Tuszyński, Paul, Chatterjee, and Sreenivasan [Phys. Rev. A 30, 2666 (1984)] purport to show that the Davydov soliton model and the Fröhlich model of far-from-equilibrium energy transport are formally equivalent. In fact, these authors do not make significant contact with essential features of the Fröhlich model, and the comparison fails.

In this Comment we respond to the critical comments of Mills [preceding Comment, Phys. Rev. A 43, 3176 (1991)] regarding our earlier paper on the relationship between Fröhlich and Davydov models of biological coherence. Arguments are given in support of our earlier calculations, which we believe appear to agree both with microscopic molecular modeling and Fröhlich’s concepts about the metabolic state.

We consider a standard map with a continuous, piecewise-linear forcing term. The piecewise linearity allows for an extremely accurate calculation of the classical manifolds and associated homoclinic tangles. A simple coding for the periodic orbits is another useful property of the map. The quantized map is then studied and the resolution of stable and unstable invariant classical structures by the quantum eigenstates is assessed.

Recently, Bidaux, Boccara, and Chaté [Phys. Rev. A 39, 3094 (1989)], introduced a probabilistic cellular automaton whose one-dimensional version exhibits a continuous transition to an absorbing state. Steady-state simulations gave critical exponents different from those of directed percolation, a surprising result, as the universality class of directed percolation is known to be very robust. I have studied the nonequilibrium critical behavior of the one-dimensional model using time-dependent Monte Carlo simulations, and determined three dynamic critical exponents, all of which are in excellent agreement with directed percolation.

Determinism with or without reversibility and the part of it plays in thermodynamics is poorly understood and rarely explored. To investigate the effects of determinism we introduce a class of cellular automata whose rules are constructed from the Boltzmann probabilities of the Ising model. This class of Ising cellular automata (ICA) has as its high-temperature limit the well-studied Kauffman model [S. A. Kauffman, J. Theor. Biol. 22, 437 (1969); Physica D 10, 145 (1984)]. The control of determinism allows us to establish a direct connection between the Kauffman model and percolation and between correlated percolation and these ICA’s. A comparison of the chaotic properties offers an informative look at the consequences of determinism. A line of critical points exists between the ‘‘frozen’’ and ‘‘chaotic’’ phases for ICA, and the zero-field critical temperature is approximately twice that of the Ising model.

The phase boundary of the collapsed phase for a directed polymer on a square lattice in the presence of an attractive substrate and monomer-monomer interactions has been calculated exactly using transfer-matrix techniques. It is shown that the first-order transition line separating the collapsed and bound phases ends up in a multicritical point, while the transition temperature for the extended-collapsed transition is independent of the adsorption potential. The crossover exponent at the FTHETA point is found to be Φ=1/3.

We formulate a Brownian-motion simulation technique to compute exactly the effective conductivity ${\mathrm{\sigma }}_{\mathit{e}}$ of general continuum (off-lattice) models of n-phase heterogeneous media having phase conductivities ${\mathrm{\sigma }}_1$,...,${\mathrm{\sigma }}_{\mathit{n}}$, where ${\mathrm{\sigma }}_{\mathit{i}}$ can be finite or infinite. The appropriate first-passage-time equations at the multiphase interface are derived to reduce significantly the computation time. The method is illustrated by calculating ${\mathrm{\sigma }}_{\mathit{e}}$ for regular and random arrays of d-dimensional, nonoverlapping spheres (d=2 and 3) for a wide range of conductivity ratios (including perfectly insulating and superconducting particles) and volume fractions.

We have studied the space and time evolution of the dense part of a laser-produced plasma obtained on a target composed of a chlorinated plastic foil covered with a samarium layer. With point-projection Kα absorption spectroscopy we measured the optical depth and the electronic temperature of the radiatively heated plasma as a function of time and space. Radiative hydrocode simulations describe correctly the experimental results. The plasma zone radiatively heated at 50–80 eV by the laser-irradiated samarium soft x rays expands just after the laser maximum when the laser-induced pressure has decreased. The obtained dense plasma exhibits shallow density and temperature gradients and could be used for dense-plasma studies.

The effective density matrix of the radiation field in the free-electron laser is computed under realistic initial conditions for the electrons and photons. The field is predicted to be a superposition of a coherent state and a chaotic state. The width of the distribution in the coherent-state expansion is given by the sum of classical and quantum-mechanical initial fluctuations of the electron beam.

