Coherent State Method Research Articles

A semiclassical trace formula using coherent states methods

We present a simple and rigorous proof of a ‘Gutzwiller type’ trace formula, using semiclassical formulas for the propagation of coherent states.

A pure quantum mechanical theory of parity effect in tunneling and evolution of spins

In recent years, the spin parity effect in magnetic macroscopic quantum tunneling has attracted extensive attention. Using the spin coherent-state path-integral method it is shown that if the HamiltonianH of a single-spin system hasM - fold rotational symmetry around z-axis, the tunneling amplitude 〈−S|e Ht |S〉 vanishes when S, the quantum number of spin, is not an integer multiple ofM/2, where |m〉 (m=-S, -S +1, ⋯, S) are the eigenstates of Sz. Not only is a pure quantum mechanical approach adopted to the above result, but also is extended to more general cases where the quantum system consists ofN spins, the quantum numbers of which can take any values, including the single-spin system, ferromagnetic particle and antiferromagnetic particle as particular instances, and where the states involved are not limited to the extreme ones. The extended spin parity effect is that if the Hamiltonian ℋ of the system ofN spins also has the above symmetry, then 〈m′N⋯m′2 m′1|e−H t |m 1 m 2⋯m N vanishes when ∑ =1 (m i−m′1) not an integer multiple ofM, where |m 1 m 2⋯m N〉=∏ α=1 |m a 〉 are the eigenstates of S a . In addition, it is argued that for large spin the above result, the so-called spin parity effect, does not mean the quenching of spin tunneling from the direction of ⊕-z to that of ±z.

Evolution of polarization in an inhomogeneous isotropic medium

The depolarization and rotation of the polarization plane of radiation propagating in a two-dimensional graded-index medium is investigated on the basis of the quantum-mechanical method of coherent states. It is shown that the degree of polarization of both linearly and circularly polarized radiation decreases with increasing distance as a result of interaction between the polarization (spin) and the path (orbital angular momentum) of the beam. The wave nature of the depolarization is emphasized. The depolarization decreases as the radiation wavelength decreases. It is found that the degree of polarization exhibits oscillations of pure diffraction origin during the propagation of light in a single-mode optical fiber. It is shown that the rotation of the polarization plane is nonuniform in character and depends on the offset and the tilt angle of the incident-beam axis relative to the fiber axis. The Berry phase is found to undergo oscillations of a wave nature during the propagation of radiation in an inhomogeneous medium. It is shown that the spread in the angle of rotation of the polarization plane increases with distance and can be determined from measurements of the degree of polarization of the radiation.

Coherent states map for MIC–Kepler system

The coherent states map for MIC–Kepler system is constructed. The quantization of this system is given by the coherent states method.

Vector coherent state realization of representations of the affine Lie algebra

The method of vector coherent states is generalized to study representations of the affine Lie algebra $\hat{sl}(2)$. A large class of highest weight irreps is explicitly constructed, which contains the integrable highest weight irreps as special cases.

Solitary waves in spin chains with biquadratic exchange and dipole-dipole interactions

Dynamical theory of solitary wave excitations in spin chains has been studied by a revised Hamiltonian in which the dipole-dipole and biquadratic exchange interactions are taken into account in addition to the Zeeman energy, uniaxial anisotropy and the exchange energy. Using the coherent states method combined with the Holstein-Primakoff bosonic representation of the spin operators, we have derived a nonlinear Schrödinger (NLS)-like equation. Several analytical solitary wave solutions of NLS-type equation have been presented in detail, with discussion of some of their implications for describing the propagation of spin waves. Some of the characteristics of these solitary waves, like their energy and the number of bosonic excitations involved in the solitary wave formation, have also been calculated.

Depolarization of light in a graded-index isotropic medium

Abstract The effect of depolarization of an incident pure state of polarization propagating through a graded-index multimode two-dimensional optical waveguide is described using the quantum-mechanical method of coherent states. It is shown that the degree of polarization for both the linearly and the circularly polarized radiation decreases with increasing distance owing to the interaction between the polarization (spin) and the beam trajectory (orbital moment). The wave nature of the depolarization is emphasized. The depolarization vanished when the wavelength tends to zero. Oscillations of the polarization degree of pure diffractional origin on propagation of light in a single-mode optical fibre are found.

