Showing papers on "Coherent states published in 1982"

Large N limits as classical mechanics

Abstract: This paper discusses the sense in which the large $N$ limits of various quantum theories are equivalent to classical limits. A general method for finding classical limits in arbitrary quantum theories is developed. The method is based on certain assumptions which isolate the minimal structure any quantum theory should possess if it is to have a classical limit. In any theory satisfying these assumptions, one can generate a natural set of generalized coherent states. These coherent states may then be used to construct a classical phase space, derive a classical Hamiltonian, and show that the resulting classical dynamics is equivalent to the limiting form of the original quantum dynamics. This formalism is shown to be applicable to the large $N$ limits of vector models, matrix models, and gauge theories. In every case, one can explicitly derive a classical action which contains the complete physics of the $N=\ensuremath{\infty}$ theory. "Solving" the $N=\ensuremath{\infty}$ theory requires minimizing the classical Hamiltonian, and this has been possible only in simple theories. The relation between this approach and other methods which have been proposed for deriving large $N$ limits is discussed in detail.

Coherent states for the time-dependent harmonic oscillator

Abstract: Exact coherent states for the time-dependent harmonic oscillator are constructed. These new coherent states have most, but not all, of the properties of the coherent states for the time-independent oscillator. For example, these coherent states give the exact classical motion, but they are not minimum-uncertainty states.

Generation of Squeezed Coherent States via a Free-Electron Laser

Abstract: Spontaneous radiation from a magnetic wiggler or undulator as used in a free-electron laser is shown to be in a squeezed state for a low-density electron beam. It is pointed out that the problem is formally analogous to radiation from a Josephson junction.

Generalized coherent states and the uncertainty principle

Abstract: We derive from a dynamical symmetry property that the linear and nonlinear Schr\"odinger equations with harmonic potential possess an infinite string of shape-preserving coherent wave-packet states with classical motion. Unlike the Schr\"odinger state with $\ensuremath{\Delta}x\ensuremath{\Delta}p=\frac{\ensuremath{\hbar}}{2}$, the uncertainty product can be arbitrarily large for these states showing that classical motion is not necessarily linked with minimum uncertainty. We obtain a generalization of Sudarshan's diagonal coherent-state representation in terms of these states.

Semiclassical approximation in the coherent states representation

Abstract: This paper presents a semiclassical theory for the computation of matrix elements of the type 〈u‖v〉 when either one or both ‖u〉 and ‖v〉 are coherent states (in different representations). Our results can be considered as an extension of Miller’s semiclassical theory [Adv. Chem. Phys. 25, 69 (1974)]. Such an extension has been presented also by Heller [J. Chem. Phys. 66, 5777 (1977)]. We were able to simplify considerably some of Heller’s results by exploiting the canonical properties of the classical coherent variables. This enabled us to relate the elements 〈u‖v〉 to certain generalized, complex generator functions in a manner that is very similar to the relations that appear in the original Miller’s theory. The advantages that are inherent in the coherent states representation are illustrated in a few elementary examples. We were able to derive an excellent approximation to the eigenstates of the harmonic oscillator which is valid even for the ground state. Furthermore, we have demonstrated that it is po...

Path integral for coherent states of the dynamical group SU(1,1)

Abstract: Path integrals over coherent states of the dynamical group (noninvariance group) SU(1,1) are constructed. From the continuous limit the relevant classical dynamics is extracted and is shown to take place in a curved phase space of the form of a Lobachevskii plane. Applications are made to the harmonic oscillator, a model of superfluid helium, the Morse oscillator, and the hydrogen atom. It is shown that when SU(1,1) is the relevant dynamical group the motion will appear oscillator‐like on the Lobachevskii plane.

Quantum manifestations of classical stochasticity. II. Dynamics of wave packets of bound states

Abstract: In this paper we consider some of the consequences of classical stochasticity phenomena in the quantum mechanical Henon–Heiles and Barbanis systems. To explore classical–quantum analogies we have introduced a quantum mechanical phase space based on the coherent state representation. Quantum Poincare maps (QPMs) were constructed from contour plots of the stationary phase‐space densities. We have observed a correlation between the topological features of a QPM at an eigenenergy E and the sensitivity ‖dE/de‖ of that energy to the strength e of the nonlinear coupling. States with extreme values of ‖dE/de‖, corresponding to both high and to low values of ‖dE/de‖, show regular regions in the quantum phase space, while states with intermediate values of ‖dE/de‖ span large parts of the quantum phase‐space regions. These general features of the QPMs apply for almost each energy multiplet, and no qualitative change in the character of the QPMs was observed above the classical critical energy Ec for the stochastic t...

