Showing papers on "Coherent states published in 1974"
TL;DR: In this article, the authors introduce even and odd coherent states, where the transition amplitudes between the energy levels of a singular nonstationary oscillator in the case of constant frequency in the remote past and future and generating functions for these amplitudes are obtained, by a method similar to the usual coherent-state method.
513 citations
93 citations
Journal Article•
66 citations
TL;DR: In this article, a harmonic oscillator is studied with the result that the oscillator performs a simple harmonic motion very stable in phase, and the amplitude changes slowly and at random.
Abstract: Classical electrodynamics with the hypothesis of a universal, Lorentz invariant, background radiation (stochastic electrodynamics) has been proposed as a possible alternative to quantum electrodynamics. The stochastic equations of motion of a charged particle are derived according to this theory, and they are compared with those of Brownian motion. A development of the equations in powers of the fine-structure constant α is considered. The harmonic oscillator is studied with the result that the oscillator performs a simple harmonic motion very stable in phase. The amplitude changes slowly and at random. The mean values of the kinetic and potential energy are calculated and agree quite well with the results of quantum electrodynamics up to first order in α. The existence of excited states is shown which prove to be very similar to the coherent states of the quantum oscillator. The calculated rate of spontaneous emission of radiation agrees with the result of quantum electrodynamics but the line width does not agree. Arguments are given which show that the quantum line width calculated according to the Weisskopf-Wigner theory cannot be correct in the case of the oscillator. A general expression for the evolution of the expectation value of any observable of the oscillator in quantum electrodynamics is also derived.
57 citations
TL;DR: In this paper, the authors considered the quantum dynamics of a parametric interaction of the electromagnetic field with a nonlinear medium, and the three nonlinear coupled Heisenberg equations of motion were solved under the short-time approximation.
Abstract: The quantum dynamics of a parametric interaction of the electromagnetic field with a nonlinear medium is considered. The three nonlinear coupled Heisenberg equations of motion are solved under the short-time approximation. The characteristic function for the normal ordering rule of association is evaluated. This function is then used to obtain the time dependence of the density operator. Assuming that the initial state of the system is a coherent state, explicit expressions for the diagonal coherent state representation of the reduced density operators for the pump as well as for the signal mode are obtained. For the pump mode, the initially coherent state remains coherent, whereas for the signal mode the diagonal coherent state representation is found to be a gaussian distribution whose variance is proportional to the average number of photons initially present in the pump mode.
49 citations
TL;DR: In this article, it was shown that for a wide variety of configurations of the pion field density operator, the density operator can be written in diagonal form in the coherent-state representation.
Abstract: Hadron production at high energies is discussed in terms of coherent states. We suggest that the scattering operator and the pion field density operator take on simple forms in the coherent-state representation. In particular, we show that for a wide variety of configurations of the pion field the density operator can be written in diagonal form in the coherent-state representation. When this is possible, one obtains the statistical theory of pion production which we have discussed recently. We also construct a solvable unitary model in which the total, elastic, and inclusive cross sections go to constants at high energy, while the exclusive cross sections go to zero like a power of energy. In order to take into account the isotopic spin of the pions, we generalize the concept of coherent states and construct states with definite charge and isotopic spin.
37 citations
TL;DR: In this paper, a variational method for approximating the eigenstates of the Hamiltonian in relativistic quantum field theory is introduced, which provides a quantum-mechanical interpretation for solitons, some of which resemble extended particles.
33 citations
01 Jan 1974
33 citations
TL;DR: In this paper, a system of radiating oscillators coupled with atomic reservoirs is considered, and the radiation density operator is calculated in the interaction picture after elimination of the atomic variables, using the differential operator representation for coherent states.
31 citations
TL;DR: In this article, the most general form of minimality-preserving Hamiltonians is found and the uncertainty products ΔqΔp are calculated for some quadratic quantum systems.
TL;DR: In this paper, the system of coherent states for complex bounded homogeneous domains is constructed and the properties of the coherent states are investigated, and the question of selecting complete subsystems connected with discrete subgroups of the motion groups of Hermitian symmetric spaces is also studied.
TL;DR: In this article, a representation of spin operators in the space of coherent spin states is found, analogous to the coherent states of the harmonic oscillator, where polynomials of order 2S play an important role.
Abstract: Some properties of so called coherent spin states, analogous to the coherent states of the harmonic oscillator, are discussed. Polynomials of order 2S play an important role. The representation of spin operators in the space of coherent spin states is found. This representation is used to study the rotation operator.
TL;DR: In this article, the transformation properties of the density operator as well as its diagonal coherent-state representation when a plane monochromatic light is passed through a compensator followed by a rotator are investigated.
Abstract: We consider the transformation properties of the density operator as well as its diagonal coherent-state representation when a plane monochromatic light is passed through a compensator followed by a rotator. Special cases of unpolarized and polarized light are considered and the general form of the density operator and its coherent-state representation is determined.
TL;DR: In this article, the moments of the photon number of the emitted field are calculated for both spontaneous and stimulated coherent emissions by a large number of two-level atoms in a Dicke state.
