Critical slowing down in optical bistability

The role of critical slowing down in optical bistability is discussed, taking fully into account the non-linear effects. In particular, we show that the critical slowing down may lead to interesting novel applications, such as compact optical delay lines and electric field to time converters.     

On the theory of slowing down gracefully

We discuss the transport of a tracer particle through the Bose?CEinstein condensate of a Bose gas. The particle interacts with the atoms in the Bose gas through two-body interactions. In the limiting regime where the particle is very heavy and the Bose gas is very dense, but very weakly interacting (??mean-field limit??), the dynamics of this system corresponds to classical Hamiltonian dynamics. We show that, in this limit, the particle is decelerated by emission of gapless modes into the condensate (Cerenkov radiation). For an ideal gas, the particle eventually comes to rest. In an interacting Bose gas, the particle is decelerated until its speed equals the propagation speed of the Goldstone modes of the condensate. This is a model of ??Hamiltonian friction??. It is also of interest in connection with the phenomenon of ??decoherence?? in quantum mechanics. This note is based on work we have carried out in collaboration with D Egli, I M Sigal and A Soffer.     

Critical slowing down of space-charge field relaxation in photorefractive sillenites

We propose a theoretical model for the recently reported anomalously long decay of a space-charge field that was resonantly excited in a photorefractive sillenite crystal [Phys. Rev. Lett. 79, 67 (1997)]. The model is based on the conventional concept of charge transfer and does not require excessively large values of the quality factor for space-charge waves. The effect in question is qualified as a critical slowing of the relaxation process as the threshold of optical oscillation is approached.     

Critical slowing down in the single crystalline relaxor SBN75

The dielectric susceptibility of strontium-barium niobate, Sr_0.75Ba_0.25Nb₂O₆, reveals strong relaxor behaviour. It is shown that the relationship between the frequency of the ac probing field and the temperature, at which the real part of the susceptibility passes through a maximum, satisfactorily follows the activated dynamic scaling law predicted for the random-field Ising model. Applicability of a power law as suggested by the dynamic scaling theory is discussed.     

Critical exponents and large-order behavior of perturbation theory

The principles of the recent calculations of critical exponents from three- and two-dimensional field theory are reviewed. They rely on the Callan-Symanzik equations, diagram calculations, and on the characterization of the asymptotic behavior of perturbation series at large order. We then present new results concerning the normalization of the large-order behavior.On leave of absence from INFN, Frascati.     

Critical slowing down in a bistable model with squeezed vacuum environment

Critical slowing down effect in a bistable model of a two-level atomic medium in a ring cavity and in contact with squeezed vacuum field is examined within the mean field approximations in the high-, low- and arbitrary-Q cavity cases. Depending on the squeezed vacuum field phase parameter, the time response to linear perturbation of the incident field near the swtiching-on point can be enhanced or reduced compared with the normal vacuum case. In the low-Q cavity case with atomic collisional broadening switching time is both increased and become insensitive to the phase of the squeezed vacuum field. Analytical expressions are given and analysed for the critical (extermal) values of the incident field. In the high-Q cavity, Gaussian field feature causes lesser-steep transition between the stable states in both the normal and squeezed vacuum cases.Received: 25 April 2004, Published online: 24 August 2004PACS: 42.65.Pc Optical bistability, multistability, and switching, including local field effects - 42.65.-k Nonlinear optics     

Critical slowing down of the Gaussian spin system on diamond—type hierarchical lattices

Based on the single-spin transition critical dynamics, we have investigated the critical slowing down of the Gaussian spin model situated on the fractal family of diamond-type hierarchical lattices. We calculate the dynamical critical exponent z and the correlation-length critical exponent ν using the dynamical decimation renormalization-group technique. The result, together with some earlier ones, suggests us to conclude that on a wide range of geometries, zν=1 is the general relationship, while the two exponents depend on the specific structure. However, we have investigated for various lattices in an earlier paper, the system studied in this paper shows highly universal z=1/ν=2 independent of the structure and the dimensionality.     