Photon statistics of a free-electron laser

Abstract: A fully quantized theory of the free-electron laser in the small-signal regime is presented which allows for a calculation of the photon statistics. For an initial vacuum, we find photon antibunching if the electron momentum is below resonance. We conjecture that, in general, the free-electron laser preserves coherent states only in the absence of gain.

Minimum-uncertainty coherent states for certain time-dependent systems

Abstract: Nieto and Simmons have defined and studied coherent states for arbitrary potentials $V(q)$. We show how to extend their results to certain time-dependent potentials $V(q,t)$. For each $V(q)$ there is a $V(q,t)$, for which we can construct time-dependent coherent states.

Comments on the coherent-state representation of a scalar field in the early universe

Abstract: Previous work on the coherent states of a cosmological scalar field is extended to illustrate the effect of spacetime curvature on the coherent-state parametrization. Coherent states for the "flat Kasner" ("Rindler wedge") cosmology are constructed as an example. It is shown that the coherent-state representation is invariant under a conformal transformation which does not alter the definition of positive frequency.

Measures for Path Integrals

Abstract: By exploitation of the overcompleteness of coherent states expressions are presented for path integrals in terms of genuine (Wiener) path-space measures for driven harmonic oscillators which when projected onto the subspace spanned by coherent-state matrix elements yield the appropriate quantum mechanical propagator.

Non-resonant effects in the fluorescent Dicke model. II. Semiclassical and quantal results

Abstract: For pt.I see ibid., vol.14, p.4171 (1981). Semiclassical and quantal time-dependent results are presented for a model of N identical two-level atoms occupying the same site (the Dicke model) and driven by a CW off-resonance laser field. The exact semiclassical time-dependent solutions are derived from an analysis of the Fokker-Planck equation for the system in the atomic coherent states representation. Steady-state behaviour predicted by these solutions is in agreement with that obtained from the exact quantal steady-state analysis in the thermodynamic limit N to infinity . The semiclassical theory predicts (in the steady state) one type of fluorescent spectrum, which is a single sharp line ( delta function) centered at the driving field frequency. This is like the case at exact resonance and below threshold. Quantum mechanically, analytical results are obtained in the strong-field limit and within the secular approximation of the master equation: the fluorescence spectrum is the usual dynamical Stark triplet, apart from a cooperative factor N2. The absorption spectrum and the second-order intensity autocorrelation function are also calculated. Numerical results are also presented for finite N(N

Gauge invariance in quantum mechanics: charged harmonic oscillator in an electromagnetic field

Abstract: The gauge-invariant formulation of quantum mechanics is applied to the charged harmonic oscillator in an electromagnetic field in the electric dipole approximation to obtain the probability that the oscillator is in a particular state at time t. This probability is compared with the corresponding 'probability' calculated from the conventional approach to the interaction of radiation with matter using the interaction A.p. The probabilities do not agree with each other. From the principle of gauge invariance it is concluded that the probability calculated from the gauge-invariant formulation is correct in this case, and that the conventional approach in general is incorrect.

Role of quark-gluon degenerate states in perturbative quantum chromodynamics

Abstract: Motivated by the fact that the noncancellation of the infrared divergences in quantum chromodynamics may be avoided by using the soft degenerate states or the coherent states in the initial state, we examine possible effects of introducing the degenerate states on the one-loop finite piece in the hard-scattering cross sections like $q\overline{q}\ensuremath{\rightarrow}\ensuremath{\gamma}X$ in the Drell-Yan process. We find the effects of the soft degenerate states cancel out among themselves leaving no finite contribution to the cross sections.

Semicoherent states and the group ISp(2, R)

Abstract: The properties of two structures arising from a particular subset of the general coherent states of ISp(2, R) are studied. At the quantum level, these states support a Hilbert space of analytic functions in two variables which generalizes the Bargmann-Segal space. At a classical level they generate a symplectic manifold on which a Hamiltonian flow is obtained through dequantization via the time-dependent variational principle. This flow provides an approximate description of the coupled motion of the centre of a wave packet and its covariance matrix in phase space.

