Perturbed Operators in Hilbert Space
Perturbed operators in Hilbert space in justification of Rayleigh-Schroedinger perturbation theory in quantum chemistry
OPERATOR↗
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Problems of intense magnetic field in gravitational collapse
Quantum theory of electron gas in magnetic fields caused by gravitational collapse
Canuto, V.↗
Group algebra, convolution algebra, and applications to quantum mechanics.
Hamiltonian symmetry group role in quantum theory in stationary states classification, transition probabilities and selection rules
Loewdin, P.-O.↗
Dielectronic recombination
Dielectronic recombination rate coefficient determined by quantum theory of resonance- collision processes, considering coupling, degeneracy and overlapping resonances
Shore, B. W.↗
Quantum cosmology. I
Hamiltonian methods applied to homogeneous cosmological models, obtaining Einstein equations, passing to quantum theory by imposing canonical commutation relations
Misner, C. W.↗
Transport properties of N2 gas at cryogenic temperatures
The viscosity and thermal conductivity of nitrogen gas for the temperature range 5 K - 135 K have been computed from the second Chapman-Enskog approximation. Quantum effects, which become appreciable at the lower temperatures, are included by utilizing collision integrals based on quantum theory. A Lennard-Jones (12-6) potential was assumed. The computations yield viscosities about 20 percent lower than those predicted for the high end of this temperature range by the method of corresponding states, but the agreement is excellent when the computed values are compared with existing experimental data.
Pearson, W. E.↗
Quaternion wave equations in curved space-time
The quaternion formulation of relativistic quantum theory is extended to include curvilinear coordinates and curved space-time in order to provide a framework for a unified quantum/gravity theory. Six basic quaternion fields are identified in curved space-time, the four-vector basis quaternions are identified, and the necessary covariant derivatives are obtained. Invariant field equations are derived, and a general invertable coordinate transformation is developed. The results yield a way of writing quaternion wave equations in curvilinear coordinates and curved space-time as well as a natural framework for solving the problem of second quantization for gravity.
Edmonds, J. D., Jr.↗
The angular dependence of partially redistributed resonance radiation
Explicit expressions for the angular distribution and frequency dependence of radiation scattered by a spatially degenerate atom undergoing collisions are derived using a previously developed formalism of the quantum theory of line broadening for an atom in its rest frame. Results valid in the impact regime for resonant scattering are presented for the cases of linear incident and scattered polarization circular incident and linear scattered polarization, and unpolarized incident radiation with no monitoring of the scattered polarization. These results relate to scattering involving a j - j + or - 1 - j atomic transition, with lower-state interactions neglected; the expressions obtained take a relatively simple form involving atomic multipolar relaxation rates of the order of k = 0 and k = 2. The angular distributions for each case are combined with the frequency dependences to yield a three-component frequency redistribution function for an s-p-s transition, the components being a coherent term, a frequency-redistributed term with the same angular dependence as the coherent term, and an isotropic frequency-redistributed term.
Ballagh, R. J.↗
Baryon symmetric big bang cosmology
Both the quantum theory and Einsteins theory of special relativity lead to the supposition that matter and antimatter were produced in equal quantities during the big bang. It is noted that local matter/antimatter asymmetries may be reconciled with universal symmetry by assuming (1) a slight imbalance of matter over antimatter in the early universe, annihilation, and a subsequent remainder of matter; (2) localized regions of excess for one or the other type of matter as an initial condition; and (3) an extremely dense, high temperature state with zero net baryon number; i.e., matter/antimatter symmetry. Attention is given to the third assumption, which is the simplest and the most in keeping with current knowledge of the cosmos, especially as pertains the universality of 3 K background radiation. Mechanisms of galaxy formation are discussed, whereby matter and antimatter might have collided and annihilated each other, or have coexisted (and continue to coexist) at vast distances. It is pointed out that baryon symmetric big bang cosmology could probably be proved if an antinucleus could be detected in cosmic radiation.
Stecker, F. W.↗
The creativity of Einstein and astronomy
A discussion of Einstein's scientific achievements for the 100th anniversary of his birth is presented. His works dealing with thermodynamics are described, along with his quantum theory of radiation. Most of the article discusses his general theory of relativity.
