the subspace invariant under the orbifold projection symmetry, and the large N dynamics of the daughter theory, restricted to the untwisted sector invariant under "theory space'' permutations, coincide. This implies equality, in the large N limit, between appropriately identified connected correlation functions in parent and daughter theories, provided the orbifold projection symmetry is not spontaneously broken in the parent theory and the theory space permutation symmetry is not spontaneously broken in the daughter. The necessity of these symmetry realization conditions for the validity of the large N equivalence is unsurprising, but demonstrating the sufficiency of these conditions is new. This work extends an earlier proof of non-perturbative large N equivalence which was only valid in the phase of the (lattice regularized) theories continuously connected to large mass and strong coupling.

A unified and complete construction of all finite dimensional irreducible representations of gl(2∣2)

Representations of the non-semisimple superalgebra gl(2∣2) in the standard basis are investigated by means of the vector coherent state method and boson-fermion realization. All finite-dimensional irreducible typical and atypical representations and lowest weight (indecomposable) Kac modules of gl(2∣2) are constructed explicitly through the explicit construction of all gl(2)⊕gl(2) particle states (multiplets) in terms of boson and fermion creation operators in the super-Fock space. This gives a unified and complete treatment of finite-dimensional representations of gl(2∣2) in explicit form, essential for the construction of primary fields of the corresponding current superalgebra at arbitrary level.

The construction of some important classes of generalized coherent states: the nonlinear coherent states method

Considering some important classes of generalized coherent states known in the literature, we demonstrated that all of them can be created via conventional methods, i.e. the 'lowering operator eigenstate' and the 'displacement operator' techniques using the 'nonlinear coherent states' approach. As a result we obtained a 'unified method' to construct a large class of coherent states which have already been introduced by different prescriptions.

Coherent state construction of representations of osp(2|2) and primary fields of osp(2|2) conformal field theory

Representations of the superalgebra osp(2|2) and current superalgebra osp(2|2) (1) k in the standard basis are investigated. All finite-dimensional typical and atypical representations of osp(2|2) are constructed by the vector coherent state method. Primary fields of the non-unitary conformal field theory associated with osp(2|2) (1) k in the standard basis are obtained for arbitrary level k.

Coherent state construction of representations of osp(2$z.sfnc;2) and primary fields of osp(2$z.sfnc;2) conformal field theory

Representations of the superalgebra osp(2|2) and current superalgebra osp(2|2)(1)k in the standard basis are investigated. All finite-dimensional typical and atypical representations of osp(2|2) are constructed by the vector coherent state method. Primary fields of the non-unitary conformal field theory associated with osp(2|2)(1)k in the standard basis are obtained for arbitrary level k.

A novel algebraic scheme for describing nonrigid molecules

An algebraic scheme for describing nonrigid polyatomic molecules is introduced and used to characterize bending motion in ‘floppy’ triatomic/tetratomic species. The salient features of quasi-linear and quasi-bent molecules are classified systematically. In particular, the ( ν 5) bending vibration supported by the ground electronic state of fulminic acid (HCNO/DCNO) is shown to exhibit the predicted behavior for nonrigidity. Likewise, the ( ν 2) bending motion of magnesium hydroxide (MgOH/MgOD) demonstrates quantitative application of this novel approach to problems of spectroscopic interest. Effective potential energy functions for these large-amplitude degrees of freedom are extracted by exploiting the method of coherent states.

Chaotic behavior, collective modes, and self-trapping in the dynamics of three coupled Bose-Einstein condensates.

The dynamics of the three coupled bosonic wells (trimer) containing N bosons is investigated within a standard (mean-field) semiclassical picture based on the coherent-state method. Various periodic solutions (configured as pi-like, dimerlike, and vortex states) representing collective modes are obtained analytically when the fixed points of trimer dynamics are identified on the N=const submanifold in the phase space. Hyperbolic, maximum and minimum points are recognized in the fixed-point set by studying the Hessian signature of the trimer Hamiltonian. The system dynamics in the neighborhood of periodic orbits (associated with fixed points) is studied via numeric integration of trimer motion equations, thus revealing a diffused chaotic behavior (not excluding the presence of regular orbits), macroscopic effects of population inversion, and self-trapping. In particular, the behavior of orbits with initial conditions close to the dimerlike periodic orbits shows how the self-trapping effect of dimerlike integrable subregimes is destroyed by the presence of chaos.

Landau Theory of Shape Phase Transitions in the Cranked Interacting Boson Model

Landau theory of phase transitions is applied to quadrupole shapes of rotating atomic nuclei within the interacting boson model (IBM) with cranking. It is shown that the coherent-state method must be generalized to allow for non-Hermitian quadrupole tensors of the coherent-state coefficients, which results in important modifications of the cranking shape-phase diagram compared to previous non-IBM studies of rotating nuclei. The parameter space has two surfaces of the first-order phase transitions and a curve of the second-order phase transition at their intersection. The phase structure of the cranked IBM closely resembles systems with competing superconducting and normal phases.