Critical slowing down of fluctuations in p-terphenyl and p-quaterphenyl observed by proton spin-lattice relaxation

The temperature evolution of the proton spin-lattice relaxation time T₁ in p-terphenyl and in p-quaterphenyl around their order-disorder phase transition has been measured. In both cases pretransitional collective fluctuations destroy the high temperature Arrhenius behaviour of the relaxation rate corresponding to a single reorientational jump motion. The spin-lattice relaxation times present then a drastic decrease until the transition temperature (T₀ = 193 K in p-terphenyl, T₀ = 238 K in p-quaterphenyl). This decrease is associated to the critical slowing down of fluctuations. In the low temperature phase the ordering phenomena lead to a sharp drop of the spin-lattice relaxation rate.     

Critical slowing down in the transverse autocorrelation function of a two dimensional planar magnet

Critical slowing down in the transverse autocorrelation function of a classical two dimensional planar magnet is discussed. It is shown that the vortex contribution to the autocorrelation function decays at a rate which goes to zero as T → T⁺_c. The slowing down is associated with the disappearance of free, mobile vortices. Relevant nuclear magnetic resonance studies are suggested.     

Light pulse slowing down up to 0.025 cm/s by photorefractive two-wave coupling

It is shown experimentally and theoretically that photorefractive wave coupling can be used for dramatic (< or approximately 0.025 cm/s) deceleration of light pulses whose width is larger than (or comparable with) the nonlinear response time. This classical nonlinear scheme exhibits similarities with the technique based on the quantum effect of electromagnetically induced transparency. The main distinctive feature of our scheme is amplification of the delayed output pulse. Advantages of the novel technique and its prospects for manipulation with light photons are discussed.     

Nonequilibrium phase transitions in coordinated biological motion: Critical slowing down and switching time

In new experiments on coordinated biological motion we measure relaxation times and switching times as the system evolves from one coordinated state to another at a critical control parameter value. Deviations from the coordinated state are induced by mechanical perturbations and relative phase is used as an order parameter to monitor the dynamics of the collective state. Clear evidence for critical slowing down, a key feature of nonequilibrium phase transitions, is found. The mean and distribution of switching times closely match predictions from a stochastic dynamic theory. Together with earlier results on critical fluctuations these findings strongly favor an interpretation of coordinative change in biological systems as a nonequilibrium phase transition.     

A remark on neutron slowing down

Using the integral representation of Dirac-function the densityW _n(U) of the neutron lethargy probability distribution after then ^th collision with nuclei of a moderator has been found. The assumption has been made that the collisions are elastic and lethargy increments in individual collisions are independent. This procedure leads to expression ofW _n(U) by an improper integral which is in turn converted to a finite sum. Further the asymptotic behaviour ofW _n(U) for great number of collisionsn has been determined.Ronov pod Radhotm, Czechoslovakia.     

On the critical slowing down in superconductors

The critical dynamics in superconductors without magnetic field is studied by straightforward application of the ?-expansion technique to a generalized Ginzburg-Landau model. It is shown that the dynamic critical exponent and the time dependent correlation function coincide with those obtained by the TDGL approach.     

Critical exponents of uranium telluride

Neutron and magnetization experiments have been used to determine the critical exponents β, γ and δ of the ferromagnet UTe, T_c = 100.7(3) K, near the Curie temperature. The values are β = 0.291(4), γ = 1.326(9) and δ = 5.23(7). Comparisons are made with values from other ferromagnetic systems.     

Critical exponents and elementary particles

Particles are shown to exist for a.e. value of the mass in single phase ⁴ lattice and continuum field theories and nearest neighbor Ising models. The particles occur in the form of poles at imaginary (Minkowski) momenta of the Fourier transformed two point function. The new inequalitydm ²/dZ, where =m ₀ ² is a bare mass² andZ is the strength of the particle pole, is basic to our method. This inequality implies inequalities for critical exponents.Supported in part by the National Science Foundation under grant PHY 76-17191Supported in part by the National Science Foundation under grant MPS 75-21212     

Critical exponents for integrable models

Phase transition in quantum systems in two space-time dimensions takes place at zero temperature. A general formula is obtained for the critical exponent describing the power decrease of zero-temperature correlation functions as long distances. This formula is valid for a large class of Bethe ansatz solvable models including the Heisenberg magnet and the one-dimensional Bose gas. The critical exponent is connected with the fractional charge; it is also expressed in terms of macroscopic characteristics of the models.