Depolarization of light in a graded-index isotropic medium

Abstract The effect of depolarization of an incident pure state of polarization propagating through a graded-index multimode two-dimensional optical waveguide is described using the quantum-mechanical method of coherent states. It is shown that the degree of polarization for both the linearly and the circularly polarized radiation decreases with increasing distance owing to the interaction between the polarization (spin) and the beam trajectory (orbital moment). The wave nature of the depolarization is emphasized. The depolarization vanished when the wavelength tends to zero. Oscillations of the polarization degree of pure diffractional origin on propagation of light in a single-mode optical fibre are found.

The q-Deformed Coherent-State Method of Normally Ordering q-Boson Operators

We extend the newly proposed coherent-state method of normally ordering boson operators to a q-deformed boson case. With the help of q-derivative, some new q-boson operator iden tities are obtained.

Classical and quantum mechanics of non-Abelian Chern-Simons particles

We investigate the classical and quantum properties of a system of SU ( N) non-Abelian Chern-Simons (NACS) particles. After a brief introduction to the subject of NACS particles, we first discuss the symplectic structure of various SU ( N) coadjoint orbits which are the reduced phase space of SU ( N) internal degrees of freedom or isospins. A complete Dirac constraint analysis is carried out on each orbit and the Dirac bracket relations among the isospin variables are calculated. Then, the spatial degrees of freedom and interaction with external gauge field are introduced by considering the total reduced phase space which is given by an associated bundle whose fiber is one of the coadjoint orbits. Finally, the theory is quantized by using the coherent state method and various quantum mechanical properties are discussed in this approach. In particular, a coherent state representation of the Knizhnik-Zamolodchikov equation is given and possible solutions in this representation are discussed.

NN¯annihilation in largeNCQCD with ρ and ω mesons

We use classical/large ${\mathit{N}}_{\mathit{C}}$ (number of colors) QCD to study nucleon-antinucleon annihilation at rest. We include pion, \ensuremath{\rho}, and \ensuremath{\omega} fields in the classical dynamics, starting from the nonlinear sigma model. We begin with a spherical blob of pionic matter with zero baryon number and energy of twice the nucleon mass. This evolves according to the classical dynamics to pion and vector meson fields into the radiation zone. The radiation fields are quantized using the method of coherent states modified to include isospin and four momentum conservation. Empirical information is extracted from that coherent state. We find good agreement with data for single particle momentum and number spectra, and with branching ratios to many annihilation channels. All this emerges with nearly no free parameters.

Branching ratios in proton antiproton annihilation from Skyrmion dynamics

We use classical Skyrmion dynamics extended to include vector mesons to describe the mesons (π, ϱ, ω) coming from proton antiproton annihilation at rest as classical fields. We then quantize these fields by the method of coherent states. This treatment gives a nearly parameter free account of the major features of the pion branching ratios in annihilation.

Representation of the five-dimensional harmonic oscillator with scalar-valued U(5) ⊇ SO(5) ⊇ SO(3)–coupled VCS wave functions

Vector coherent state methods, which reduce the U(5) ⊇ SO(5) ⊇ SO(3) subgroup chain, are used to construct basis states for the five-dimensional harmonic oscillator. Algorithms are given to calculate matrix elements in this basis. The essential step is the construction of SO(5) ⊇ SO(3) irreps of type [v,0]. The methodology is similar to that used in two recent papers except that one-dimensional, as opposed to multidimensional, vector-valued wave functions are used to give conceptually simpler results. Another significant advance is a canonical resolution of the SO(5) ⊇ SO(3) multiplicity problem.

