Low Density Regime Research Articles

Percolation of randomly distributed growing clusters: the low initial density regime

We investigate the problem of growing clusters, which is modeled by two dimensional disks and three dimensional droplets. In this model we place a number of seeds on random locations on a lattice with an initial occupation probability, $p$. The seeds simultaneously grow with a constant velocity to form clusters. When two or more clusters eventually touch each other they immediately stop their growth. The probability that such a system will result in a percolating cluster depends on the density of the initially distributed seeds and the dimensionality of the system. For very low initial values of $p$ we find a power law behavior for several properties that we investigate, namely for the size of the largest and second largest cluster, for the probability for a site to belong to the finally formed spanning cluster, and for the mean radius of the finally formed droplets. We report the values of the corresponding scaling exponents. Finally, we show that for very low initial concentration of seeds the final coverage takes a constant value which depends on the system dimensionality.

In situ concentration measurements around the transition between two dendritic growth regimes

A transition between two different dendritic growth regimes in the electrodeposition of a metal from a binary electrolyte was studied using two different optical techniques. These regimes are observed respectively at current densities below and above the limiting diffusion current density. In situ concentration measurements around the transition were performed by laser interferometry and optical absorption due to Cu 2+ ion. These measurements reveal that concentration profiles and their time evolution are different in the two growth regimes: before the transition, corresponding to the high current density regime, concentration gradients are uniform throughout the cell, and the concentration increases with time at the anode. After the transition to low current density regime, the concentration gradient in front of the most prominent dendrite increases markedly, while the concentration becomes almost constant at the anode. At the transition, the time evolution of the cell potential slows down significantly.

Thermodynamics of d-dimensional hard sphere fluids confined to micropores

We derive an analytical expression of the second virial coefficient of d-dimensional hard sphere fluids confined to slit pores by applying Speedy and Reiss' interpretation of cavity space. We confirm that this coefficient is identical to the one obtained from the Mayer cluster expansion up to second order with respect to fugacity. The key step of both approaches is to evaluate either the surface area or the volume of the d-dimensional exclusion sphere confined to a slit pore. We, further, present an analytical form of thermodynamic functions such as entropy and pressure tensor as a function of the size of the slit pore. Molecular dynamics simulations are performed for d = 2 and d = 3, and the results are compared with analytically obtained equations of state. They agree satisfactorily in the low density regime, and, for given density, the agreement of the results becomes excellent as the width of the slit pore gets smaller, because the higher order virial coefficients become unimportant.

Wall material and roughness effects on transmittable shear stresses of magnetorheological fluids in plate–plate magnetorheometry

A direct comparison of plate–plate magnetorheometry results for nonmagnetic (titanium/brass) and ferromagnetic plates is presented, using a modified Anton Paar magnetocell MRD180/1T. Necessary corrections to derive the true flux density in the magnetorheological fluid (MRF) from the online Hall probe reading and to account for the gap opening effect caused by normal forces on shear stress and flux density are addressed. The measured shear stress versus magnetic flux density characteristics agree in the low flux density regime <0.1 T but yield distinctly higher transmittable shear stresses for ferromagnetic plates at elevated flux densities (49% increase at 1 T for 90% by weight carbonyl iron powder (CIP) and 84% for 85% by weight CIP). Remarkably, the normal force, if corrected for its magnetostatic part, remains independent of the type of plates up to about 0.6 T. We address the role of normal forces, of magnetic interactions between CIP and wall, as well as the role of wall roughness in a solid body friction model. A systematic variation of wall properties and materials was achieved by introducing both a modular rotor and stator, which ease the variation of the walls in contact to the MRF. The transmittable shear stress of nonmagnetic plates (e.g., brass) may be increased up to the level of ferromagnetic disks by a higher wall roughness or by grooves. No shear stress increase is obtained for grooves in ferromagnetic plates, which is explained by the different local flux density modulation at the grooves for ferromagnetic compared to nonmagnetic plates. Finally, we address the effect of ferromagnetic and nonmagnetic coatings on brass and steel disks, and show that, e.g., a layer of CIP on brass efficiently increases the transmittable shear stress.

