Most developments of Čerenkov radiation are in terms of the Fourier components of the fields and power emitted by a single electron. When many electrons in a compact bunch are emitted from an accelerator, the bunch radiates coherently and at a lower frequency than for a single electron. The theory for the time structure of the fields arising from a charge bunch is developed, and it is shown that the source of the radiation is di/dt. Present detector technology should be able to resolve these fields.

In this paper we discuss a longitudinal multimode quantum theory of the free-electron laser (FEL) within the framework of a nonrelativistic Hamiltonian. Furthermore, we study the evolution of the radiation field starting from the vacuum state and present the analytical expression in first order in the electron recoil of the probability amplitude of finding $l_j$ photons in the longitudinal jth mode. In conclusion we show the possibility of a self-consistent formalism adequate for numerical calculations to evaluate the evolution of the FEL radiation field from the quantum to the classical regime.

We develop a formulation of quantum damping theory in which the explicit nature of inputs from a heat bath, and of outputs into it, is taken into account. Quantum Langevin equations are developed, in which the Langevin forces are the field operators corresponding to the input modes. Time-reversed equations exist in which the Langevin forces are the output modes, and the sign of damping is reversed. Causality and boundary conditions relating inputs to system variables are developed. The concept of ‘‘quantum white noise’’ is formulated, and the formal relationship between quantum Langevin equations and quantum stochastic differential equations (SDE’s) is established. In analogy to the classical formulation, there are two kinds of SDE’s: the Ito and the Stratonovich forms. Rules are developed for converting from one to the other. These rules depend on the nature of the quantum white noise, which may be squeezed. The SDE’s developed are shown to be exactly equivalent to quantum master equations, and rules are developed for computing multitime-ordered correlation functions with use of the appropriate master equation. With use of the causality and boundary conditions, the relationship between correlation functions of the output and those of the system and the input is developed. It is possible to calculate what kind of output statistics result, provided that one knows the input statistics and provided that one can compute the system correlation functions.

The effect of stochastic laser phase fluctuations on nonlinear optical phenomena are investigated within the phase-diffusion model. Averaged equations of motion are derived in the limit of infinitely short correlation times and the results are applied to multiphoton absorption and to four-wave mixing. The effect of the stochastic phase fluctuations is shown to be equivalent to a $T_2$ dephasing process, and a procedure is described for the inclusion of this equivalence in many nonlinear-optical problems. When a given mode contributes n photons to a multiphoton absorption process, its contribution to the width of the multiphoton transition is $n^2$ times its own stochastic width. When correlated lasers are used as the excitation sources in four-wave-mixing experiments, (new) stochastic-fluctuation-induced extra resonances in four-wave mixing (SFIER4) will be observed, in complete analogy to the extra resonances induced by collisions [pressure-induced extra resonances in form-wave mixing (PIER4)].

In this paper we show that a high-frequency electrostatic plasma instability occurs because of a new mode-coupling effect in plasma turbulence (bremsstrahlung instability). In the presence of a coherent low-frequency whistler mode and a high-frequency electrostatic test wave, this instability occurs because of a resonant interaction between electrons and modulated electric fields. The growth of the high-frequency wave occurs at the particular phase relative to the coherent whistler mode. The theory agrees with the recent experiments in space and laboratory.

We study the universality behavior and scaling property associated with an arbitrary M-furcation fixed point in a one-dimensional iterative map. We use both the direct-search method and the renormalization-group method to evaluate the fixed-point function $f^{\mathrm{*}}$(x) and the universal constants α and δ. The agreement between these two methods is very satisfactory. The basin of attraction of $f^{\mathrm{*}}$(x) forms a nearly self-similar Cantor set. We use this approximate self-similarity property to compute the capacity and the information dimensions of the attractor. We summarize M-furcation results for all M≤7 basic cycles in several tables.

To interpret modern data on the dynamic structure factor for dense fluids, we have devised new and reliable methods of extracting the real and imaginary parts of the dynamic memory function of the current-current correlation function, without resorting to Laplace transforms of the experimental data. The numerical precision of these new methods is demonstrated. Also we show how our results can be used as a test of the propagation of collective modes in dense fluids, and how this relates to a recent controversy. Finally a new expression for the scattering function is suggested to improve the physical interpretation of experimental data.

We consider the annihilation reaction A+A→0 on the real line with an initial equilibrium distribution of particles A (points or rods); the particles move freely before annihilating, with independent initial velocities. For the dichotomic distribution of velocities P(v=c)=1-P(v=-c)=p, we determine the fraction S(t) of particles surviving at time t: (1) If p=(1/2), S(t)∼$t^{\mathrm{-}1/2}$ by a central-limit effect; (2) if p≠(1/2), S(t)∼‖2p-1‖+${\mathrm{At}}^{\mathrm{-}3/2}$exp(-Bt) with known constants A and B. We also determine the asymptotic spatial distribution of surviving particles. From these results we derive some bounds on the decay of S(t) for other velocity distributions, and we compare them to the decay of S(t) for diffusive (Brownian) motion.