Ensemble dynamics of intermittency and power-law decay

A spectral decomposition of the Frobenius–Perron operator is constructed for one-dimensional maps with intermittent chaos, using the method of coherent states. A technique using the spectral density function is applied to the the well-known cusp map, which generates weak type-II intermittency. Higher-order corrections are obtained to the leading 1/t long-time behavior of the x−x autocorrelation.

Spin phase-space semiclassics for weak spin orbit coupling

We apply the semiclassical spin coherent state method for the density of states by Pletyukhov et al (2002 Phys. Rev. Lett. 89 116601) in the weak spin–orbit coupling limit and recover the modulation factor in the semiclassical trace formula found by Bolte and Keppeler (1998 Phys. Rev. Lett. 81 1987; 1999 Ann. Phys., NY 274 125).

Focusing of beams into subwavelength area in an inhomogeneous medium

Propagation and focusing of nonparaxial Gaussian beams with spherical wavefront in a graded-index medium are investigated using quantum-theoretical method of coherent states. Explicit expressions for the trajectory and width of a beam taking into account all correction terms to the paraxial approximation have been obtained. Electromagnetic field distributions in longitudinal and lateral directions are simulated. Diffraction of strongly focused high-aperture wave beams is investigated theoretically. The ratio of intensities of evanescent and propagating fields is calculated for different values of focused spot.

Clebsch–Gordan coefficients of SU(3) in SU(2) and SO(3) bases

New algorithms are developed for the purpose of optimizing the efficient calculation of SU(3) Clebsch–Gordan coefficients in both SU(2)- and SO(3)-coupled bases. The new algorithms make use of the fact that highest weight states in a tensor product space are easily identified by vector coherent state methods. The methods are developed for SU(3) but apply to other compact semi-simple Lie groups.

QUANTUM DYNAMICS OF COUPLED BOSONIC WELLS WITHIN THE BOSE–HUBBARD PICTURE

We relate the quantum dynamics of the Bose–Hubbard model (BHM) to the semiclassical nonlinear equations that describe an array of interacting Bose condensates by implementing a standard variational procedure based on the coherent state method. We investigate the dynamics of the two-site BHM from the purely quantum viewpoint by recasting first the model within a spin picture and using then the related dynamical algebra. The latter allows us to study thoroughly the energy spectrum structure and to interpret quantally the classical symmetries of the two-site dynamics. The energy spectrum is also evaluated through various approximations relying on the coherent state approach.

Overlap integral for quantum skyrmions

Making use of the method of spin coherent states, we obtained an analytical form of the overlap integral for quantum skyrmions.

Possible existence of topological excitations in quantum spin models in low dimensions

The possibility of existence of topological excitations in the anisotropic quantum Heisenberg model in one and two spatial dimensions is studied using coherent state method. It is found that a part of the Wess-Zumino term contributes to the partition function, as a topological term for ferromagnets in the long wavelength limit in both one and two dimensions. In particular, the XY limit of the two-dimensional anisotropic ferromagnet is shown to retain the topological excitations, as expected from the quantum Kosterlitz-Thouless scenario.

Solving Gauge Invariant Systems without Gauge Fixing: The Physical Projector in 0+1 Dimensional Theories

The projector onto gauge invariant physical states was recently constructed for arbitrary constrained systems. This approach, which does not require gauge fixing nor any additional degrees of freedom beyond the original ones—two characteristic features of all other available methods for quantising constrained dynamics—is put to work in the context of a general class of quantum mechanical gauge invariant systems. The cases of SO(2) and SO(3) gauge groups are considered specifically, and a comprehensive understanding of the corresponding physical spectra is achieved in a straightforward manner, using only standard methods of coherent states and group theory which are directly amenable to generalisation to other Lie algebras. Results extend considerably the few examples available in the literature from much more subtle and delicate analyses implying gauge fixing and the characterization of modular space.

Soliton spin excitations in an anisotropic Heisenberg ferromagnet with octupole-dipole interaction

We investigate the nonlinear spin dynamics of an anisotropic Heisenberg ferromagnetic spin chain with octupole-dipole interaction in the semiclassical limit using the coherent-state method combined with the Holstein-Primakoff bosonic representation of spin operators. The dynamics is found to be governed by a generalized nonlinear Schr\odinger equation in the continuum limit. For specific values of the exchange, octupole-dipole interactions, and also of the anisotropy parameters, through Painlev\'e singularity structure analysis, we have identified an integrable spin chain model with soliton spin excitations. We carry out a multiple scale perturbation analysis to find the discreteness effect on the soliton excitations in the more general nonintegrable case.

Two signal processing problems involving coherent states methods

We discuss the relevance of the methods based on coherent states in signal processing applications, and illustrate them with a couple of practical examples, namely problems of waveform detection in a noisy environment, and problems of spectral analysis for nonstationary time series.