We examine the possibility of inferring energy spectra and their concomitant eigenstates on the basis of incomplete information concerning the system’s ground state. In addition, the possibility of considering, as prior information, the expectation values of a partially unknown Hamiltonian also is examined and shown to be feasible.

We show that a ‘‘canonical’’ form of the positive P representation has a simple interpretation as the statistics of four detectors, two of which make redundant position measurements, while the other two simultaneously make redundant momentum measurements. This interpretation allows us to understand the additional degrees of freedom for the canonical positive P representation.

Taking advantage of the generalized variational principle, previously introduced alternative effective Hamiltonians are shown to satisfy variational properties for the lowest energies. Geometrical and arithmetical properties establishing connections with the Rayleigh quotient are emphasized. An illustration of the considerable improvement in convergence properties, obtained by their use in perturbative and iterative expansions, is given by an application to the Mathieu equation.

Partial solubility in quantum mechanics is investigated by studying the logarithmic derivative of the wave function. By explicitly isolating the singularities of the logarithmic derivative, a modified Ricatti equation for the regular component is obtained. For the finite Laurent series potentials considered, we derive the constraints on the coupling constants to obtain closed-form solutions for a subset of eigenstates. With an appropriate change of variables the method is generalized in order to cope with more general potentials. In this way, new families of partially solvable potentials related to the already known exactly solvable ones are identified.

Apparently different criteria are used to arrive at the integral representations of Jost functions. In dealing with this we present a guideline to rederive these results only from the Volterra integral equation satisfied by the Jost solutions. Both on- and off-shell Jost-type functions are considered. Using one of our formal results, we derive a useful expression for the s-wave Coulomb off-shell Jost solution.

The two-dimensional hydrogen problem is solved analytically. In the nonrelativistic case, exact formulas for energy eigenvalues and eigenfunctions for both the discrete and continuous parts of the spectrum, dipole matrix elements, dc Stark effect, single- and two-photon transition rates, and fine and hyperfine structures are obtained. Comparison is made between the two- and the three-dimensional cases. Some interesting aspects of the solution unique to the two-dimensional case are discussed.

In this paper, we derive the exact analytic solution for the relativistic (2+1)-dimensional hydrogen atom, both with and without the Chern-Simons field. The atomic spectra without the Chern-Simons field is expanded in powers of the fine-structure constant and compared to the nonrelativistic spectra with the fine-structure splitting, while the Chern-Simons spectrum is investigated in detail for different anomalous angular-momentum values. Fractional statistics and charge are a natural consequence of the Chern-Simons eigenfunctions. The semion (particle with exotic statistical phase factor ±i) ground state for such a hydrogen atom collapses.

The geometric (Berry) phase is shown to have its origin in the nontrivial geometry of the fiber bundle: Hilbert space→space of states. The nontrivial geometry comes simply from the scalar product in Hilbert space. A comprehensive treatment of the geometrical phase is presented, bringing together the various ideas in the literature.

It is shown that for a three-dimensional harmonic oscillator there exist families of Gaussian wave packets that retain their shape during the time evolution, i.e., the wave packet rotates around its center without spreading or deforming. This generalizes the concept of coherent vibrational motion to coherent rotational motion.

We present the theoretical energy eigenvalues of the ${}_{}{}^1{}_{}{}^{}$S ground state and the (pp${)}^3$${\mathit{P}}^{\mathit{e}}$ state of ${\mathrm{H}}^{\mathrm{-}}$ calculated in a simple configuration-interaction procedure, using a finite set of ${\mathit{L}}^2$-basis functions constructed from one-electron hydrogenic orbitals. The energy corrections, due to the electron-electron interaction between configurations with various combinations of bound (negative-energy) and continuum (positive-energy) orbitals, are examined in detail. In particular, our calculation has shown that the continuum-continuum type of configurations contribute approximately 15% and 13%, respectively, to the electron affinity of the ${}_{}{}^1{}_{}{}^{}$S ground state and the (pp${)}^3$${\mathit{P}}^{\mathit{e}}$ state of ${\mathrm{H}}^{\mathrm{-}}$. In addition, our calculation has shown that the calculated oscillator strength for the transition from the ${}_{}{}^1{}_{}{}^{}$S ground state of ${\mathrm{H}}^{\mathrm{-}}$ to the lowest ${}_{}{}^1{}_{}{}^{}$P Feshbach resonance below the n=2 threshold is significantly reduced (nearly 30%) by the presence of the continuum-continuum type of configurations in the ground-state wave function.