Isentropic curves at magnetic phase transitions

Experiments on cold atom systems in which a lattice potential is ramped up on a confined cloud have raised intriguing questions about how the temperature varies along isentropic curves, and how these curves intersect features in the phase diagram. In this paper, we study the isentropic curves of two models of magnetic phase transitions- the classical Blume-Capel Model (BCM) and the Fermi Hubbard Model (FHM). Both Mean Field Theory (MFT) and Monte Carlo (MC) methods are used. The isentropic curves of the BCM generally run parallel to the phase boundary in the Ising regime of low vacancy density, but intersect the phase boundary when the magnetic transition is mainly driven by a proliferation of vacancies. Adiabatic heating occurs in moving away from the phase boundary. The isentropes of the half-filled FHM have a relatively simple structure, running parallel to the temperature axis in the paramagnetic phase, and then curving upwards as the antiferromagnetic transition occurs. However, in the doped case, where two magnetic phase boundaries are crossed, the isentrope topology is considerably more complex.

Anomalous reflection properties in high density limit fibril shaped PIC‐J aggregates in microcavity structure

AbstractWe report our recent observations on anomalous reflection properties of organic microcavity containing PIC J‐aggregates in fibril‐shaped structures as one of their highest‐density limiting case. Even in ordinary low density PIC‐Js dispersed in polymer matrices, they easily go into the exciton‐photon strong coupling regime and new quantum states, i.e. exciton‐polaritons, are formed. Vacuum Rabi‐splitting, an indicator of the coupling strength, can be controlled by the density of PIC‐Js in the microcavities in low density regime. Fibril‐shaped PIC‐J aggregates are bundle‐like, self‐assembled higher‐order structure of Js and are considered as a high‐density limiting case. Angular dependence of the local reflection spectra are observed by our improved microscopy. While in the low density cases, clear anti‐crossing behaviours of the two branches appear, which is the evidence of the polariton formations, the highest‐density limiting cases show one or two anomalous reflection dip structures with almost no angular dependence. The result is inconsistent with neither ordinary polariton reflection property nor bare exciton nor cavity photon properties. We tentatively consider that the anomaly is inherent to the fibril formation and is caused by possible breakdown of polariton coherence due to the inter‐fiber energy transfer. (© 2011 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Equilibrium and off-equilibrium trap-size scaling in one-dimensional ultracold bosonic gases

We study some aspects of equilibrium and off equilibrium quantum dynamics of dilute bosonic gases in the presence of a trapping potential. We consider systems with a fixed number of particles N and study their scaling behavior with increasing the trap size. We focus on one-dimensional (1D) bosonic systems, such as gases described by the Lieb-Liniger model and its Tonks-Girardeau limit of impenetrable bosons, and gases constrained in optical lattices as described by the Bose-Hubbard model. We study their quantum (zero-temperature) behavior at equilibrium and off equilibrium during the unitary time evolution arising from changes of the trapping potential, which may be instantaneous or described by a power-law time dependence, starting from the equilibrium ground state for a initial trap size. Renormalization-group scaling arguments, analytical and numerical calculations show that the trap-size dependence of the equilibrium and off-equilibrium dynamics can be cast in the form of a trap-size scaling in the low-density regime, characterized by universal power laws of the trap size, in dilute gases with repulsive contact interactions and lattice systems described by the Bose-Hubbard model. The scaling functions corresponding to several physically interesting observables are computed. Our results are of experimental relevance for systems of cold atomic gases trapped by tunable confining potentials.

BCS Wave-Function Approach to the BEC-BCS Crossover of Exciton-Polariton Condensates

The crossover between low and high density regimes of exciton-polariton condensates is examined using a BCS wave-function approach. Our approach is an extension of the BEC-BCS crossover theory for excitons, but includes a cavity photon field. The approach can describe both the low density limit, where the system can be described as a Bose-Einstein condensate (BEC) of exciton-polaritons, and the high density limit, where the system enters a photon-dominated regime. In contrast to the exciton BEC-BCS crossover where the system approaches an electron-hole plasma, the polariton high density limit has strongly correlated electron-hole pairs. At intermediate densities, there is a regime with BCS-like properties, with a peak at nonzero momentum of the singlet pair function. We calculate the expected photoluminescence and give several experimental signatures of the crossover.

