Factorisation in large-N limit of lattice gauge theories revisited

We prove using the Schwinger-Dyson equations that the factorisation property holds for all gauge-invariant Green’s function in the large-N limit of a Wilson-Polyakov lattice gauge theory.     

The O(N) vector model in the large-N limit revisited: multicritical points and double scaling limit

The multicritical points of the O(N)-invariant N vector model in the large-N limit are re-examined. Of particular interest are the subtleties involved in the stability of the phase structure at critical dimensions. In the limit N → ∞ while the coupling g → g_c in a correlated manner (the double scaling limit) a massless bound state O(N) singlet is formed and powers of 1/N are compensated by IR singularities. The persistence of the N → ∞ results beyond the leading order is then studied with particular interest in the possible existence of a phase with propagating small mass vector fields and a massless singlet bound state. We point out that under certain conditions the double scaled theory of the singlet field is non-interacting in critical dimensions.     

The phase state revisited: the Heisenberg limit in a quantum nondemolition measurement and the nonclassical depth of the state

We consider a quantum nondemolition measurement, the apparatus consisting of a Mach–Zehnder single-photon (signal) interferometer where in one arm the signal interacts (through a Kerr medium) with a probe beam. This interaction affects the visibility of the interferometer and induces a phase shift in the state of the probe beam. Here we investigate the effects of such interaction when the probe state is in the truncated phase state, |Θ_m〉=(1+N)^−1/2∑_n=0^Ne^inΘ_m|n〉, analyze the Heisenberg limit for the phase shift measurement, and its possible relation to the nonclassical depth of the state.     

The Gacs-Kurdyumov-Levin automaton revisited

We study a one-dimensional cellular automaton that was originally proposed as a candidate for exhibiting nonergodic behavior under noise. We prove that the deterministic model has the eroder property for two and only two invariant states. Moreover, we give the best possible estimates for the corresponding erosion times. We then review the results we have obtained from extensive computer simulations for the stochastic model and for a mixed model and argue that they suggest numerical and heuristic evidence in favour of ergodic behavior for all nonzero values of the noise parameter.     

The Franson experiment revisited

Previously, the Franson experiment was challenged as a true test of local realism. In this Letter we review this situation and show that this experiment reveals a peculiar behavior when we try to, simultaneously, explain second and fourth order interferences. In order to enhance this idea, a proposed local model is discussed.     

The Onsager-Casimir relations revisited

We study the fate of the Onsager-Casimir reciprocity relations for a continuous system when some of its variables are eliminated adiabatically. Just as for discrete systems, deviations appear in correction terms to the reduced evolution equation that are of higher order in the time scale ratio. The deviations are not removed by including correction terms to the coarse-grained thermodynamic potential. However, via a reformulation of the theory, in which the central role of the thermodynamic potential is taken over by an associated Lagrangian-type expression, we arrive at a modified form of the Onsager-Casimir relations that survives the adiabatic elimination procedure. There is a simple relation between the time evolution of the redefined thermodynamic forces and that of the basic thermodynamic variables; this relation also survives the adiabatic elimination. The formalism is illustrated by explicit calculations for the Klein-Kramers equation, which describes the phase space distribution of Brownian particles, and for the corrected Smoluchowski equation derived from it by adiabatic elimination of the velocity variable. The symmetry relation for the latter leads to a simple proof that the reality of the eigenvalues of the simple Smoluchowski equation is not destroyed by the addition of higher order corrections, at least not within the framework of a formal perturbation expansion in the time scale ratio.     

The cosmological constant revisited

I briefly review the observational evidence for a small cosmological constant at the present epoch. This evidence mainly comes from high redshift observations of Type 1a supernovae, which, when combined with CMB observations strongly support a flat Universe with Ω _m + Ω_A ⋍ 1. Theoretically a cosmological constant can arise from zero point vacuum fluctuations. In addition ultra-light scalar fields could also give rise to a Universe which is accelerating driven by a time dependent Λ-term induced by the scalar field potential. Finally a Λ dominated Universe also finds support from observations of galaxy clustering and the age of the Universe.     

The Hamilton-Jacobi equation revisited

A new analysis of the nature of the solutions of the Hamilton-Jacobi equation of classical dynamics is presented based on Caratheodory’s theorem concerning canonical transformations. The special role of a principal set of solutions is stressed, and the existence of analogous results in quantum mechanics is outlined.     

