This paper proposes a quantum nondemolition measurement scheme for the photon number. The signal and probe optical waves interact via the optical Kerr effect. The optical phase of the probe wave is selected as the readout observable for the measurement of the photon number of the signal wave. The measurement accuracy Δn and the imposed phase noise Δφ of the signal wave satisfy Heisenberg’s uncertainty principle with an equality sign, 〈(Δn${)}^2$〉〈(Δφ${)}^2$〉=(1/4). .AE

The dynamical solution of the driven classical anharmonic (AH) oscillator is obtained through a region of optical bistability. The dynamical solution is observed to switch from the lowest to highest steady-state (SS) root near a SS turning point with evidence of critical slowing down. The solution of a widely used multiple-photon version of the AH model is also obtained and is found to give qualitatively similar behavior. The average number of photons observed dramatically increases in the bistable region and exhibits damped oscillations.

Coherent transient effects due to phase modulation of recoilless γ radiation are considered both theoretically and experimentally. Transients are observed in transmission experiments when the incident radiation field interferes with the induced polarization of the Mössbauer absorber. The transient effects studied in this work resemble those observed in NMR and laser spectroscopy. They offer several new features for Mössbauer measurements. A theory for the time dependence of the recoilless radiation is derived semiclassically with use of a density-matrix formalism. Transient effects in scattering geometry are also briefly commented upon. The theory is applied to several cases of experimental interest. Time-dependent distortions affecting the line shape in conventional Mössbauer measurements are considered, e.g., the transmission minimum is delayed approximately for the lifetime of the excited nuclear state.

The time dependence of the oscillatory transient excited by a rapid sweep through the resonance is derived. Transient experiments with sinusoidal phase modulation allow metrological calibration of mechanical displacements. The separation between adjacent zeros of the interference oscillations corresponds to a displacement of the source by half a wavelength of the γ radiation. As compared with conventional Mössbauer measurements, more efficient separation of the source and absorber parameters can be achieved in transient experiments. In addition, the linewidths and line positions are obtained in terms of the modulation frequency which simplifies the calibration of the energy scale.

If the phase of the incident radiation is rapidly switched, a simultaneous change is observed in the transmission intensity. An exact expansion shows that, with a thick absorber and an appropriate center shift between the source and absorber line positions, this intensity change can be as large as eight times the maximum conventional resonance absorption. Distortions due to nonideal phase modulation are considered as well. Most measurements were performed with use of the 93-keV Mössbauer resonance of ${}_{}{}^{67}{}_{}{}^{}\mathrm{Zn}$ in ZnO. Comparative results are also presented from ${}_{}{}^{57}{}_{}{}^{}\mathrm{Fe}$ experiments with sinusoidal phase modulation. In transient experiments with ${}_{}{}^{67}{}_{}{}^{}\mathrm{Zn}$, mechanical displacements of the order of ${10}^{\mathrm{-}13}$ m were resolved.

As a further application the recoilless fractions of both the ${}_{}{}^{67}{}_{}{}^{}\mathrm{Ga}$:ZnO source ($f_s$) and of the enriched ${}_{}{}^{67}{}_{}{}^{}\mathrm{ZnO}$ powder absorber ($f_a$) were determined and found to be equal: $f_s$=0.0212(16) and $f_a$=0.0213(18). In phase-switching experiments, filtering of the driving voltage was used to prevent excitation of mechanical resonances of the piezoelectric drive. With a relatively thick absorber and zero center shift, the observed change in the transmitted intensity was three times the conventional resonance absorption. Good agreement between the theoretical calculations and the experimental data was found.

We solve the master equation for the coordinate-coordinate damped harmonic oscillator for initial superpositions of coherent states. In the zero-temperature case the solution remains a simple superposition of coherent states. While the underdamped oscillator evolves all initial superpositions into mixtures of coherent states the overdamped oscillator does so selectively. For finite temperatures coherent states are no longer preserved, and we find a decrease in the variance of the off-diagonal coordinate-basis density-matrix elements below the coherent-state value. This variance decreases with increasing bath temperature. In the overdamped case there is negligible associated spreading of the diagonal coordinate-basis density-matrix elements. Thus the coordinate basis is an example of Zurek’s pointer basis and the coordinate damped oscillator models the coordinate-basis density-matrix diagonalization which occurs in a coordinate measurement.

The conditional probability that a particle at site m at time 0 will be at site n at time t is studied numerically and analytically on the Sierpiński gasket. The Laplace transform of $G_{\mathrm{nm}}$(t), $G_{\mathrm{nm}}$(s), is found to behave on average as &) for large &. Fluctuations about this average behavior are found to be mild when the distance between sites m and n is taken to be the ‘‘lacunar’’ distance. Analytic arguments for the asymptotic behavior of $G_{\mathrm{mn}}$(s), based on the scaling of coupling constants under renormalization, are made. $G_{\mathrm{nm}}$(t) is found to have the asymptotic behavior &${)}^{\nu }$], ν=$d_w$($d_w$${\mathrm{-}1)}^{\mathrm{-}1}$ in agreement with a result of Fisher [J. Chem. Phys. 44, 616 (1966)]. The relationship of this form of $G_{\mathrm{nm}}$(t) to that proposed by Banavar and Willemsen is clarified.