Zeldovich, Y. B.↗
Semi-classical Reissner-Nordstrom model for the structure of charged leptons
The lepton self-mass problem is examined within the framework of the quantum theory of electromagnetism and gravity. Consideration is given to the Reissner-Nordstrom solution to the Einstein-Maxwell classical field equations for an electrically charged mass point, and the WKB theory for a semiclassical system with total energy zero is used to obtain an expression for the Einstein-Maxwell action factor. The condition obtained is found to account for the observed mass values of the three charged leptons, and to be in agreement with the correspondence principle.
Rosen, G.↗
Entropic uncertainty relation at finite temperature
We discussed how much information is lost when a particle is in equilibrium with the thermal reservoir of temperature T = 1/beta. The universal temperature correction to the r.h.s. of U(X,P:psi) greater than or = 1 + ln(pi) is determined. For this purpose, it is convenient to employ the framework of thermo-field dynamics (TFD). This formulation of finite-temperature (T not = 0) quantum theory utilizes the doubled Hilbert space, the normal operator (A) acting on the objective space, and its corresponding tildian operator on the fictitious space. The physical probability density associated with the measurement of the normal operator, A, is given, and the information entropy at T not = 0 is defined. The results describe how the thermal disturbance effects in S sub X or S sub P (delta X or delta P) can be suppressed by squeezing with keeping U = S sub X + S sub P (delta X x delta P) its minimum value.
Abe, Sumiyoshi↗
Phase of the quantum harmonic oscillator with applications to optical polarization
The phase of the quantum harmonic oscillator, the temporal distribution of a particle in a square-well potential, and a quantum theory of angles are derived from a general theory of complementarity. Schwinger's harmonic oscillator model of angular momenta is modified for the case of photons. Angular distributions for systems of identical and distinguishable particles are discussed. Unitary and antiunitary time reversal operators are then presented and applied to optical polarization states in birefringent media.
Shepard, Scott R.↗
Phase space localization for anti-de Sitter quantum mechanics and its zero curvature limit
Using techniques of geometric quantization and SO(sub 0)(3,2)-coherent states, a notion of optimal localization on phase space is defined for the quantum theory of a massive and spinning particle in anti-de Sitter space time. It is shown that this notion disappears in the zero curvature limit, providing one with a concrete example of the regularizing character of the constant (nonzero) curvature of the anti-de Sitter space time. As a byproduct a geometric characterization of masslessness is obtained.
Elgradechi, Amine M.↗
Source conductance scaling for high frequency superconducting quasiparticle receivers
It has been suggested that the optimum source conductance G(sub s) for the superconductor-insulator-superconductor (SIS) quasiparticle mixer should have a l/f dependence. This would imply that the critical current density of SIS junctions used for mixing should increase as frequency squared, a stringent constraint on the design of submillimeter SIS mixers, rather than in simple proportion to frequency as previously believed. We have used Tucker's quantum theory of mixing for extensive numerical calculations to determine G(sub s) for an optimized SIS receiver. We find that G(sub s) is very roughly independent of frequency (except for the best junctions at low frequency), and discuss the implications of our results for the design of submillimeter SIS mixers.
Ke, Qing↗
Nonclassical states of the second optical harmonic in the presence of self-action
The quantum theory of coherent radiation frequency doubling in crystals with quadratic and cubic optical nonlinearities is developed. The possibility of producing the quadrature-squeezed state of the second harmonic (SH) field is shown. The nonclassical SH states arise due to self-action effect.
Chirkin, A. S.↗
Bloch vector projection noise
In the optical measurement of the Bloch vector components describing a system of N two-level atoms, the quantum fluctuations in these components are coupled into the measuring optical field. This paper develops the quantum theory of optical measurement of Bloch vector projection noise. The preparation and probing of coherence in an effective two-level system consisting of the two ground states in an atomic three-level lambda-scheme are analyzed.
Wang, Li-Jun↗
Further evidence for the EPNT assumption
We recently proved a theorem extending the Greenberger-Horne-Zeilinger (GHZ) Theorem from multi-particle systems to two-particle systems. This proof depended upon an auxiliary assumption, the EPNT assumption (Emptiness of Paths Not Taken). According to this assumption, if there exists an Einstein-Rosen-Podolsky (EPR) element of reality that determines that a path is empty, then there can be no entity associated with the wave that travels this path (pilot-waves, empty waves, etc.) and reports information to the amplitude, when the paths recombine. We produce some further evidence in support of this assumption, which is certainly true in quantum theory. The alternative is that such a pilot-wave theory would have to violate EPR locality.
Greenberger, Daniel M.↗