Phase relaxation and pattern formation in holographic gapless charge density waves

We study the dynamics of spontaneous translation symmetry breaking in holographic models in presence of weak explicit sources. We show that, unlike conventional gapped quantum charge density wave systems, this dynamics is well characterized by the effective time dependent Ginzburg-Landau equation, both above and below the critical temperature, which leads to a “gapless” algebraic pattern of metal-insulator phase transition. In this framework we elucidate the nature of the damped Goldstone mode (the phason), which has earlier been identified in the effective hydrodynamic theory of pinned charge density wave and observed in holographic homogeneous lattice models. We follow the motion of the quasinormal modes across the dynamical phase transition in models with either periodic inhomogeneous or helical homogeneous spatial structures, showing that the phase relaxation rate is continuous at the critical temperature. Moreover, we find that the qualitative low-energy dynamics of the broken phase is universal, insensitive to the precise pattern of translation symmetry breaking, and therefore applies to homogeneous models as well.

Stable coherent mode-locking based on $$\pi$$ pulse formation in single-section lasers

Here we consider coherent mode-locking (CML) regimes in single-section cavity lasers, taking place for pulse durations less than atomic population and phase relaxation times, which arise due to coherent Rabi oscillations of the atomic inversion. Typically, CML is introduced for lasers with two sections, the gain and absorber ones. Here we show that, for certain combination of the cavity length and relaxation parameters, a very stable CML in a laser, containing only gain section, may arise. The mode-locking is unconditionally self-starting and appears due to balance of intra-pulse de-excitation and slow interpulse-scale pump-induced relaxation processes. We also discuss the scaling of the system to shorter pulse durations, showing a possibility of mode-locking for few-cycle pulses.

Theoretical Analysis of Liquid–Ice Interaction in the Unsaturated Environment with Application to the Problem of Homogeneous Mixing

The process of ice–liquid water interaction in the unsaturated environment is explored both analytically and with the help of a numerical simulation. Ice–liquid water interaction via the condensation–evaporation mechanism is considered in relation to the problem of homogeneous mixing in an unmovable air volume. The process is separated into three stages: the homogenization stage, during which the rapid alignment of thermodynamic and microphysical parameters in the mixing volume takes place; the glaciation stage, during which the liquid droplets evaporate; and the ice stage, which leads to attaining a thermodynamic equilibrium. Depending on the initial temperature, humidity, and mixing ratios of liquid water and of ice water, the third stage may result in two outcomes: existence of ice particles under zero supersaturation with respect to ice or a complete disappearance of ice particles. Three characteristic times are associated with the microphysical stages: the phase relaxation time associated with droplets, the glaciation time determined by the Wegener–Bergeron–Findeisen process, and the phase relaxation time associated with ice. Since the duration of the second and third microphysical stages may be of the same order as the homogenization time or even longer, the homogeneous mixing scenario is more probable in mixed-phase clouds than in liquid clouds. It is shown that mixing of a mixed-phase cloud with a dry environment accelerates cloud glaciation, leading to a decrease in the glaciation time by more than 2 times. The conditions of fast ice particles’ disappearance due to sublimation are analyzed as well.

Influence of Microphysical Variability on Stochastic Condensation in a Turbulent Laboratory Cloud

Diffusional growth of droplets by stochastic condensation and a resulting broadening of the size distribution has been considered as a mechanism for bridging the cloud droplet growth gap between condensation and collision–coalescence. Recent studies have shown that supersaturation fluctuations can lead to a broadening of the droplet size distribution at the condensational stage of droplet growth. However, most studies using stochastic models assume the phase relaxation time of a cloud parcel to be constant. In this paper, two questions are asked: how variability in droplet number concentration and radius influence the phase relaxation time and what effect it has on the droplet size distributions. To answer these questions, steady-state cloud conditions are created in the laboratory and digital inline holography is used to directly observe the variations in local number concentration and droplet size distribution and, thereby, the integral radius. Stochastic equations are also extended to account for fluctuations in integral radius and obtain new terms that are compared with the laboratory observations. It is found that the variability in integral radius is primarily driven by variations in the droplet number concentration and not the droplet radius. This variability does not contribute significantly to the mean droplet growth rate but does contribute significantly to the rate of increase of the size distribution width.

Supersaturation Fluctuations during the Early Stage of Cumulus Formation

On time scales that are long compared to the phase relaxation time, a quasi-steady supersaturation sqs is expected to exist in clouds. On shorter time scales, however, turbulent fluctuations of temperature and water vapor concentration should generate fluctuations in supersaturation. The variability of temperature, water vapor, and supersaturation has been measured in situ with submeter resolution in warm, continental, shallow cumulus clouds. Several cumuli with horizontal extents of order 100 m were sampled during their first appearance and development to depths of ~100 m in a growing boundary layer. Fluctuations of the saturation ratio are observed to be approximately normally distributed with standard deviations on the order of 1%. This variability is almost one order of magnitude larger than sqs calculated using simultaneous measurements of the vertical velocity component and the droplet size distribution. It is argued that, depending on the ratio of the phase relaxation and the turbulent mixing time, substantial fluctuations in the supersaturation field can exist on small spatial scales, centered on sqs for the mean state. The observations also suggest that, on larger scales, fluctuations of the supersaturation field are damped by cloud droplet growth. Droplets with diameters of up to 20 μm were observed in the shallow cumulus clouds, whereas the adiabatic diameter was less than 10 μm. Such large droplets may be explained by a few droplets experiencing the highest observed supersaturations for a certain time. Consequences for aerosol activation and droplet size dispersion in a highly fluctuating supersaturation field are briefly discussed.