A discussion of new bistability phenomena observed in electron-paramagnetic-resonance spectra is given. The effects depend on the number of paramagnetic centers and their positions in the cavity and occur also in the presence of a microwave linear response of the sample. Very accurate measurements with two different techniques show that the response of the resonator corresponds to a double well with two resonant frequencies when proper threshold conditions are exceeded. Theoretical results, based on circuit network theory combined with the Bloch equation response of a spin system at magnetic resonance, fully explain the measurements. The influence of different physical parameters on the mechanism driving the overall phenomenon is determined. The main features of the observed effects are discussed in terms of applications to the study of instabilities and noise effects.

We present a revision of the theory of finite laser bandwidth effects on degenerate four-wave mixing (DFWM) of Alber, Cooper, and Ewart (ACE) [Phys. Rev. A 31, 2344 (1985)]. The same model is used for intense, broad-bandwidth pump lasers interacting with a weak monochromatic probe in a medium composed of two-level atoms. The density-matrix equations describing the time evolution of the atomic polarization coupled to fluctuating fields are solved using an appropriate decorrelation approximation. A steady-state analytical solution is found for resonant and near-resonant DFWM, for intensities that do not saturate the medium. For more intense fields it is found to be necessary to form a more complicated set of differential equations for all products of the field and atomic density-matrix elements. The results show that as in the ACE theory, increasing the bandwidth b leads to an increased effective saturation intensity. However, we find the DFWM reflectivity scales as 1/$b^2$ when the probe is monochromatic and not 1/b as in the ACE theory. Furthermore, the saturation behavior of nonresonant DFWM is found to differ from the predictions of ACE. Atomic motion effects are shown to yield a Doppler-broadened line shape and also to affect the saturation behavior of the signal.

A complex effective Hamiltonian (CEH) approach is formulated in the semiclassical (quantum-molecule–classical-field) representation for the study of ir multiphoton-dissociation processes. This formulation enables one to evaluate the dissociation dynamics in terms of the discrete states only. The effects of the bound–continuum-state interactions are manifested in the CEH matrix by the addition of level shifts and imaginary decay widths to the unperturbed bound-state energies and bound-bound dipole-coupling elements. The periodicity of the CEH matrix in time is preserved, allowing the use of Floquet theory to exactly evaluate the time development of the system. This CEH formulation requires that transitions between continuum states can be safely ignored, that the bound-continuum dipole couplings vary slowly with the continuum state energy ɛ, and that time t is sufficiently long. High field intensities also tend to make these requirements more stringent. It is found that the CEH matrix in the semiclassical representation can be asymmetric with respect to the level shifts and decay widths. For the ir multiphoton dissociation of a nonrotating model diatomic molecule in the ground electronic state, a rather truncated form of the CEH is tested against a discretized continuum plus optical potential method. Despite the high field intensity and relatively short laser pulse used in these tests, the results indicate that this CEH method works well provided the bound-continuum dipole-coupling elements vary slowly with ɛ. As can be expected, the validity of the CEH is limited when the bound-continuum dipole couplings vary strongly with ɛ, which is the case with our model diatomic molecule. The nature of the bound-continuum interactions can apparently have considerable effect on the dissociation dynamics.

We develop an effective-medium theory for nonlinear, ellipsoidal particles embedded in a host medium. Specifically, we treat spheroidal-shaped particles and give results for oriented and random configurations of the particles. We discuss metallic particles embedded in a linear dielectric medium and examine the enhancement of their nonlinear response at the surface-plasmon resonances.

A quantum theory of two-photon correlated-spontaneous-emission lasers (CEL’s) is developed, starting from the exact atom-field interaction Hamiltonian for cascade three-level atoms interacting with a single-mode radiation field. We consider the situation where the active atoms are prepared initially in a coherent superposition of three atomic levels and derive a master equation for the field-density operator by using a quantum theory for coherently pumped lasers. The master equation is transformed into a Fokker-Planck equation for the antinormal-ordering Q function. The drift coefficients of the Fokker-Planck equation enable us to study the steady-state operation of the two-photon CEL’s analytically. We have studied both resonant two-photon CEL for which there is no threshold, and off-resonant two-photon CEL for which there exists a threshold. In both cases the initial atomic coherences provide phase locking, and squeezing in the phase quadrature of the field is found. The off-resonant two-photon CEL can build up from a vacuum when its linear gain is larger than the cavity loss (even without population inversion). Maximum squeezing is found in the no-population-inversion region with the laser intensities far below saturation in both cases, which are more than 90% for the resonant two-photon CEL and nearly 50% for the off-resonant one. Approximate steady-state Q functions are obtained for the resonant two-photon CEL and, in certain circumstances, for the off-resonant one.