THEORY OF SPONTANEOUS RADIATION BY BOSONS IN QUASI-CLASSICAL TRAJECTORY-COHERENT APPROXIMATION

The first order quantum correction is obtained for the characteristics of spontaneous radiation as a functional of a classical trajectory by means of quasi-classical trajectory–coherent states method for relativistic spinless particle in an arbitrary external electro-magnetic field. It is shown that the power of boson radiation coincides up to O (ħ2), ħ → 0 with the power of electron radiation averaged over spin states calculated by the TC-states of the Dirac equation. Certain specific examples are considered on the base of a general formula for the radiation power in the non-relativistic approximation, in particular, an expression for the radiation power in an axially symmetric magnetic field is obtained.

Coherent state formulation of pion radiation from nucleon-antinucleon annihilation.

We assume that nucleon-antinucleon annihilation is a fast process leading to a classical coherent pion pulse. We develop the quantum description of such pion waves based on the method of coherent states. We study the consequences of such a description for averages of charge types and moments of distributions of pion momenta with isospin and four-momentum conservation taken into account. We briefly discuss the applicability of our method to annihilation at rest, where we find agreement with experiment, and suggest other avenues for its use.

SUBSONIC AND SUPERSONIC SOLITONS IN AN ANHARMONIC LINEAR CHAINS WITH SECOND-NEIGHBOUR INTERACTION

Based on the method of coherent states, the nonlinear effects caused by the interaction between electrons and acoustic lattice vibrations in an anharmonic linear chains are investigated in the secolid-neighbour interaction approximation. While the continous limits of the equations of motion is considered self -consistently, the cubic anharmonicity of the deformable potential leads to a new nonlinear equation for the electronic orobability amolitute, which gives a new solitary solution in the form of hyperelliptic integral. This shows that besides the bell-solitons there also exists a second type of solitary excitation with the shape of a kink.

On the supersymplectic homogeneous superspace underlying the OSp(1/2) coherent states

In this work Onofri and Perelomov’s coherent states methods are extended to the recently introduced OSp(1/2) coherent states. These latter are shown to be parametrized by points of a supersymplectic supermanifold, namely, the OSp(1/2)/U(1) homogeneous superspace, which is clearly identified with a supercoadjoint orbit of OSp(1/2) by exhibiting the corresponding equivariant supermoment map. Moreover, this supermanifold is shown to be a nontrivial example of Rothstein’s supersymplectic supermanifolds. More precisely, it is shown that its supersymplectic structure is completely determined in terms of SU(1,1)-invariant (but unrelated) Kähler 2-form and Kähler metric on the unit disc. This result leads to the definition of the notions of a super-Kähler supermanifold and a super-Kähler superpotential, the geometric structure of the former being encoded into the latter.

Slave fermions, slave bosons, and semions from bosonization of the two-dimensional t-J model.

We extend Abelian and non-Abelian bosonization formulas found in a previous paper, in combination with coherent-state methods, to present a systematic derivation of the slave-fermion, slave-boson, and semion representations of the two-dimensional t-J model in path-integral form. The slave-fermion and slave-boson representations are shown to arise from two different gauge fixing constraints introduced in the path-integral representation of the bosonized t-J model. For each representation we discuss the approximations leading to a mean-field theory. In the mean-field theory based on the semion representation, the holons are shown to be ``Dirac semions.''

A loop representation for the quantum Maxwell field

Quantization of the free Maxwell field in Minkowski space is carried out using a loop representation and shown to be equivalent to the standard Fock quantization. Because it is based on coherent state method, this framework may be useful in quantum optics. It is also well suited for the discussion of issues related to flux quantization in condensed matter physics. The authors' own motivation, however, came from a non-perturbative approach to quantum gravity. The concrete results obtained in this work for the Maxwell field provide independent support for that approach. In addition, they offer some insight into the physical interpretation of the mathematical structures that play, within this approach, an essential role in the description of the quantum geometry at Planck scale.

The Coherent-State Method of Normally Ordering Multimode Exponential Operators

This work shows that the coherent-state method provides us a very simple approach to normally ordering multimode exponential operators, many of which can't be normally ordered simply by the technique of integration within an ordered product (IWOP).