Single-file diffusion on a periodic substrate

An assembly of "nonpassing" particles diffusing on a one-dimensional periodic substrate is shown to undergo single-file diffusion for both noiseless (ballistic) and stochastic dynamics. The dependence of the corresponding diffusion coefficients on the density and temperature of the particles and on the substrate parameters is determined by means of numerical simulations and analytically interpreted within the formalism of standard Brownian motion.     

Single-file diffusion of colloids in one-dimensional channels

We study the diffusive behavior of colloidal particles which are confined to one-dimensional channels generated by scanning optical tweezers. At long times t, the mean-square displacement is found to scale as t(1/2), which is expected for systems where single-file diffusion occurs. In addition, we experimentally obtain the long-time, self-diffusive behavior from the short-time collective density fluctuations of the system as suggested by a recent analytical approach [Phys. Rev. Lett. 90, 180602 (2003)].     

Single-file diffusion of atomic and colloidal systems: asymptotic laws

We present a general derivation of the non-Fickian behavior for the self-diffusion of identically interacting particle systems with excluded mutual passage. We show that the conditional probability distribution of finding a particle at position x(t) after time t, when the particle was located at x(0) at t=0, follows a Gaussian distribution in the long-time limit, with variance 2W(t) approximately t(1/2) for overdamped systems and with variance 2W(t) approximately t for classical systems. The asymptotic behavior of the mean-squared displacement, W(t), is shown to be independent of the nature of interactions for homogeneous systems in the fluid state. Moreover, the long-time behavior of self-diffusion is determined by short-time and large-scale collective density fluctuations.     

Single-file transport of water molecules through a carbon nanotube

Recent molecular dynamics simulations of water transport through the interior channel of a carbon nanotube in contact with an aqueous reservoir showed that conduction occurred in bursts with collective water motion. A continuous-time random-walk model is used to describe concerted transport through channels densely filled with molecules in a single-file arrangement, as also found in zeolites, as well as ion channels and aquaporins in biological membranes. Theoretical predictions for different collective properties of the single-file transport agree with the simulation results.     

Variational and diffusion Monte Carlo simulations of a hydrogen molecular ion in a spherical box

The variational and diffusion Monte Carlo approaches are used to study the ground-state properties of a hydrogen molecular ion in a spheroidal box. In this work, we successfully treat the zero-point motion of protons in the same formalism with as of electrons and avoid the Born–Oppenheimer approximation in density function theory. The study shows that the total energy increases with the decrease in volume, and that the distance between protons decreases as the pressure increases.Considering the motion of protons, the kinetic energy of the electron is higher than that of the fixed model under the same conditions and increases by 5%. The kinetic energy of the proton is found to be small under high pressure, which is only a fraction of the kinetic energy of the electron.     

Single-file motion of polyatomic molecules in one-dimensional nanoporous materials

In a continuation of the study of the mobility of fluids adsorbed in nanoporous materials, molecular dynamics simulations are used to investigate the behaviour of polyatomic ethane molecules adsorbed in AlPO₄-5. The current work is based on the use of the united atom approach as a better model than the single-centre ethane used to date. Ethane molecules are modelled as rigid diatoms, and as a result the molecules have more degrees of freedom in the form of the rotational components that are absent in the single-centre ethane model. This represents a more sophisticated model for ethane and is used in the simulations to test earlier findings. Simulations with binary mixtures of methane and ethane also have been conducted with three mixture compositions. The transition from ordinary diffusion to single-file motion for a finite residence time is found to occur at a methyl group diameter of 4.75 Å. This is identical to the ethane diameter in the earlier study. Thus, only the minimum dimension determines the transition size. Also it is shown that the diatomic molecules undergo free rotation within the channel even when they are in the single-file mode of motion. In the case of binary mixtures, the methane molecules still undergo ordinary diffusion. Ethane molecules exhibit single-file motion at a methyl group diameter of 4.75 Å. The diffusion coefficient of methane decreases with increasing ethane size, while the trends in the single-file mobility of ethane as a function of methyl group diameter are nonlinear.     

Cecotti-Fendley-Intriligator-Vafa index in a box

The Cecotti-Fendley-Intriligator-Vafa (CFIV) index in two-dimensional N=(2,2) models is revisited. We address the problem of “elementary” (nontopological) excitations over a kink solution, in the one-kink sector (using the Wess-Zumino or Landau-Ginzburg models with two vacua as examples). In other words, we limit ourselves to the large-β limit. The excitation spectrum over the BPS-saturated at the classical level kink is discretized through a large box with judiciously chosen boundary conditions. The boundary conditions are designed in such a way that half of supersymmetry is preserved as well as the BPS kink itself, and relevant zero modes. The excitation spectrum acquires a mass gap. All (discretized) excited states enter in four-dimensional multiplets (two bosonic states + two fermionic). Their contribution to indCFIV vanishes level-by-level. The ground state contribution produces |indCFIV|=1.     