Isotherms for the adsorption of a fluid can be obtained from standard theories of fluids by regarding the surface as a single giant sphere dissolved in the fluid. The amount adsorbed is then an integral over the giant-sphere–fluid-molecule correlation function. Simple considerations show that the critical exponent for the adsorption isotherm is related to γ, the critical exponent for the compressibility. Using the mean-spherical approximation, it is argued that the adsorption-isotherm critical exponent is γ/2 if the surface-fluid interaction is sufficiently short-ranged. This result is in reasonable agreement with the recent experimental findings of Blümel and Findenegg.

We present a theory of attractors on finite sets which is applicable to finite-state systems such as computing structures and other systems which display a hierarchy of organizations with a discrete time evolution. Because computing with attractive fixed points can lead to reliable behavior [B. A. Huberman and T. Hogg, Phys. Rev. Lett. 52, 1048 (1984)], the theory deals with dissipative processes, i.e., those which contract volumes in phase space. The stability of such systems is quantified and analytic expressions are obtained for the appropriate indices in some limiting cases. It is also shown that trees with ultrametric topologies provide the natural language for these systems. The theory is extended to include several practical constraints, and connections are made with experimental quantities which can be measured in particular architectures.

We have developed an algorithm which generates a random close packing of equal spheres from a random distribution of points. Each point is the center of an inner and an outer sphere. The inner diameter defines the true density and the outer a nominal density. The algorithm eliminates overlaps among outer spheres while slowly shrinking the outer diameter. The two diameters approach each other, and the eventual coincidence of true and nominal densities terminates the procedure. The spheres in the packing, which is inherently homogeneous and isotropic, are close together but not touching. Thus, near neighbors are defined as those within a specified distance, δ, of touching. When the outer diameter is contracted relatively quickly, the number of near neighbors depends strongly on δ. As the contraction rate approaches zero, this dependence decreases sharply. We speculate that the limiting value is exactly 6 for all δ≤${10}^{\mathrm{-}3}$. Packing fractions between 0.642 and 0.649, which are easily achieved by this method, are higher than any experimental or previously simulated values, but are consistent with Berryman’s extrapolation [Phys. Rev. A 27, 1053 (1983)] from the radial distribution function for hard spheres. The algorithm can also be used for packing hyperspheres in higher dimensions.

Third-order nonlinear susceptibilities of several organic solvents are measured by third-harmonic generation at two laser wavelengths: 1.064 and 1.907 μm. The method used allows a determination of the modulus and phase by interference with the harmonic field generated in the liquid-cell windows. Air contribution to the resulting harmonic intensities is studied in detail. An experimental correction for this effect is proposed and verified for some solvents. Results are discussed within the bond-additivity model.

Fractal objects strongly screen external fields; only a small ‘‘surface’’ portion of the object is exposed appreciably to the field. We have studied this exposed surface of several random fractals as measured by random walkers and by ballistic particles launched from outside and absorbed by the fractal. The number of absorbing sites weighted by their rate of absorption shows an apparent power-law scaling with fractal mass. For diffusion-limited aggregates, ballistically generated aggregates, and screened-growth clusters in two dimensions, this power-law relationship is for the most part in accord with mean-field predictions of previous work. This accord is poorest for the objects of lowest fractal dimensionality. We have confirmed that this scaling is different from that of the old-growth–new-growth interface studied previously. We also find that a ‘‘hierarchy’’ of fractal dimensions describes the external surface of diffusion-limited aggregates.

A study of nonlinear plasma mass and energy diffusion reveals that the diffusion coefficients uniquely determine one of two diffusion patterns. After a short initial transient time, either an organized universal pattern, described by a time-space separable solution, is formed or transport is inhibited, allowing only a partial organization of diffusion into a universal pattern. Consequently, in the second case, unlike the first, the asymptotic shape of the solution will depend to some extent on its initial state.

Wavelengths and atomic parameters for the satellite spectrum of the 1$s^2$-1s2p parent lines of ${\mathrm{Ar}}^{16+}$ have been calculated using a multiconfiguration intermediate-coupling scheme with a statistical Thomas-Fermi potential. These data, together with radial charge-state distributions given by an impurity transport code, are used to calculate theoretical spectra. The comparison with experimental x-ray spectra from the TFR tokamak plasma shows good agreement between calculated and observed wavelengths. The fitting of relative line intensities in the synthetic spectra to observed values improves the understanding of plasma impurity transport.

Experimental results of the coherent dynamic structure factor S(k,ω), obtained by inelastic neutron scattering, are presented for liquid argon at three densities along the 120-K isotherm. The wave numbers k, covered by the experiment, range from 38 to 72 ${\mathrm{nm}}^{\mathrm{-}1}$. The transition of S(k,ω) to its free-gas behavior (the limit for k→∞) is compared with theoretical calculations. It appears that the experimental results can be described satisfactorily by theoretical calculations for a Lennard-Jones system, whereas the large-k expansion for a hard-spheres system fails to describe the present argon results.