Overlapping-gate architecture for silicon Hall bar field-effect transistors in the low electron density regime

We report the fabrication and study of Hall bar field-effect transistors in which an overlapping-gate architecture allows four-terminal measurements of low-density two-dimensional electron systems while maintaining a high density at the Ohmic contacts. Comparison with devices made using a standard single gate show that measurements can be performed at much lower densities and higher channel resistances, despite a reduced peak mobility. We also observe a voltage threshold shift which we attribute to negative oxide charge, injected during electron-beam lithography processing.

Fast magnetic reconnection in low-density electron-positron plasmas

Two-dimensional particle-in-cell simulations have been performed to study magnetic reconnection in low-density electron-positron plasmas without a guide magnetic field. Impulsive reconnection rates become of the order of unity when the background density is much smaller than 10% of the density in the initial current layer. It is demonstrated that the outflow speed is less than the upstream Alfvén speed, and that the time derivative of the density must be taken into account in the definition of the reconnection rate. The reconnection electric fields in the low-density regime become much larger than the ones in the high-density regime, and it is possible to accelerate the particles to high energies more efficiently. The inertial term in the generalized Ohm’s law is the most dominant term that supports a large reconnection electric field. An effective collisionless resistivity is produced and tracks the extension of the diffusion region in the late stage of the reconnection dynamics, and significant broadening of the diffusion region is observed. Because of the broadening of the diffusion region, no secondary islands, which have been considered to play a role to limit the diffusion region, are generated during the extension of the diffusion region in the outflow direction.

Direct observation of single-charge-detection capability of nanowire field-effect transistors

A single localized charge can quench the luminescence of a semiconductor nanowire, but relatively little is known about the effect of single charges on the conductance of the nanowire. In one-dimensional nanostructures embedded in a material with a low dielectric permittivity, the Coulomb interaction and excitonic binding energy are much larger than the corresponding values when embedded in a material with the same dielectric permittivity. The stronger Coulomb interaction is also predicted to limit the carrier mobility in nanowires. Here, we experimentally isolate and study the effect of individual localized electrons on carrier transport in InAs nanowire field-effect transistors, and extract the equivalent charge sensitivity. In the low carrier density regime, the electrostatic potential produced by one electron can create an insulating weak link in an otherwise conducting nanowire field-effect transistor, modulating its conductance by as much as 4,200% at 31 K. The equivalent charge sensitivity, 4 × 10(-5) e Hz(-1/2) at 25 K and 6 × 10(-5) e Hz(-1/2) at 198 K, is orders of magnitude better than conventional field-effect transistors and nanoelectromechanical systems, and is just a factor of 20-30 away from the record sensitivity for state-of-the-art single-electron transistors operating below 4 K (ref. 8). This work demonstrates the feasibility of nanowire-based single-electron memories and illustrates a physical process of potential relevance for high performance chemical sensors. The charge-state-detection capability we demonstrate also makes the nanowire field-effect transistor a promising host system for impurities (which may be introduced intentionally or unintentionally) with potentially long spin lifetimes, because such transistors offer more sensitive spin-to-charge conversion readout than schemes based on conventional field-effect transistors.

Dielectric confinement in quantum dots of arbitrary shape within the local spin density approximation: Diluted regimes in elongated quantum dots

We propose a simplified and computationally feasible model accounting for the dielectric confinement in arbitrarily shaped many-electron quantum dots, within the local spin density approximation. The model yields quite a good agreement with full configuration interaction calculations including exact dielectric confinement. The model is used to study the influence of the dielectric confinement on the electronic charge distribution of elongated quantum dots in the low density regime.

