Phase relaxation of Faraday surface waves

Surface waves on a liquid air interface excited by a vertical vibration of a fluid layer (Faraday waves) are employed to investigate the phase relaxation of ideally ordered patterns. By means of a combined frequency-amplitude modulation of the excitation signal a periodic expansion and dilatation of a square wave pattern is generated, the dynamics of which is well described by a Debye relaxator. By comparison with the results of a linear theory it is shown that this practice allows a precise measurement of the phase diffusion constant.Comment: 5 figure

Crossover from a square to a hexagonal pattern in Faraday surface waves

We report on surface wave pattern formation in a Faraday experiment operated at a very shallow filling level, where modes with a subharmonic and harmonic time dependence interact. Associated with this distinct temporal behavior are different pattern selection mechanisms, favoring squares or hexagons, respectively. In a series of bifurcations running through a pair of superlattices the surface wave pattern transforms between the two incompatible symmetries. The close analogy to 2D and 3D crystallography is pointed out.Comment: 4 pages, 4 figure

Liquid n-hexane condensed in silica nanochannels: A combined optical birefringence and vapor sorption isotherm study

The optical birefringence of liquid n-hexane condensed in an array of parallel silica channels of 7nm diameter and 400 micrometer length is studied as a function of filling of the channels via the vapor phase. By an analysis with the generalized Bruggeman effective medium equation we demonstrate that such measurements are insensitive to the detailed geometrical (positional) arrangement of the adsorbed liquid inside the channels. However, this technique is particularly suitable to search for any optical anisotropies and thus collective orientational order as a function of channel filling. Nevertheless, no hints for such anisotropies are found in liquid n-hexane. The n-hexane molecules in the silica nanochannels are totally orientationally disordered in all condensation regimes, in particular in the film growth as well as in the the capillary condensed regime. Thus, the peculiar molecular arrangement found upon freezing of liquid n-hexane in nanochannel-confinement, where the molecules are collectively aligned perpendicularly to the channels' long axes, does not originate in any pre-alignment effects in the nanoconfined liquid due to capillary nematization.Comment: 7 pages, 5 figure

Preferred orientation of n-hexane crystallized in silicon nanochannels: A combined x-ray diffraction and sorption isotherm study

We present an x-ray diffraction study on n-hexane in tubular silicon channels of approximately 10 nm diameter both as a function of the filling fraction f of the channels and as a function of temperature. Upon cooling, confined n-hexane crystallizes in a triclinic phase typical of the bulk crystalline state. However, the anisotropic spatial confinement leads to a preferred orientation of the confined crystallites, where the crystallographic direction coincides with the long axis of the channels. The magnitude of this preferred orientation increases with the filling fraction, which corroborates the assumption of a Bridgman-type crystallization process being responsible for the peculiar crystalline texture. This growth process predicts for a channel-like confinement an alignment of the fastest crystallization direction parallel to the long channel axis. It is expected to be increasingly effective with the length of solidifying liquid parcels and thus with increasing f. In fact, the fastest solidification front is expected to sweep over the full silicon nanochannel for f=1, in agreement with our observation of a practically perfect texture for entirely filled nanochannels

Real-time observation of interfering crystal electrons in high-harmonic generation

Accelerating and colliding particles has been a key strategy to explore the texture of matter. Strong lightwaves can control and recollide electronic wavepackets, generating high-harmonic (HH) radiation which encodes the structure and dynamics of atoms and molecules and lays the foundations of attosecond science. The recent discovery of HH generation in bulk solids combines the idea of ultrafast acceleration with complex condensed matter systems and sparks hope for compact solid-state attosecond sources and electronics at optical frequencies. Yet the underlying quantum motion has not been observable in real time. Here, we study HH generation in a bulk solid directly in the time-domain, revealing a new quality of strong-field excitations in the crystal. Unlike established atomic sources, our solid emits HH radiation as a sequence of subcycle bursts which coincide temporally with the field crests of one polarity of the driving terahertz waveform. We show that these features hallmark a novel non-perturbative quantum interference involving electrons from multiple valence bands. The results identify key mechanisms for future solid-state attosecond sources and next-generation lightwave electronics. The new quantum interference justifies the hope for all-optical bandstructure reconstruction and lays the foundation for possible quantum logic operations at optical clock rates

Energy evolution in time-dependent harmonic oscillator

The theory of adiabatic invariants has a long history, and very important implications and applications in many different branches of physics, classically and quantally, but is rarely founded on rigorous results. Here we treat the general time-dependent one-dimensional harmonic oscillator, whose Newton equation $\ddot{q} + \omega^2(t) q=0$ cannot be solved in general. We follow the time-evolution of an initial ensemble of phase points with sharply defined energy $E_0$ at time $t=0$ and calculate rigorously the distribution of energy $E_1$ after time $t=T$, which is fully (all moments, including the variance $\mu^2$) determined by the first moment $\bar{E_1}$. For example, $\mu^2 = E_0^2 [(\bar{E_1}/E_0)^2 - (\omega (T)/\omega (0))^2]/2$, and all higher even moments are powers of $\mu^2$, whilst the odd ones vanish identically. This distribution function does not depend on any further details of the function $\omega (t)$ and is in this sense universal. In ideal adiabaticity $\bar{E_1} = \omega(T) E_0/\omega(0)$, and the variance $\mu^2$ is zero, whilst for finite $T$ we calculate $\bar{E_1}$, and $\mu^2$ for the general case using exact WKB-theory to all orders. We prove that if $\omega (t)$ is of class ${\cal C}^{m}$ (all derivatives up to and including the order $m$ are continuous) $\mu \propto T^{-(m+1)}$, whilst for class ${\cal C}^{\infty}$ it is known to be exponential $\mu \propto \exp (-\alpha T)$.Comment: 26 pages, 5 figure