We calculate the input-output characteristics of an optical amplifier that consists of an inverted-population medium placed inside a high-Q Fabry-Pérot cavity. Expressions are derived for the output second- and fourth-order spectral and temporal correlation functions, and more generally for the output characteristic functional, in terms of the corresponding input quantities. The photocount first and second factorial moments are obtained for both homodyne and direct detection of the amplifier input and output. The general results are applied to several cases of practical interest, including inputs that have coherent or chaotic coherence properties. Particular attention is paid to the effects of amplification on specific nonclassical varieties of input light. It is shown that a maximum of only twofold amplification is permitted if any squeezing present in the input is to survive as squeezing in the output light. Similarly, for the preservation of photon antibunching in amplification, we show, by consideration of a kind of free-space number-state input, that only small gains are allowed. The amplifier model treated here provides a detailed example of the limitations imposed by quantum mechanics on the minimum noise generated by a multimode linear amplifier. In particular, we show that minimum noise occurs in a cavity that is asymmetric with respect to mirror reflectivities, for which we derive the corresponding conditions. In addition, we demonstrate the ability of the amplifier to improve upon signal-to-noise ratio, otherwise limited by low detector quantum efficiency.

It is shown that, introducing quantum-mechanical degrees of freedom for the pump field, one can model optical-pumping processes of a laser with sub-Poissonian statistics. For a class of pump models containing regular pumping at one end of the range and Poissonian pumping at the other, the exact stationary moments for the pump-field-averaged laser field are calculated in the strong-saturation limit of the lasing transition. It is demonstrated that, in a photodetection experiment of the laser output, complete noise suppression in the photocurrent fluctuation spectrum is, at least in principle, achievable. Finally, an approximate Fokker-Planck equation for photon distribution of the laser field with explicit appearance of the pump-light intensity correlation function in the diffusion term is derived and solved in the stationary limit.

We investigate the third-order nonlinear-optical susceptibility ${\chi }^{\mathrm{}\left(3\right)\mathrm{}}$ in molecular aggregates and its scaling with aggregate size. The aggregate is modeled as a collection of N-interacting, homogeneously broadened two-level systems, where the interaction includes both the static dipole-dipole coupling and superradiant coupling. Our expression for ${\chi }^{\mathrm{}\left(3\right)\mathrm{}}$, derived using Liouville-space Green-function techniques, contains contributions from excitons as well as biexcitons. The scaling of ${\chi }^{\mathrm{}\left(3\right)\mathrm{}}$ with aggregate size and its dependence on the laser detuning and homogeneous and inhomogeneous dephasing rates are analyzed. ${\chi }^{\mathrm{}\left(3\right)\mathrm{}}$ contains terms that scale as ∼$N^2$ and ∼N(N-1). However, under off-resonant conditions these terms interfere destructively, resulting in a linear ∼N scaling, which is precisely what is expected for N monomers. Detailed calculations of phase-conjugate degenerate four-wave mixing and pump-probe spectroscopy are performed. In the first case we predict the existence of a narrow dephasing-induced resonance superposed on the broader superradiant exciton line shape. Pump-probe spectroscopy shows a series of biexciton absorption lines, some of which are superradiantly broadened.

We study the phase diagram and other general macroscopic properties of an interacting spin (or particle) system out of equilibrium, namely, a reaction-diffusion Ising model whose time evolution occurs as a consequence of a combination of spin-flip (Glauber) and spin-exchange (Kawasaki) processes. The Glauber rate at site x when the configuration is s, say c(s;x), satisfies detailed balance at a reciprocal temperature β, while the Kawasaki rate for the interchange between nearest-neighbor sites x and y, Γc(s;x,y), satisfies detailed balance at temperature β’. We derive hydrodynamic-type macroscopic equations from the stochastic microscopic model for β’,β≥0 and large Γ when time and space are rescaled by Γ and √Γ , respectively, and study the homogeneous steady solutions of those equations when Γ→∞. We state some general theorems for β’=0 and solve explicitly the model with different choices c(s;x) for systems of arbitrary dimension d when β’=0 and also for d=1 when β’≠0. We also describe new Monte Carlo data for finite Γ, β’=0, and d=1,2. The latter suggests, in particular, the existence of phase transitions for d=1, finite Γ, and some choices for c(s;x).

We present a functional integral formalism suited to the study of classical kinetic theory. We start from the Liouville equation and show within this new formalism how to naturally derive the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy. As an example of the interest of this method, we apply it to a high-temperature plasma and derive in a remarkably simple way the Balescu- Lenard collision operator. The relationship with the standard diagrammatic approach is discussed.

A nonlinear collisional-radiative model for determination of nonequilibrium production of electrons, excited atoms, and bound-bound, dielectronic and continuum line intensities in stationary partially ionized atomic nitrogen is presented. Populations of 14 atomic levels and line intensities are calculated in plasma with 8000≤$T_e$≤15 000 K and ${10}^{12}$≤$N_t$≤${10}^{18}$ ${\mathrm{cm}}^{\mathrm{-}3}$. Transport of radiation is included by coupling the rate equations for production of the electrons and excited atoms with the radiation escape factors, which are not constant but depend on plasma conditions.