Abstract: Photon statistics are obtained from exact closed-form solutions for both spontaneous and stimulated coherent emissions by a large number of two-level atoms in a Dicke state. Depending on the initial excitation level of the atoms, three types of photon statistics are obtained for the emitted radiation field. Moments of the photon number of the emitted field are calculated in the case of initial atomic coherent states as well as Dicke states, and in the case of n-photon stimulating pulses as well as coherent stimulating pulses. In the particular case of an initial "superradiant" Dicke state stimulated by a coherent-radiation field, the emitted radiation pulse is also fully coherent. In other cases the photon distributions undergo large fluctuations.
TL;DR: In this article, the Bloch coherent states for a spin or a system of spins and the Glauber coherent state for bosons are examined from the viewpoint of Lie algebras.
Abstract: The Bloch coherent states for a spin or a system of spins and the Glauber coherent states for bosons are examined from the viewpoint of Lie algebras. It is pointed out that the Bloch coherent states are vectors in the space spanned by the basis functions for an irreducible representation of the unitary unimodular group SU(2), and that the Glauber coherent states are vectors in the space spanned by the basis functions for the infinite‐dimensional irreducible representation of a contracted group of SU(2). A deeper understanding of many of the useful properties of these coherent states is gained.
TL;DR: In this paper, the radiation of an arbitrary time-dependent quadratic quantum system is calculated by means of the coherent-state method, and the results are shown to be consistent with the results in this paper.
TL;DR: In this paper, it was shown that a pure coherent state can be an eigenstate of the Hamiltonian of the noninteracting boson system when the symmetry breaking term is added to it.
Abstract: The coherent-state representation of the density operator for an ideal Bose gas in a thermal equilibrium is introduced. It is shown that a pure coherent state can be an eigenstate of the Hamiltonian of the non-interacting boson system when the symmetry breaking term is added to it. However, at the limit of the vanishing “classical field” only zero-energy states can be a coherent state. It is also proved that the pure coherent state is the lowest energy state among all the zero-momentum states. The temperature dependence of the coherent state is then discussed. The diminution of the coherent state can clearly be seen as the temperature rises from zero to the critical temperature.
TL;DR: In this article, a general method of representation of density operators in terms of outer products of coherent states with nonsingular weight function and only two real variables of integration for every mode is given.
TL;DR: In this article, the properties of the coherent state appearing in the Bose-Einstein condensation of an ideal Bose gas are discussed and the thermodynamic functions in the presence of such a coherent state are derived.
Abstract: The properties of the coherent state appearing in the Bose-Einstein condensation of an ideal Bose gas are discussed. The thermodynamic functions in the presence of such a coherent state are obtained. The density correlation function is derived. It is shown that the density correlation function reduces to the London-Placzek formula as temperature rises above the critical temperature of the Bose-Einstein condensation.
TL;DR: In this paper, the Hartree-Fock single particle wave functions of spherical nuclei are approximated by harmonic oscillator wave functions and the best fitting value of the oscillator parameter is calculated for each single particle state.
Abstract: Hartree—Fock single particle wave functions of spherical nuclei are approximated by harmonic oscillator wave functions. The best fitting value of the oscillator parameter is calculated for each single particle state. The systematics of the oscillator parameters is studied. The validity of the harmonic oscillator model is examined.
TL;DR: In this article, a general definition for the change of the coherence of photon fields is introduced, based on the comparison of the deviations from optimally fitted fully coherent states which are shown by the initial and final states.
Abstract: A general definition for the change of the coherence of photon fields is introduced. It is based on the comparison of the deviations from optimally fitted fully coherent states which are shown by the initial and final states. The disturbance of the coherence of a fully coherent state caused by forward scattering is treated as an example and compared with the results for the disturbance of coherence of second order obtained in a previous investigation.
TL;DR: In this paper, a non-diagonal representation for density operators of radiation in terms of coherent states is given, which involves only two integrations per mode, and the weight functions are expressed as coherence functions and occupation number space matrix elements of the density operators.
Abstract: Some new non-diagonal representations for density operators of radiation in terms of coherent states are given. These involve only two integrations per mode. The weight functions are expressed in terms of coherence functions and of occupation number space matrix elements of the density operators. When a compact form of the weight function in the diagonal representation does not exist, one of these new representations may become preferable. One such example is discussed.
TL;DR: In this article, the authors studied the domains of definition of the operators used to factorize the generalized Veneziano model within the Hilbert space defined by the harmonic oscillator creation and annihilation operators aμ(r)†, aμ (r).
Abstract: The domains of definition of the operators used to factorize the generalized Veneziano model are studied within the Hilbert space defined by the harmonic oscillator creation and annihilation operators aμ(r)†, aμ(r). These individual operators may not be well behaved, although, of course, the matrix elements used in the conventional operational factorization are well defined. Concerning the individual operators, it is shown that the ground‐state vertex written as V(p)=exp[−∑r=1∞ (p·a (r)+)/√ r]exp[∑r=1∞ (p·a (r))/√ r] is nowhere defined within the Hilbert space; the product with a twisting operator Ω(q)V(p) is, however, densely defined, as is the symmetrical three‐reggeon vertex. The propagator D(p) is bounded everywhere, away from its poles. The twisting operator Ω(p) is undefined on finite occupation states, but is densely defined on a subset of coherent states; its Hermitian conjugate Ω+(p) is densely defined on both finite occupation and coherent states. It is found that a suitable rewritten form of th...