Relationship Between the Interacting Boson Model and the Bohr Collective Hamiltonian

Abstract: It is demonstrated that the Interacting Boson Model I (IBM), which is described by a Hamiltonian of six coupled harmonic oscillators, (one s-boson and 5 d-bosons), where the total number of bosons, N, is constant of the motion, can be transformed into a Bohr-Mottelson model (BMM) described by a Hamiltonian with the familiar five dimensional quadrupole oscillator degrees of freedom. The correspondence is one-to-one for a BMM acting in a sub-space of the full five-dimensional harmonic oscillator space. The proof depends on a well-known non-linear realization of the generators of SU(6) (which are the basic building blocks of the IBM) in terms of the five BMM bosons and the number N. The orthonormal basis vectors of the BMM are obtained. The relationship between the limiting symmetries of the IBM and the geometrically simple limits of the BMM is described with the aid of the concept of potential energy surface. The form of the BMM Hamiltonian is given for the adiabatic limit. Finally we show that previous work on this problem involving coherent states and the generator coordinate method is incomplete.

Quantum Statistical Properties of Photon and Phonon Fields in Brillouin Scattering with Intense Pumping

Abstract: The quantum statistical properties of Brillouin scattering of intense laser light are derived including the coupling of Stokes, anti-Stokes and phonon modes, if the anti-Stokes interaction prevails. Making use of the coherent-state technique, the Heisenberg equations of this process are solved neglecting the loss mechanism, and the normal quantum characteristic function and the normal generating function are derived. The time dependences of the photon distribution and its factorial moments are demonstrated if the phonon, Stokes and anti-Stokes modes are initially in a coherent state and periodical anti-bunching of the field is found when the phases of the incident fields fulfil certain phase conditions; the field can also return to the coherent state again.

Dephasing in isolated one-dimensional quantum systems

Abstract: The time evolution of harmonic oscillator coherent states in one-dimensional symmetrical and non-symmetrical non-harmonic quantum systems is studied numerically. Recurrencies are found for the symmetrical system within a time scale of fifty classical oscillations by studying the initial state population probability as a function of time. For some of the initial wave packets, however, a decay like behaviour was observed in the time scale under investigation. The numerical results are discussed in terms of four different time scales.

Coherent state propagation in open systems

Abstract: We introduce the generalized coherent states (G.C.S.) as eigenstates of the unitarily equivalent representations of the annihilation operator. The G.C.S. extension in phase space evolves with time and keeps the uncertainly product (with correlation) at its minimum. The conditions for the propagation of the G.C.S. in a time-dependent field are derived. In the presence of dissipation, an equation of motion is found that describes the G.C.S. decay towards the ground state; its results are compared with those of non-linear Schrodinger equations.

Photon and phonon statistics of Brillouin scattering

Abstract: The statistical properties for the couples of modes in Brillouin scattering are derived making use of the coherent state technique. Assuming the initial fields to be coherent, it is shown that periodical antibunching, bunching as well as coherent state behaviour can occur, provided that the anti-Stokes interaction prevails. This is demonstrated with the help of the photocount distributions and their reduced factorial moments.

Photoelectron Counting Probabilities for Non-classical Fields

Abstract: The single-mode photoelectron counting formula derived using the Glauber-Sudarshan diagonal coherent state representation is generalised to fields for which no well behaved Glauber-Sudarshan P-distribution exists using the generalized P-representation. From this formula the photocount distributions for a number-state and a squeezed-state are calculated.

Coherent states with classical motion: from an analytic method complementary to group theory

Abstract: From the motivation of Schroedinger, that of finding states which follow the motion which a classical particle would have in a given potential, we discuss generalizations of the coherent states of the harmonic oscillator. We focus on a method which is the analytic complement to the group theory point of view. It uses a minimum uncertainty formalism as its basis. We discuss the properties and time evolution of these states, always keeping in mind the desire to find quantum states which follow the classical motion.

Coherent state versus localized state quantum dynamics of isomerization reactions

Abstract: Two physically reasonable models can be conceived to describe the quantum dynamics of isomerization processes: the localized state model and the coherent state model. This paper discusses the differences in the time behavior of these two models. For energies well above the reaction barrier, the two models give identical results, however, for energies near or below the barrier — the domain of the localized states — coherent states show a different behaviour.