The Armstrong experiment revisited

When a high-voltage direct-current is applied to two beakers filled with water or polar liquid dielectrica, a horizontal bridge forms between the two beakers. This experiment was first carried out by Lord Armstrong in 1893 and then forgotten until recently. Such bridges are stable by the action of electrohydrodynamic (EHD) forces caused by electric field gradients counteracting gravity. Due to these gradients a permanent pumping of liquid from one beaker into the other is observed. At macroscopic scale several of the properties of a horizontal water bridge can be explained by modern electrohydrodynamics, analyzing the motion of fluids in electric fields. Whereas on the molecular scale water can be described by quantum mechanics, there is a conceptual gap at mesoscopic scale which is bridged by a number of theories including quantum mechanical entanglement and coherent structures in water – theories that we discuss here. Much of the phenomenon is already understood, but even more can still be learned from it, since such “floating” liquid bridges resemble a small high voltage laboratory of their own: The physics of liquids in electric fields of some kV/cm can be studied, even long time experiments like neutron or light scattering are feasible since the bridge is in a steady-state equilibrium and can be kept stable for hours. It is also an electro-chemical reactor where compounds are transported through by the EHD flow, enabling the study of electrochemical reactions under potentials which are otherwise not easily accessible. Last but not least the bridge provides the experimental biologist with the opportunity to expose living organisms such as bacteria to electric fields without killing them, but with a significant influence on their behavior, and possibly, even on their genome.     

The eikonal approximation revisited

Summary Certain problems in optical scattering are best understood when the more complicated exact scattering theory is replaced by an approximation. The Fraunhofer approximation is a well-known example. In the past ten years a considerable amount of work has been done in various disciplines towards assessing the usefulness of a new approximation referred to in the literature either as the eikonal approximation or as the high-energy approximation. The purpose of this paper is to provide a much needed review of this work and in addition to examine the historical evolution of this approximation which essentially started in optics when Bruns introduced the term eikonal in 1895. Part of this work was done when SKS was at Saha Institute of Nuclear Physics, Calcutta, and at Institute of Wetland Management and Ecological Design, Calcutta, India.     

The dripping faucet revisited

High accuracy experimental results on the nonlinear dynamical behaviour of a dripping faucet are presented. The distribution functions for droplet sizes and drip intervals together with return maps are studied for various dripping rates. Increasing this control parameter, chaotic behaviour is obtained and discussed. (c) 1996 American Institute of Physics.     

The trousers problem revisited

Anderson and DeWitt considered the quantization of a massless scalar field in a spacetime whose spacelike hypersurfaces change topology and concluded that the topology change gives rise to infinite particle and energy production. We show here that their calculations are insufficient and that their propagation rule is unphysical. However, our results using a more general propagation rule support their conclusion.     

The modulation instability revisited

The modulational instability (or “Benjamin-Feir instability”) has been a fundamental principle of nonlinear wave propagation in systems without dissipation ever since it was discovered in the 1960s. It is often identified as a mechanism by which energy spreads from one dominant Fourier mode to neighboring modes. In recent work, we have explored how damping affects this instability, both mathematically and experimentally. Mathematically, the modulational instability changes fundamentally in the presence of damping: for waves of small or moderate amplitude, damping (of the right kind) stabilizes the instability. Experimentally, we observe wavetrains of small or moderate amplitude that are stable within the lengths of our wavetanks, and we find that the damped theory predicts the evolution of these wavetrains much more accurately than earlier theories. For waves of larger amplitude, neither the standard (undamped) theory nor the damped theory is accurate, because frequency downshifting affects the evolution in ways that are still poorly understood.     

The scar mechanism revisited

Unstable periodic orbits are known to originate scars on some eigen-functions of classically chaotic systems through recurrences causing that some part of an initial distribution of quantum probability in its vicinity returns periodically close to the initial point. In the energy domain, these recurrences are seen to accumulate quantum density along the orbit by a constructive interference mechanism when the appropriate quantization (on the action of the scarring orbit) is fulfilled. Other quantized phase space circuits, such as those defined by homoclinic tori, are also important in the coherent transport of quantum density in chaotic systems. The relationship of this secondary quantum transport mechanism with the standard mechanism for scarring is here discussed and analyzed.     

The Zeeman effect revisited

We announce three new rigorous results for the quantum mechanical hydrogen atom in constant magnetic field: (i) Borel summability of the small field perturbation series, (ii) detailed large field asymptotics, and (iii) non-degeneracy of the ground state Ω₀ and a proof that it has $\text{L}{}_{\mathrm{z}}\text{Ω}{}_0\text{= 0}$ for all values of the field.     

The weak coupling limit as a quantum functional central limit

We show that, in the weak coupling limit, the laser model process converges weakly in the sense of the matrix elements to a quantum diffusion whose equation is explicitly obtained. We prove convergence, in the same sense, of the Heisenberg evolution of an observable of the system to the solution of a quantum Langevin equation. As a corollary of this result, via the quantum Feynman-Kac technique, one can recover previous results on the quantum master equation for reduced evolutions of open systems. When applied to some particular model (e.g. the free Boson gas) our results allow to interpret the Lamb shift as an Ito correction term and to express the pumping rates in terms of quantities related to the original Hamiltonian model.