Showing papers on "Coherent states published in 1972"
TL;DR: In this paper, it was shown that the atomic coherent states are the quantum analogs of classical dipoles, and that they can be produced by classical fields, and the derivation of the properties of the quantum coherent states is made easier by the use of a powerful disentangling theorem for exponential angular momentum operators.
Abstract: For the description of an assembly of two-level atoms, atomic coherent states can be defined which have properties analogous to those of the field coherent states. The analogy is not fortuitous, but is shown to be related to the group contraction of exponential operators based on the angular momentum algebra to exponential operators based on the harmonic-oscillator algebra. The derivation of the properties of the atomic coherent states is made easier by the use of a powerful disentangling theorem for exponential angular momentum operators. A complete labeling of the atomic states is developed and many of their properties are studied. In particular it is shown that the atomic coherent states are the quantum analogs of classical dipoles, and that they can be produced by classical fields.
845 citations
TL;DR: In this article, all invariants, the coherent states and the Green function for a particle moving in time-dependent uniform perpendicular electric and magnetic fields are constructed, and the transition amplitudes and probabilities between the energy levels and their generating functions are constructed too.
59 citations
TL;DR: In this article, an exact solution for the retarded Green's function of the radiation field is calculated for a quantum model consisting of three interacting boson fields-photon, exciton, and phonon.
Abstract: Quantum field-theoretical methods are applied to the problem of determining how the exciton-lattice interaction affects the dispersion of an electromagnetic field associated with the exciton-radiation interaction. An exact solution for the retarded Green's function of the radiation field is calculated for a quantum model consisting of three interacting boson fields-photon, exciton, and phonon. The classical Green's function of a damped-harmonic-oscillator model of a dielectric is shown to be a special case of this quantum Green's function. Two sets of dispersion relations are derived; one set has well-defined energy, the other has well-defined momentum. Results of the theory clearly suggest that the exciton-lattice interaction is capable of literally damping out the "polariton" effects associated with the exciton-radiation interaction in the field solutions with well-defined energy. A Poynting theorem based on the classical model is also derived which includes effects of both spatial dispersion and damping.
57 citations
TL;DR: In this article, the authors constructed a simple model which exhibits some of the properties discussed by van Hove in his study of the Pauli master equation and showed that in the limit as the interaction becomes weaker and of longer range, the evolution of the chosen oscillator becomes a diffusion equation.
Abstract: We construct a simple model which exhibits some of the properties discussed by van Hove in his study of the Pauli master equation. The model consists of an infinite chain of quantum oscillators which are coupled so that the interaction Hamiltonian is quadratic. We suppose the chain is in equilibrium at an inverse temperature β and study the return to equilibrium when a chosen oscillator is given an arbitrary perturbation. We show that in the limit as the interaction becomes weaker and of longer range, the evolution of the chosen oscillator becomes a diffusion equation. Moreover we give an explicit example where the evolution of the chosen oscillator has the Markov property and where the Pauli master equation is exactly satisfied.
43 citations
TL;DR: In this article, the order parameter in an assembly of superconducting grains may be represented by a set of vectors in the complex plane, which achieve ordering through a phase transition between "paracoherent" and coherent states once Josephson coupling is established between grains.
30 citations
ESRO1
TL;DR: In this article, a unified analysis of the inelastic scattering of ions by metal surfaces is formulated for a large class of “stripping reaction” experiments such as Field Ion Emission, Field Ion Desorption, Ion Neutralization, etc.
28 citations
TL;DR: In this paper, a relativistic formulation of the simple harmonic oscillator is discussed, which is derived from a Lorentz-invariant variational principle, and it differs from the customary HOG formulation in that it is derivable from a Lipschitz invariant principle.
Abstract: A relativistic formulation of the simple harmonic oscillator is discussed. It differs from the customary formulation in that it is derivable from a Lorentz-invariant variational principle. A consistent relativistic quantization procedure is thereby admitted.
27 citations
TL;DR: Measurement of the two-photon time distribution in a mixture of light from a He-Ne laser and a Gaussian source of the same central frequency agrees well with the prediction of coherence theory when the laser is represented by a single coherent state.
Abstract: Measurement of the two-photon time distribution in a mixture of light from a He–Ne laser and a Gaussian source of the same central frequency agrees well with the prediction of coherence theory when the laser is represented by a single coherent state. The peak in the distribution near zero time difference is made up of contributions due to the second-order interference between pairs of Gaussian photons and between laser and Gaussian photons.
17 citations
TL;DR: In this article, a model of hadron states is presented by means of minimum-uncertainty wave packets in transverse internal position or momentum operators which can be defined in the infinite-momentum frame (IMF) basis for the Poincare group.
Abstract: A convenient description of hadron states is presented by means of minimum-uncertainty wave packets in transverse internal position or momentum operators which can be defined in the infinite-momentum frame (IMF) basis for the Poincare group. The center of mass of the hadron is described either by its momentum or its IMF position operator, while its internal structure is fixed by taking coherent states symmetrical in the internal co-ordinates. The resulting physical picture of hadrons as extended objects with a stable structure agrees with Yang’s model of droplets with optimum universal size. The reduction of products of states in the infinite-momentum frame with respect to our basis introduces Clebsch-Gordan coefficients which asymptotically depend only on certain scaling variables, thus allowing us to trace their emergence to a general framework. These are precisely the scaling variables connected with different high-energy regions where limiting behavior patterns for hadronic cross-sections, like diffraction, Bjorken scaling, Feynman scaling and limiting fragmentation are known to occur.