Hole spin relaxation in intrinsic andp-type bulk GaAs

We investigate hole spin relaxation in intrinsic and $p$-type bulk GaAs from a fully microscopic kinetic spin Bloch equation approach. In contrast to the previous study on hole spin dynamics, we explicitly include the intraband coherence and the nonpolar hole-optical-phonon interaction, both of which are demonstrated to be of great importance to the hole spin relaxation. The relative contributions of the D'yakonov-Perel' and Elliott-Yafet mechanisms on hole spin relaxation are also analyzed. In our calculation, the screening constant, playing an important role in the hole spin relaxation, is treated with the random phase approximation. In intrinsic GaAs, our result shows good agreement with the experiment data at room temperature, where the hole spin relaxation is demonstrated to be dominated by the Elliott-Yafet mechanism. We also find that the hole spin relaxation strongly depends on the temperature and predict a valley in the density dependence of the hole spin relaxation time at low temperature due to the hole-electron scattering. In $p$-type GaAs, we predict a peak in the spin relaxation time against the hole density at low temperature, which originates from the distinct behaviors of the screening in the degenerate and nondegenerate regimes. The competition between the screening and the momentum exchange during scattering events can also lead to a valley in the density dependence of the hole spin relaxation time in the low density regime. At high temperature, the effect of the screening is suppressed due to the small screening constant. Moreover, we predict a nonmonotonic dependence of the hole spin relaxation time on temperature associated with the screening together with the hole-phonon scattering. Finally, we find that the D'yakonov-Perel' mechanism can markedly contribute to the .... (omitted due to the limit of space)

Chemical potential and internal energy of the noninteracting Fermi gas in fractional-dimensional space

Chemical potential and internal energy of a noninteracting Fermi gas at low temperature are evaluated using the Sommerfeld method in the fractional-dimensional space. When temperature increases, the chemical potential decreases below the Fermi energy for any dimension equal to 2 and above due to the small entropy, while it increases above the Fermi energy for dimensions below 2 as a result of high entropy. The ranges of validity of the truncated series expansions of these quantities are extended from low to intermediate temperature regime as well as from high to relatively low density regime by using the Pade approximant technique.

Electronic phase coherence and relaxation in graphene field effect transistor

Using the low-field magnetoresistance measurement we have studied the electronic phase coherence of the graphene field effect transistor for different carrier types and densities. The characteristic time scales such as phase coherence time ( τ ϕ ), intervalley scattering time ( τ i ), and momentum relaxation time have been deduced by weak localization fit to the magnetoresistance. We found that the magnitude of τ ϕ shows similar magnitudes for both types of charge carriers. In the lower density regime including the Dirac point, τ ϕ increases rapidly as the density of carrier increases. However, τ i shows a weak dependence of carrier type and density. The momentum relaxation time becomes saturated below 3 K regardless of carrier type and density, which is in contrast to the temperature dependence of τ ϕ .

Localization of electrons and formation of two-dimensional Wigner spin lattices in a special cylindrical semiconductor stripe

We consider a two-dimensional (2D)electron gas residing on the surface of a cylinder of a given radius $R$ in the presence of a parabolic confinement along the axis of the cylinder. In this way the system of electrons forms a closed cylindrical stripe (wire). Using the local spin-density technique we first consider localization of electrons within of a potential barrier embedded in the wire. Barriers with sharp retangularlike features are populated in steps because of Coulomb blockade. The nature of a single bound state in a short soft barrier (quantum point contacts) at pinch-off is discussed in terms Coulomb blockade. For a shallow barrier-free wire we retrace the structural transitions at low electron densities from a single chain of localized states to double and triple chains (Wigner spin lattices). The present system is related to the model of a inhomogeneous quantum wire introduced recently by G\"u\ifmmode \mbox{\c{c}}\else \c{c}\fi{}l\"u et al. [Phys. Rev. B 80, 201302(R) (2009)]. An important aspect is, however, the present extension into higher electron densities as well as to the low-density regime and the formation of 2D Wigner microlattices.