Two disks in a box

Exact analytical expressions are derived for the thermodynamic properties of two discs in square and rhomboidal boxes with hard walls, and in a square cell with periodic boundaries. With periodic boundaries the equation of state has a van der Waals loop and a second order cusp. In a box with hard walls there is a third order “glass transition” which seems to capture the essence of the glass transition observed in systems of a few hundred hard spheres.     

Neutrinos in a spherical box

The purpose of the present paper is to study the neutrino properties as they may appear in the low-energy neutrinos emitted in the triton decay \(_1^3 H \to _2^3 He + e^ - + \bar \nu _e \) with maximum neutrino energy of 18.6 keV. The technical challenges to this end can be summarized as building a very large TPC capable of detecting low-energy recoils, down to a few 100 eV, within the required low-background constraints. More specifically, we propose the development of a spherical gaseous TPC of about 10 m in radius and a 200-MCi triton source in the center of curvature. One can list a number of exciting studies concerning fundamental physics issues that could be made using a large volume TPC and low-energy antineutrinos: (i) The oscillation length involving the small angle δ = sinθ₁₃, directly measured in our ν_e disappearance experiment, is fully contained inside the detector. Measuring the counting rate of neutrino-electron elastic scattering as a function of the distance of the source will give a precise and unambiguous measurement of the oscillation parameters free of systematic errors. In fact, first estimates show that, even with a year's data taking, a sensitivity of a few percent for the measurement of the above angle will be achieved. (ii) The low-energy detection threshold offers a unique sensitivity for the neutrino magnetic moment which is about two orders of magnitude beyond the current experimental limit of 10^?10μ_B. (iii) Scattering at such low neutrino energies has never been studied and any departure from the expected behavior may be an indication of new physics beyond the Standard Model. We present a summary of various theoretical studies and possible measurements, including a precise measurement of the Weinberg angle at very low momentum transfer.     

Relativistic particle in a three-dimensional box

We generalize the work of Alberto, Fiolhais and Gil and solve the problem of a Dirac particle confined in a 3-dimensional box. The non-relativistic and ultra-relativistic limits are considered and it is shown that the size of the box determines how relativistic the low-lying states are. The consequences for the density of states of a relativistic fermion gas are briefly discussed.     

Black hole formation in a box

Evidence is presented for Hawking's viewpoint that in an insulated box in thermal equilibrium, black holes should form and evaporate in a statistically time-symmetric way. In particular, it is shown that if a black hole can evaporate adiabatically, it is much more likely to form adiabatically than by Jeans instability.     

Quantum fluctuations in a single electron box

Recent experiments have demonstrated that the numbern of additional electrons on a small metallic island is a staircase function of a continuous external chargen _x for temperaturesT small compared to the single electron charging energyU. We show that the finite conductanceg of the tunnel barrier connecting the island to the external gate gives rise to quantum fluctuations inn which lead to a smearing of the staircase even at zero temperature. In the experimentally relevant case of wide junctions and in the limit of small conductanceg1 the slope <n>/n _x at the turning point between two plateaus saturates at a finite value of order 1/g asT0 instead of diverging likeU/T as predicted with thermal fluctuations only. The experimentally observed broadening however is still much larger which is probably due to extrinsic effects.     

Stark effect in a wedge-shaped quantum box

The effect of an external applied electric field on the electronic ground-state energy of a quantum box with a geometry defined by a wedge is studied by carrying out a variational calculation. This geometry could be used as an approximation for a tip of a cantilever of an atomic force microscope. We study theoretically the Stark effect as function of the parameters of the wedge: its diameter, angular aperture and thickness; as well as function of the intensity of the external electric field applied along the axis of the wedge in both directions; pushing the carrier towards the wider or the narrower parts. A confining electronic effect, which is sharper as the wedge dimensions are smaller, is clearly observed for the first case. Besides, the sign of the Stark shift changes when the angular aperture is changed from small angles to angles θ>π. For the opposite field, the electronic confinement for large diameters is very small and it is also observed that the Stark shift is almost independent with respect to the angular aperture.     

Grain-boundary diffusion in nanocrystals with a time-dependent diffusion coefficient

A solution to the equation of grain-boundary diffusion is obtained under conditions where migration of the diffusant from the boundaries into the grains is absent and the diffusion coefficient decreases with time from an increased value to a value characteristic of equilibrium grain boundaries. The specific features of the grain-boundary diffusion in nanocrystals are qualitatively analyzed in terms of this solution.     

Fermi hypernetted chain calculations in a periodic box

The Fermi hypernetted chain theory is reformulated to perform calculations with a finite number of fermions in a periodic box. The proposed method is expected to be useful to estimate the finite size effects in Quantum Monte Carlo simulations. Moreover, it can deal with anisotropic correlations as well as with different shaped boxes. Results are given for the neutron matter Bethe homework Hamiltonian and for nuclear matter with spin–isospin dependent central interactions. It is found that finite size effects come from both the kinetic and the potential energy expectation values.