Showing papers on "Quantum published in 1971"
TL;DR: In this paper, the ground state of a system of either fermions or bosons interacting in one dimension by a 2-body potential V(r) = g/r2 was investigated.
Abstract: We investigate the ground state of a system of either fermions or bosons interacting in one dimension by a 2‐body potential V(r) = g/r2. In the thermodynamic limit, we determine the ground state energy and pair correlation function.
579 citations
TL;DR: In this article, it was shown that large quantum fluctuations occur only if the initial total occupancy of the excited state differs from the total number of atoms at most by a number of order unity.
Abstract: We discuss the solution of the "superradiance master equation" derived in a preceding paper. During the first few photon transient times the cooperative atomic decay goes through a non-adiabatic oscillatory regime. For later times the decay takes place monotonically in time with the electromagnetic field following it adiabatically. The emitted light pulse has different statistical properties for an incoherently and a coherently prepared "superradiant" atomic initial state. The former case is characterized by large quantum fluctuations and strong atom-atom and atom-field correlations. In the latter case quantum fluctuations are small and the system behaves essentially classically. By also solving for a class of coherently prepared intermediate initial states we show that large quantum fluctuations occur only if the initial total occupancy of the excited state differs from the total number of atoms at most by a number of order unity.
362 citations
TL;DR: In this article, an approximation for the eigenstate of a general 1-dimensional quantum many-body system with a 2-body potential V(r) = g/r2 was presented.
Abstract: We continue our investigation of a system of either fermions or bosons interacting in one dimension by a 2‐body potential V(r) = g/r2. We first present an approximation for the eigenstates of a general 1‐dimensional quantum many‐body system. We then apply this approximation to the g/r2 potential, allowing complete determination of the thermodynamic properties. Finally, comparing the results with those properties known exactly, we conjecture that the approximation is, in fact, exact for the g/r2 potential.
317 citations
TL;DR: In this article, the classical limit of the quantum S matrix (the "classical S matrix") for the scattering process is applied to rigid rotor-atom collisions (rotational excitation), and the linear atom-diatom system is investigated with regard to how much averaging is necessary to quench these quantum effects.
Abstract: A previously developed theory in which exact solutions of the classical equations of motion for a complex collision system (i.e., numerically computed trajectories) can be used to generate the classical limit of the quantum mechanical S matrix (the “classical S matrix”) for the scattering process is applied to rigid rotor–atom collisions (rotational excitation). Comparison with essentially exact quantum results shows that transition probabilities (the square modulus of an S‐matrix element) between individual quantum states are given reasonably accurately by classical dynamics provided the interference terms are properly accounted for; a strictly classical approach (neglect of interference) gives poor agreement with the quantum values. For averaged collision properties, however, it is found that interference and tunneling effects are rapidly quenched. The linear atom–diatom system (vibrational excitation) and the rigid rotor–atom system are both investigated with regard to this question, namely, how much averaging is necessary to quench these quantum effects. Results indicate that even summation over a few quantum states is often sufficient to make a completely classical treatment appropriate.
155 citations
TL;DR: In this article, a special perturbation theory which directly describes the alteration of decaying states by an external perturbations is presented. But the complexity of the complex energies of the decaying states appears in this theory only when lifetime effects are taken into account.
Abstract: This paper constructs a special perturbation theory which directly describes the alteration of decaying states by an external perturbation. The complex energies of the decaying states appear in this theory. When lifetime effects are taken into account, we find that the criteria for quantum degeneracy are slightly strengthened and sharpened. We also discuss the smooth merger of the properties of decaying states and those of true eigenstates in the case of long lifetimes.
69 citations
65 citations
01 Mar 1971
TL;DR: In this paper, a report is given of observations of the ionization of atomic cesium by the simulataneous absorption of three ruby laser quanta, showing that circularly polarized light produces ionization about twice as efficiently as linearly polarized light.
Abstract: : A report is given of observations of the ionization of atomic cesium by the simulataneous absorption of three ruby laser quanta. The results appear to be in qualitative agreement with theory, and indicate that circularly polarized light produces ionization about twice as efficiently as linearly polarized light, suggesting a new kind of polarized electron source. (Author)
56 citations
TL;DR: Transition state theory is tested against accurate rate constants for the collinear H + H 2 reaction on a realistic potential energy surface as mentioned in this paper, which is fairly accurate at high temperatures but is very inaccurate at low temperatures.
52 citations
TL;DR: In this paper, a quantum-mechanical impact theory for the combined effects of Doppler and pressure broadening is developed from quantum radiation theory, compared with other semiclassical theories and certain simplifying approximations relevant to cases of experimental and theoretical interest.