In the familiar Green-Kubo expressions, transport coefficients are related to equilibrium fluctuations. The equilibrium ensemble which generates these fluctuations is obtained by setting the thermodynamic force to zero. For the special case of electrical conductivity, we show how the transport coefficient is related to fluctuations in the conjugate equilibrium ensemble where the thermodynamic flux, rather than the force, is set to zero. We show that the conjugate equilibrium correlation function so obtained is the memory function of the flux autocorrelation function.

We consider processes where the sites of an infinite, uniform lattice are filled irreversibly and cooperatively, with the rate of adsorption at a site depending on the state of its nearest neighbors (only). The asymmetry between empty and filled sites, associated with irreversibility, leads one to consider the closed infinite coupled hierarchies of rate equations for probabilities of connected and singly, doubly, etc., disconnected empty subconfigurations and results in an empty-site-shielding property. The latter allows exact solutions, via truncation, of these equations in one dimension and is used here to determine probabilities of filled s-tuples, $f_s$ ($f_1$≡θ is the coverage), and thus of clusters of exactly s filled sites, $n_s$≡$f_s$-2$f_{s+1\mathrm{}}$+$f_{s+2\mathrm{}}$ for s≤13 and 11, respectively. When all rates are nonzero so that clusters can coalesce, the $f_s$ and $n_s$ distributions decay exponentially as s→∞, and we can accurately estimate the asymptotic decay rate λ(θ)≡ ${\lim }_{\mathrm{s}\to \mathrm{\infty }}$ ${\mathrm{f}}_{\mathrm{s}+1\mathrm{}}$/${\mathrm{f}}_{\mathrm{s}}$≡ ${\lim }_{\mathrm{s}\to \mathrm{\infty }}$ ${\mathrm{n}}_{\mathrm{s}+1\mathrm{}}$/${\mathrm{n}}_{\mathrm{s}}$, where 0=λ(0)≤λ(θ)≤λ(1)=1. Divergent behavior of the average cluster size, as θ→1, is also considered. In addition, we develop a novel technique to determine directly the asymptotic decay rate λ(θ) and indicate its extension to higher-dimensional irreversible cooperative filling (and to other dynamic processes on lattices).

We consider processes where the sites of an infinite, uniform, one-dimensional lattice are filled irreversibly and cooperatively, with the rates $k_i$, depending on the number i=0,1,2 of filled nearest neighbors. Furthermore, we suppose that filling of sites with both neighbors already filled is forbidden, so $k_2$=0. Thus, clusters can nucleate and grow, but cannot coalesce. Exact truncation solutions of the corresponding infinite hierarchy of rate equations for subconfiguration probabilities are possible. For the probabilities of filled s-tuples $f_s$ as a function of coverage, θ≡$f_1$, we find that $f_s$/$f_{s+1\mathrm{}}$=D(θ)s+C(θ,s), where C(θ,s)/s→0 as s→∞. This corresponds to faster than exponential decay. Also, if ρ≡$k_1$/$k_0$, then one has D(θ)∼(2ρθ${)}^{\mathrm{-}1}$ as θ→0. The filled-cluster-size distribution $n_s$ has the same characteristics. Motivated by the behavior of these families of $f_s$/$f_{s+1\mathrm{}}$-vs-s curves, we develop the natural extension of $f_s$ to s≤0. Explicit values for $f_s$ and related quantities for ‘‘almost random’’ filling, $k_0$=$k_1$, are obtained from a direct statistical analysis.

Random walks in two-dimensional environments with a positionally random drift force are analyzed. If the force is constrained to be divergence-free, then the mean-square displacement is superdiffusive 〈$x^{2^{\mathrm{}\left(t\right)}}$¯〉∼t (lnt${)}^{1/2}$. If in addition the force has a component which is curl-free, there are two cases: If the two components are independent, the long-time behavior is diffusive with only logarithmic corrections; on the other hand, if the two components of the force are, respectively, parallel and perpendicular to the gradients of a single strongly fluctuating potential, the long-time behavior is subdiffusive and dominated by the longitudinal part.

We propose to utilize a high–phase-velocity wave driven indirectly within the plasma via a nonlinear interaction of two high-frequency pump waves in order to improve the efficiency of rf current drive as compared to the one induced by lower-hybrid waves. The use of this wave can be advantageously combined with a lower-hybrid wave having a slower phase velocity to generate a stochastic band in phase space due to a nonlinear interaction of resonances which results in a raised plateau in the electron velocity distribution function, leading to the generation of a current in the plasma. The threshold for onset of stochasticity is evaluated for the relativistic motion of electrons in a two–electrostatic-wave system and the dynamics of the electrons in this configuration is described through a generalized relativistic Fokker-Planck equation, the solution of which enables a prediction of the efficiency ratio J/$P_d$. The efficiency of generating the beat wave itself is estimated and the constraints on the radiation sources needed for its production are considered. The dependency of the J/$P_d$ ratio on the parameters of the system is investigated. The advantages of this current-drive scheme as compared to the scheme constrained by the accessibility conditions are discussed.