15 citations
TL;DR: In this article, a quantum description of light passing through the turbulent atmosphere was developed for arbitrary statistics of incident light, moments of arbitrary order are calculated and a modified photodetection equation is derived.
Abstract: A quantum description of light passing through the turbulent atmosphere recently proposed by Tatarski is developed for arbitrary statistics of incident light, moments of arbitrary order are calculated and a modified photodetection equation is derived. Another description by Diament and Teich is shown to be also quantum but both the descriptions are valid under various conditions. A comparison of the Tatarski and Diament and Teich descriptions is performed and results for the monochromatic coherent state of a field are discussed as a special case.
14 citations
TL;DR: In this article, the normalizable states that minimize the uncertainty product of the oscillator phase operators are determined and some of their physical properties are discussed, and a physical classification of these states has been made and the class of ''analogous'' states to the well-known coherent states is defined.
Abstract: The normalizable states that minimize the uncertainty product of the oscillator phase operators are determined and some of their physical properties are discussed. A physical classification of these states has been made and the class of ``analogous'' states to the well‐known coherent states is physically defined.
TL;DR: The Green's functions for the simplest quantum mechanical systems are presented in closed analytical forms in this article, including linear harmonic oscillators, the three-dimensional isotropic oscillator, the Morse oscillator and the Kratcer potential.
Abstract: The Green's functions for the simplest quantum mechanical systems the linear harmonic oscillator, the three-dimensional isotropic oscillator, the Morse oscillator, the Kratcer potential, and the double-minimum potential V(x) = (mw2/2)(/x/−R)2 are presented in closed analytical forms.
TL;DR: In this article, the interaction of a two-level atom with the radiation field in a cavity is discussed in quantum mechanical terms that are closely analogous to those used in discussing the classical Langevin equation; the quantum Langevin equations for this case, however, is nonlinear.
Abstract: The interaction of a two-level atom with the radiation field in a cavity is discussed in quantum mechanical terms that are closely analogous to those used in discussing the classical Langevin equation; the quantum Langevin equation for this case, however, is nonlinear. A technique is developed for finding the measurable properties of the solution of the equations exactly; the properties of the solution are compared with those for the harmonic oscillator.
TL;DR: In this article, a class of perturbation problems is considered, in which the Rayleigh-Schrodinger perturbations series for the ground state eigenvalue and eigenvector are presumed to diverge.
Abstract: A class of perturbation problems is considered, in which the Rayleigh-Schrodinger perturbation series for the ground state eigenvalue and eigenvector are presumed to diverge. This class includes the (:φ2m:g(x))2, (m=2, 3) quantum field theory models and the quantum mechanical anharmonic oscillator. It is shown that, using matrix elements and vectors which occur in the series coefficients, one may construct convergent approximants to the eigenvalue and eigenvector. Results of a calculation of the ground state energy of thex4 anharmonic oscillator are given.
TL;DR: In this article, the coherent state formalism is applied to the calculation of the phonon frequencies in quantum crystals, and the normal mode frequencies are determined using an expansion in powers of the displacement.
Abstract: The coherent state formalism is applied to the calculation of the phonon frequencies in quantum crystals. The normal mode frequencies are determined using an expansion in powers of the displacement...
TL;DR: In this paper, a harmonic oscillator in a uniform, time varying electric field for which an exact solution is easy to obtain using the Magnus expansion for the evolution operator is provided. But the wavefunction of the oscillator is obtained in the adiabatic and impulse limits assuming the field to be switched on in an exponential fashion.
Abstract: When a system of particles in a bound state is placed in an external field the quantum state of the system depends on the manner in which the field is produced. The two limiting cases of interest are the adiabatic and impulse limits. Since the system does not approach a stationary state in either limit, in general, it is necessary to consider solutions of the time dependent Schrodinger equation. An example of this approach is provided by the problem of a harmonic oscillator in a uniform, time varying electric field for which an exact solution is easy to obtain using the Magnus expansion for the evolution operator. This operator contains the position and momentum in a particularly simple way that allows it to be interpreted in terms of position and momentum shifts produced by the field. The wavefunction of the oscillator is obtained in the adiabatic and impulse limits assuming the field to be switched on in an exponential fashion. Results obtained for these two limiting cases are then shown to be independent of the manner in which the field reaches its final steady value.
TL;DR: By means of a coherent state representation, Capel's theory of the de Haas-van Alphen effect in the case of magnetic breakdown derived using a pathological group is shown to be valid for arbitrary magnetic flux as discussed by the authors.
CERN1
TL;DR: In this article, a method for calculating multiple coherent bremsstrahlung in crystals making use of the coherent state of the radiation was proposed, and an asymptotic solution of the equations of motion is given and discussed.
Abstract: It is recalled that the Born approximation might become grossly insufficient for calculating the bremsstrahlung of electrons in crystals when the energy of the incoming electron is sufficiently high. We therefore devised a method for calculating multiple coherent bremsstrahlung in crystals making use of the coherent state of the radiation. The method is valid when pair creation is negligible and, therefore, when the energy of the photon is very small as compared to the energy of the electron. An asymptotic solution of the equations of motion is given and discussed. The solution is valid for positrons and not for electrons.
TL;DR: Second quantization is used to expand the product of two harmonic oscillator wavefunctions, of two different particles, centred on different sites, in terms of relative and center of mass coordinate dependent functions.
Abstract: Second quantization is used to expand the product of two harmonic oscillator wavefunctions, of two different particles, centred on different sites, in terms of relative and centre of mass coordinate dependent functions.