Abstract: A quantum-mechanical impact theory for the combined effects of Doppler and pressure broadening is developed from quantum radiation theory. The results are compared with other semiclassical theories and certain simplifying approximations relevant to cases of experimental and theoretical interest are discussed.
48 citations
TL;DR: In this paper, a bound electron with external radiation fields of finite intensity is treated with the standard quantum-electrodynamical (QED) formalism of Feynman and Dyson and the Green's function for the equation so obtained enables us to compute the induced transition probabilities for various systems of interest.
Abstract: The interaction of a bound electron with external radiation fields of finite intensity is treated with the standard quantum-electrodynamical (QED) formalism of Feynman and Dyson. We first construct an equation for a bound electron in finite-intensity radiation fields, such as those encountered in early molecular-beam experiments and in recent masers and lasers. The Green's function for the equation so obtained enables us to compute the induced transition probabilities for various systems of interest. In this paper, we carry out the calculations on the two-level and three-level systems explicitly, where we find that, to order ${e}^{4}$, the QED method based on forward scattering and the semiclassical treatment differ. As we consider only the interaction of electrons with low-energy photons, we may ignore the virtual photon processes, in accordance with the low-energy theorem. As a result, this treatment contains only finite calculations. We demonstrate explicitly that our results are in qualitative agreement with the molecular-beam experiments of Kusch, for which the semiclassical treatment of Salwen fails to predict the results. Consequently, we expect an intensity-dependent effect which can be properly explained only by QED and not by the semiclassical treatment. We also include the effect of nonelectromagnetic relaxation on the induced transition probability of a two-level system, for which we obtain an expression slightly different from that used by Ramsey for the hydrogen maser. Finally, we derive some expressions which will be of interest in experiments related to lasers and masers.
45 citations
TL;DR: In this paper, a theory for Doppler and pressure broadening in neutral gases is derived as a limiting case of a more general quantum mechanical theory and compared with other semiclassical theories and methods of calculation are discussed.
Abstract: A semiclassical theory for Doppler and pressure broadening in neutral gases is derived as a limiting case of a more general quantum mechanical theory. This theory is compared with other semiclassical theories and methods of calculation are discussed.
TL;DR: In this article, the authors performed classical trajectory calculations for the collinear H+H2 exchange reaction using the same potential energy surface previously adopted for exact quantum mechanical calculations, over a relative kinetic energy range sufficient to produce vibrational excitation of products.
01 Jan 1971
TL;DR: In this article, order α6mc2 corrections to the fine structure splitting of the He4 atom were investigated based on the covariant Bethe-Salpeter equation including external potential to take account of the nuclear Coulomb field.
Abstract: Order α6mc2 corrections to the fine structure splitting of the deepest triplet P state (23P0,1,2) of the He4 atom have been investigated. The investigation is based on the covariant Bethe-Salpeter equation including external potential to take account of the nuclear Coulomb field. All order α6mc2 corrections which arise from Feynman diagrams involving the exchange of one, two, and three photons, as well as radiative corrections to the electron magnetic moment have been found. The results are presented in a form suitable for computerized numerical evaluation.
TL;DR: In this paper, it was shown that by narrowing the n region adjacent to the junction, the threshold current decreases without decreasing the differential quantum efficiency, and epitaxial growth of all layers was used, and diffusion was avoided.
Abstract: We report new results with the large optical cavity (LOC) injection lasers previously described. It is shown that by narrowing the n region adjacent to the junction, the threshold current decreases without decreasing the differential quantum efficiency. Furthermore, epitaxial growth of all layers was used, and diffusion was avoided. Fabry‐Perot mode threshold current densities as low as 1700 A/cm2 were obtained with differential quantum efficiencies of about 50% and power conversion efficiencies of 20% at room temperature.
TL;DR: CF 4 and C 8 F 18 collisionally remove excess energy, presumably vibrational, from CH 2 ( 1 A 1 ) as mentioned in this paper, and showed that Δ H fo 0 [1 CH 2 [1 A 1 ] ≈ 101 kcal/mole.
TL;DR: In this paper, the speculations of Chester, Andreev and Lifshitz, and Leggett concerning the possibility of Bose-Einstein condensation and/or superfluidity in quantum crystals are examined.
Abstract: The speculations of Chester, Andreev and Lifshitz, and Leggett concerning the possibility of Bose-Einstein condensation and/or superfluidity in quantum crystals are examined. The existing body of experimental data on these systems places extremely strong constraints on the experimental realization of these speculations.