When a binary mixture is periodically driven through its consolute point, two distinct regimes are found. In one regime the system ultimately separates into two phases; in the other regime the system remains in a disordered single phase. This transition has been studied by light scattering in a critical mixture of isobutyric acid and water. The system behaves differently in these two regimes, though a characteristic spinodal ring is observed in both of them. In the disordered phase very strong composition fluctuations appear. In the ordered phase there is clear evidence of mean-field behavior. The structure factor S(k,t) exhibits a self-similarity in both regimes, but its scaling form is different. In the ordered state, S(k,t)∼1/$k^4$ for large wave number k. This implies that the scattering is dominated by the sharp interfaces between the domains. In the disordered state, S(k,t) exhibits a weaker dependence on k. Where possible the measurements are compared with a theory of periodic spinodal decomposition by Onuki. The number of parameters in the theory is insufficient to explain all of our measurements.

The nature of stable, inhomogeneous patterns and the character of the evolution to such attracting states is studied for a model dynamical system consisting of a two-dimensional array of coupled, discrete-time oscillators. The orbit scaling structure of a single quadratic map can be transcribed onto the map parameter-coupling parameter plane for the homogeneous states arising from subharmonic bifurcations in the coupled-map array. The study of the evolution of various types of initial inhomogeneity shows how the different patterns arise, some of which resemble those observed in physical systems. Some features of the evolution process can be understood in terms of the stability analysis about the homogeneous state.

The idea of phase dynamics is introduced into the statistical domain-growth problem by extending the earlier work of Ohta, Jasnow, and Kawasaki [Phys. Rev. Lett. 49, 1223 (1982)]. This is combined with defect dynamics necessitated by the multivaluedness of the phase variable to study random domain growth of clock models. In two dimensions the problem is approximately reduced to that of a purely dissipative two-dimensional Coulomb gas. We predict the asymptotic $t^{1/2}$ growth law, although pinning effects by defects (vertices) can complicate the behavior at shorter times. Possible extension to Potts models is briefly discussed.

We draw attention to a new reference system. This is a system of charged hard spheres embedded in a rigid, uniform, and neutralizing background. The model is attractive since analytical expressions such as the free energy, internal energy, structure factor, etc., are available. The usefulness of the model as applied to the variational study of thermodynamic properties of liquid alkali metals is explored. This model is then compared with similar thermodynamic calculations using separately the neutral hard spheres and the classical one-component plasma as reference systems. Results from this comparison show that the charged-hard-sphere system may be preferred as a reference liquid over the neutral-hard-sphere system or, from the economical and computational viewpoint, over the one-component-plasma system.

Quasiperiodic (incommensurate) patterns consisting of an array of solitons are found in a convecting nematic fluid subjected to spatially periodic forcing. The solitons are regions of local compression of the convective rolls and are well described by solutions to the sine-Gordon equation. The commensurate-incommensurate transition is continuous for weak forcing, but becomes discontinuous as the forcing amplitude increases. This behavior indicates the existence of a tricritical point on the phase transition line.

A theory of nonlinear three-wave interaction is presented, where a finite bandwidth of the interacting waves is considered (Δω≠0). Dissipative processes are neglected, and a Hamiltonian formulation is used. The evolution equations for the wave intensities are obtained with the aid of a projection-operator method, similar to those used in nonequilibrium statistical mechanics, but our formulation is deterministic and no statistical hypothesis is needed. These equations generalize the well-known fixed-phase equations (Δω=0) and are formally analogous to them, if the ballistic and memory effects are neglected.

The nonlocal effect of quantum mechanics upon the classical chaos around the separatrix in a Hamiltonian system is investigated by extending the definition of the Melnikov function in the semiclassical approximation. It is shown that the quantum correction of the Melnikov function is related to the quantum fluctuation of the energy on the stable and unstable manifolds. This correction is a constant shift of the center of oscillation of the classical Melnikov function from zero. Because of this shift, the effect of quantum mechanics suppresses the classical chaos around the separatrix. Physical estimates are made of the magnitude of the quantum effect for a double-well oscillator system. As examples, we treat the case of the electron for the molecular scale and the proton for the nuclear scale, and also comment on the ammonia molecules ${\mathrm{NH}}_3$, ${\mathrm{ND}}_3$, and ${\mathrm{NT}}_3$.