Inelastic neutron scattering experiments have been performed on liquid neon at a temperature of 35 K and pressures of 8 and 14 MPa. The spectra were corrected for all known experimental effects. Normalized results for the coherent dynamic structure factor S(k,ω) were obtained for wave numbers k between 3 and 22 ${\mathrm{nm}}^{\mathrm{-}1}$, all below the position of the first peak, at $k_0$=23.5 ${\mathrm{nm}}^{\mathrm{-}1}$, in the static structure factor S(k). The S(k), calculated by numerical integration of S(k,ω), is compared with neutron diffraction data and with S(k) of argon at corresponding thermodynamic conditions. Quantum corrections to the second frequency moment of S(k,ω) are examined, and a quasiclassical approximation of S(k,ω) is discussed. When comparing S(k,ω) of neon and argon it appears that, except for some small deviations, the principle of corresponding states is valid. The experimental data can well be described by means of one (extended) heat mode and two (extended) sound modes. The sound modes are clearly manifest as shoulders in S(k,ω) which shift, for increasing k, to larger ω and disappear gradually as k approaches $k_0$. The obtained sound dispersion curve, including a sound propagation gap near $k_0$, is consistent with theoretical predictions and with recent results from neutron scattering experiments on argon and from computer simulations. An interpretation in terms of k-dependent transport coefficients is discussed.

Higher-order corrections to the quasilinear diffusion coefficient are obtained for Hamiltonian maps which are locally approximated by the standard map. Using the Fermi map [E. Fermi, Phys. Rev. 75, 1169 (1949); M. A. Lieberman and A. J. Lichtenberg, Phys. Rev. A 5, 1852 (1972)] as an example, we numerically integrate the Fokker-Planck equation for the action and compare the resulting distribution function with direct solutions of the mapping equations. The second moment of the distribution is compared with the diffusion measured in the numerical experiments. Both show oscillations (as a function of the initial velocity) similar to those found in the standard map. In addition, we numerically find the invariant distribution in the Fermi map. We observe dips in the distribution of actions. We calculate the size of islands surrounding stable fixed points and show that the dips correspond to these islands. Thus chaotic orbits uniformly fill the phase space available to them.

We present the first nonequilibrium molecular-dynamics simulations of viscoelasticity in two-dimensional fluids. The shear viscosity is found to depend logarithmically upon the frequency; however, the divergence at low frequencies is shielded by a ‘‘turnover regime’’ where the shear viscosity becomes independent of frequency. The stress-stress autocorrelation function is shown to have a $t^{\mathrm{-}1}$ long-time tail, and the coefficient matches the coefficient of the logarithmic frequency dependence of the shear viscosity. The Goddard-Miller relation between the frequency and strain-rate dependence of the shear viscosity is shown to be incorrect. Superharmonic excitations are observed in both the shear stress and the pressure.

A theory is proposed describing Raman band profiles of binary mixtures of van der Waals liquids. Extensive use is made of the fact that the Hamiltonian of these systems is invariant under permutations of molecules of the same chemical species. It is shown that the evolution of the half-width of a Raman band with concentration varies according to whether vibrational modulation is slow or fast. Widely different spectral effects are predicted for ‘‘chemical’’ and isotopic solutions. This difference is due to the fluctuations of the chemical composition in a given site of the liquid and to the structure-breaking effects which are present in the former case and absent in the latter.

The escape of a particle from a potential well under the influence of both thermal (generalized Langevin) noise and friction and an external periodic driving force is studied in the low-friction limit. We consider three models: (a) additive thermal noise and a completely coherent driving force; (b) additive thermal noise and a phase-diffusing driving force; (c) coherent driving force and multiplicative random noise. The last two models are characterized by dephasing which affects the escape dynamics both qualitatively and quantitatively. In all three cases the escape rate is resonantly enhanced; however, while the first case is characterized by a finite energy peak in the steady-state distribution function, the presence of strong dephasing in the other two cases leads to a generalized Boltzman distribution with an effective temperature which depends resonantly on the external pumping. The relevance of this work to recent experimental results on the resonant activation of a Josephson junction out of its zero-voltage state is discussed.

A geometric representation for information theory is introduced by recourse to a covariant formulation, according to the customary procedure employed in connection with Riemann spaces. The central tool of this representation is the metric tensor that characterizes the particular dynamics of a given system and yields the corresponding quantal invariants.

We consider Ullersma’s model of a damped harmonic oscillator interacting with a heat bath. We show that for large damping the oscillator does not undergo Brownian motion at any temperature. For high temperatures non-Markovian effects show up in initial slips only. For low temperatures we find, as further anomalies, power-law decay of time-dependent expectation values as well as a strong squeezing of the displacement and momentum uncertainties; again these anomalies are most strongly pronounced for strong damping.