TL;DR: In this article, the time development of quantum lattice systems is studied with a weaker assumption on the growth of the potential than has been considered previously, and it is shown that the time complexity of the lattice system can be reduced with respect to the growth rate of potential.
Abstract: The time development of quantum lattice systems is studied with a weaker assumption on the growth of the potential than has been considered previously.
TL;DR: In this article, the Rosenfeld-Condon formula for the angle of optical rotation is derived without recourse to Maxwell's equations, and the relationship between refractive index and molecular polarizability is also derived using quantum electrodynamics.
Abstract: The phenomenon of optical activity is analyzed as a quantum two‐state process with transitions between photon states of perpendicular plane polarizations, but with the same momentum. The matrix element connecting the two states is computed using quantum electrodynamics. The Rosenfeld—Condon formula for the angle of optical rotation is derived without recourse to Maxwell's equations. The relationship between refractive index and molecular polarizability is also derived using quantum electrodynamics. The theory is extended to obtain the difference between refractive indices of an optically active medium with respect to right and left circularly polarized light and the difference is related to optical rotation.
TL;DR: In this article, the Schrodinger equation for a two-state quantum-mechanical system with sinusoidal perturbation is numerically integrated with respect to time, and a general formula for the induced transition probability is extracted.
Abstract: The Schr\"odinger equation for a two-state quantum-mechanical system with sinusoidal perturbation is numerically integrated with respect to time. From these results a general formula for the induced transition probability (as a function of time, perturbation frequency, and perturbation strength) is extracted.
TL;DR: In this article, the weak-coupling solution of the generalized Prigogine-Resibois master equation for the model of the Wigner-Weisskopf atom in a one-dimensional radiation field is studied.
Abstract: A study is undertaken to cast light on difficulties, which arose in the first two papers of this series, pertaining to the occurrence of negative probabilities in the weak‐coupling solution of the generalized Prigogine‐Resibois master equation for the model of the Wigner‐Weisskopf atom in a one‐dimensional radiation field. The Schrodinger equation is solved exactly for the model with the initial condition for spontaneous emission, and then the weak‐coupling approximations to the solution, both for an infinite and for a finite system, are derived as inverse Laplace transform integrals. An extensive analysis, theoretical and numerical, of these is undertaken, and comparison is made with the corresponding results based on the master equation. In particular, quantitative estimates of the Poincare recurrence times for finite systems are made. It is found that considerable differences exist between the statistical‐mechanical and quantum‐mechanical results, but that both manifest nonanalyticity in the coupling p...
TL;DR: Based on quantum transitions of membrane dipoles, the four fundamental properties of nerve impulse are derived: the all-or-none response, the strength-duration relation, refractoriness and refractory period and frequency modulation.
TL;DR: In this article, the problem of internal conversion in a highly excited singlet state of a large molecule in the statistical limit in terms of a consecutive decay problem was considered, and the Wigner-Weisskopf approximation was utilized to handle the sequential decay.
Abstract: In this paper we consider the problem of internal conversion in a highly excited singlet state of a large molecule in the statistical limit in terms of a consecutive decay problem. The Wigner-Weisskopf approximation was utilized to handle the problem of sequential decay. We have elucidated the features of the radiative decay, such as the decay pattern, the decay times and the quantum yields of a ‘statistical’ second-excited singlet state in different spectral regions.
TL;DR: In this paper, the masterequation is treated in Liouvillespace as Hilbertspace for a class of non-hermitean Liouvilleoperators describing thermal and nonthermal contact with reservoirs.
Abstract: The masterequation is treated in Liouvillespace as Hilbertspace for a class of non-hermitean Liouvilleoperators describing thermal and nonthermal contact with reservoirs. It is shown that these Liouvilleoperators are equivalent to normal operators; their eigenvectors and -values are given. For the solution of the resolvent equation the interaction-Liouvilleoperator is approximated by an operator of finite rank, which can be treated exactly.
01 Jan 1971
TL;DR: In this paper, a quantum technique is described for the calculation of the energy and width of shape resonances, which appears to be the only such method applicable to resonances with very long lifetimes.
Abstract: A quantum technique is described for the calculation of the energy and width of shape resonances. It appears to be the only such method applicable to resonances with very long lifetimes. Results for a Lennard‐Jones potential are presented and compared with previous quantum and semiclassical calculations.
TL;DR: In this article, the quantum mechanical excess density of states ρ(E) was given in terms of the S matrix by (i/2π) Tr{SdS+/dE], where Q is the collision lifetime matrix of Smith.