Quantum field theory for the three-body constrained lattice Bose gas. II. Application to the many-body problem

We analyze the ground state phase diagram of attractive lattice bosons, which are stabilized by a three-body onsite hardcore constraint. A salient feature of this model is an Ising type transition from a conventional atomic superfluid to a dimer superfluid with vanishing atomic condensate. The study builds on an exact mapping of the constrained model to a theory of coupled bosons with polynomial interactions, proposed in a related paper [11]. In this framework, we focus by analytical means on aspects of the phase diagram which are intimately connected to interactions, and are thus not accessible in a mean field plus spin wave approach. First, we determine shifts in the mean field phase border, which are most pronounced in the low density regime. Second, the investigation of the strong coupling limit reveals the existence of a new collective mode, which emerges as a consequence of enhanced symmetries in this regime. Third, we show that the Ising type phase transition, driven first order via the competition of long wavelength modes at generic fillings, terminates into a true Ising quantum critical point in the vicinity of half filling.

Influence of laser parameters and staining on femtosecond laser-based intracellular nanosurgery

Femtosecond (fs) laser-based intracellular nanosurgery has become an important tool in cell biology, albeit the mechanisms in the so-called low-density plasma regime are largely unknown. Previous calculations of free-electron densities for intracellular surgery used water as a model substance for biological media and neglected the presence of dye and biomolecules. In addition, it is still unclear on which time scales free-electron and free-radical induced chemical effects take place in a cellular environment. Here, we present our experimental study on the influence of laser parameters and staining on the intracellular ablation threshold in the low-density plasma regime. We found that the ablation effect of fs laser pulse trains resulted from the accumulation of single-shot multiphoton-induced photochemical effects finished within a few nanoseconds. At the threshold, the number of applied pulses was inversely proportional to a higher order of the irradiance, depending on the laser repetition rate and wavelength. Furthermore, fluorescence staining of subcellular structures before surgery significantly decreased the ablation threshold. Based on our findings, we propose that dye molecules are the major source for providing seed electrons for the ionization cascade. Consequently, future calculations of free-electron densities for intracellular nanosurgery have to take them into account, especially in the calculations of multiphoton ionization rates.

Autocorrelations in the totally asymmetric simple exclusion process and Nagel-Schreckenberg model

We study via Monte Carlo simulation the dynamics of the Nagel-Schreckenberg model on a finite system of length L with open boundary conditions and parallel updates. We find numerically that in both the high and low density regimes the autocorrelation function of the system density behaves like 1-|t|/τ with a finite support [-τ,τ] . This is in contrast to the usual exponential decay typical of equilibrium systems. Furthermore, our results suggest that in fact τ=L/c , and in the special case of maximum velocity v{max}=1 (corresponding to the totally asymmetric simple exclusion process) we can identify the exact dependence of c on the input, output and hopping rates. We also emphasize that the parameter τ corresponds to the integrated autocorrelation time, which plays a fundamental role in quantifying the statistical errors in Monte Carlo simulations of these models.

Experimental Study on Nonlocality of Heat Transport in LHD

The observation of a significant rise of the core electron temperature Te in response to edge cooling in a helical plasma was first made on the Large Helical Device (LHD). When the phenomenon takes place, the core electron heat flux is reduced abruptly without changing the thermodynamic values in the region of interest (core). Thus, the phenomenon observed in LHD can be equated to a “nonlocal transport phenomenon,” observed so far only in tokamaks. The nonlocal transport phenomenon in LHD takes place in almost the same parametric domain (i.e., in a high-temperature and low-density regime) as in tokamaks. Meanwhile, various new aspects of the nonlocal transport phenomenon have been revealed by the LHD experiments; for example, (1) in LHD, the nonlocal transport phenomenon has been observed in net current-free plasmas sustained only by electron cyclotron heating. This experimental result can completely rule out the contribution of the toroidal plasma current as a reason for the nonlocal transport phenomenon. (2) It has been found that during the nonlocal transport phenomenon, there appears a strong correlation between core electron heat flux and edge Te gradient on a timescale shorter than the diffusion time and a spatial scale longer than the microturbulence correlation length. At that time, it was also found that an envelope of density fluctuations is modulated with a low frequency (≤2 kHz), which suggests the existence of a long-ranged turbulent structure in the plasma, where the nonlocal transport phenomenon can appear.