The interplay of charge diffusion, a hitherto neglected phenomenon, and Coulomb repulsion in the finite-amplitude electroconvection of a layer of insulating liquid subjected to weak unipolar injection is discussed. Analytical considerations and numerical simulations show that there exists a fundamental nondimensional parameter that relates the strength of the Coulomb repulsion to the diffusion coefficient. Unless this parameter is much larger than 1, diffusion must be included. A projection of the two-dimensional charge conservation equation into a one-dimensional space allows us to obtain good estimates of the charge-density distribution for any value of this parameter.

Molecular-dynamics calculations have been carried out for a Brownian particle inmersed in a simple Lennard-Jones fluid with temperature and pressure constraints. To guarantee the equilibrium properties of the bath system, the Nosé-Hoover method has been used. The memory function has been obtained through the Mori coefficients, and the Toxvaerd algorithm is used. The analysis of the results shows that the diffusion coefficient is independent of the mass when the Brownian particle has the same volume as the solvent particles. Only a weak mass dependence appears when the volume of the Brownian particle is increased.

The magnetic electron-drift vortex mode in a magnetized plasma is investigated using the Braginskii transport equations for the electrons. In a sufficiently inhomogeneous external magnetic field, the mode can become unstable, causing enhanced local magnetic fluctuations. The latter give rise to an anomalous electron thermal flux that significantly affects the transport characteristics of the plasma. Using the conventional quasilinear approach, the corresponding anomalous thermal conductivity is obtained.

The free-decay renormalization-group theory for Navier-Stokes turbulence [Zhou, Vahala, and Hossain, Phys. Rev. A 37, 2590 (1988)] is extended to the case of forced turbulence. An eddy-damping function is obtained, which is nonlocal in time and space. Using a multitime scale perturbation analysis, a time-local renormalized eddy viscosity is determined as a fixed point of an integro-difference recursion relation. It exhibits a mild cusp behavior for the particular forcing exponent that gives the Kolmogorov energy spectrum, similar to that for free-decaying turbulence. As in the free-decay theory, the triple nonlinearity in the renormalized Navier-Stokes equation is essential for the cusp to occur near the boundary between the unresolvable and resolvable scales. Unlike the ε-expansion theory, however, the renormalized eddy viscosity exhibits a wave-number dependence in the supergrid scales. The standard inertial wave-number scaling of the eddy viscosity is recovered for the Kolmogorov energy spectrum. A numerical value for the Kolmogorov constant is obtained using the Yakhot-Orszag equivalence assumption $C_K$=1.44. .AE

An analytic theory using WKBJ methods for selection with local perturbations in the Saffman-Taylor [Proc. R. Soc. London, Ser. A 245, 312 (1958)] problem is presented. I obtain qualitative agreement with previously published phenomenology, including symmetric narrowed fingers for local reductions in the surface-tension parameter, narrowed asymmetric fingers for local increases, and scaling of the tip curvature and asymmetry with the square root of the surface-tension parameter. The source of the universality in the perturbed problem is discussed, giving some explanation of why the experimental perturbations can be modeled by locally varying surface tension. Very good quantitative agreement between theory and a numerical simulation of the same perturbation is shown, with no adjustable parameters to fit. Finally, I outline experiments to test new behavior predicted by the theory; a quantitative prediction observable experimentally is given.

Using the idea of the Gaussian effective potential due to Stevenson [Phys. Rev. D 30, 1712 (1984)], the effect of quantum fluctuations on chaotic behavior is studied in the Hénon-Heiles and four-leg potentials.

The general theory of nonlinear relaxation times is developed for the case of Gaussian colored noise. General expressions are obtained and applied to the study of the characteristic decay time of unstable states in different situations, including white and colored noise, with emphasis on the distributed initial conditions. Universal effects of the coupling between colored noise and random initial conditions are predicted.

The decay of an unstable state under the influence of external colored noise has been studied by means of analog experiments and digital simulations. For both fixed and random initial conditions, the time evolution of the second moment 〈$x^2$(t)〉 of the system variable was determined and then used to evaluate the nonlinear relaxation time. The results obtained are found to be in excellent agreement with the theoretical predictions of the immediately preceding paper [Casademunt, Jiménez-Aquino, and Sancho, Phys. Rev. A 40, 5905 (1989)].

We introduce a simple model of ‘‘avalanches’’ in which there is continuous deposition of mass on a ‘‘tilted’’ substrate, with avalanches occurring whenever the mass at a given site reaches a preassigned threshold value $h_c$. The avalanche is defined to sweep away all mass which is downhill from the initiation event. Basic dynamical features are studied, including the distribution of avalanche sizes and the time intervals between avalanches. For a one-dimensional ‘‘slope’’ of length L, the average &, and in the continuum limit the averaged steady-state mass distribution a distance &. Qualitatively similar results are found for avalanches on a two-dimensional substrate. Contrasts between the present avalanche model and models of self-organized criticality are discussed.