One Dimensional Magnetized TG Gas Properties in an External Magnetic Field

With Girardeau's Fermi-Bose mapping, we have constructed the eigenstates of a TG gas in an external magnetic field. When the number of bosons $N$ is commensurate with the number of potential cycles $M$, the probability of this TG gas in the ground state is bigger than the TG gas raised by Girardeau in 1960. Through the comparison of properties between this TG gas and Fermi gas, we find that the following issues are always of the same: their average value of particle's coordinate and potential energy, system's total momentum, single-particle density and the pair distribution function. But the reduced single-particle matrices and their momentum distributions between them are different.Comment: 6 pages, 4 figure

Coagulation by Random Velocity Fields as a Kramers Problem

We analyse the motion of a system of particles suspended in a fluid which has a random velocity field. There are coagulating and non-coagulating phases. We show that the phase transition is related to a Kramers problem, and use this to determine the phase diagram, as a function of the dimensionless inertia of the particles, epsilon, and a measure of the relative intensities of potential and solenoidal components of the velocity field, Gamma. We find that the phase line is described by a function which is non-analytic at epsilon=0, and which is related to escape over a barrier in the Kramers problem. We discuss the physical realisations of this phase transition.Comment: 4 pages, 3 figure

Dynamical diffraction in sinusoidal potentials: uniform approximations for Mathieu functions

Eigenvalues and eigenfunctions of Mathieu's equation are found in the short wavelength limit using a uniform approximation (method of comparison with a `known' equation having the same classical turning point structure) applied in Fourier space. The uniform approximation used here relies upon the fact that by passing into Fourier space the Mathieu equation can be mapped onto the simpler problem of a double well potential. The resulting eigenfunctions (Bloch waves), which are uniformly valid for all angles, are then used to describe the semiclassical scattering of waves by potentials varying sinusoidally in one direction. In such situations, for instance in the diffraction of atoms by gratings made of light, it is common to make the Raman-Nath approximation which ignores the motion of the atoms inside the grating. When using the eigenfunctions no such approximation is made so that the dynamical diffraction regime (long interaction time) can be explored.Comment: 36 pages, 16 figures. This updated version includes important references to existing work on uniform approximations, such as Olver's method applied to the modified Mathieu equation. It is emphasised that the paper presented here pertains to Fourier space uniform approximation

Surface effects on nanowire transport: numerical investigation using the Boltzmann equation

A direct numerical solution of the steady-state Boltzmann equation in a cylindrical geometry is reported. Finite-size effects are investigated in large semiconducting nanowires using the relaxation-time approximation. A nanowire is modelled as a combination of an interior with local transport parameters identical to those in the bulk, and a finite surface region across whose width the carrier density decays radially to zero. The roughness of the surface is incorporated by using lower relaxation-times there than in the interior. An argument supported by our numerical results challenges a commonly used zero-width parametrization of the surface layer. In the non-degenerate limit, appropriate for moderately doped semiconductors, a finite surface width model does produce a positive longitudinal magneto-conductance, in agreement with existing theory. However, the effect is seen to be quite small (a few per cent) for realistic values of the wire parameters even at the highest practical magnetic fields. Physical insights emerging from the results are discussed.Comment: 15 pages, 7 figure

Classical and Quantum Chaos in a quantum dot in time-periodic magnetic fields

We investigate the classical and quantum dynamics of an electron confined to a circular quantum dot in the presence of homogeneous $B_{dc}+B_{ac}$ magnetic fields. The classical motion shows a transition to chaotic behavior depending on the ratio $\epsilon=B_{ac}/B_{dc}$ of field magnitudes and the cyclotron frequency ${\tilde\omega_c}$ in units of the drive frequency. We determine a phase boundary between regular and chaotic classical behavior in the $\epsilon$ vs ${\tilde\omega_c}$ plane. In the quantum regime we evaluate the quasi-energy spectrum of the time-evolution operator. We show that the nearest neighbor quasi-energy eigenvalues show a transition from level clustering to level repulsion as one moves from the regular to chaotic regime in the $(\epsilon,{\tilde\omega_c})$ plane. The $\Delta_3$ statistic confirms this transition. In the chaotic regime, the eigenfunction statistics coincides with the Porter-Thomas prediction. Finally, we explicitly establish the phase space correspondence between the classical and quantum solutions via the Husimi phase space distributions of the model. Possible experimentally feasible conditions to see these effects are discussed.Comment: 26 pages and 17 PstScript figures, two large ones can be obtained from the Author

Oscillatory Tunnel Splittings in Spin Systems: A Discrete Wentzel-Kramers-Brillouin Approach

Certain spin Hamiltonians that give rise to tunnel splittings that are viewed in terms of interfering instanton trajectories, are restudied using a discrete WKB method, that is more elementary, and also yields wavefunctions and preexponential factors for the splittings. A novel turning point inside the classically forbidden region is analysed, and a general formula is obtained for the splittings. The result is appled to the \Fe8 system. A previous result for the oscillation of the ground state splitting with external magnetic field is extended to higher levels.Comment: RevTex, one ps figur

Inhibition of Tendon Cell Proliferation and Matrix Glycosaminoglycan Synthesis by Non-Steroidal Anti-Inflammatory Drugs in vitro

The purpose of this study was to investigate the effects of some commonly used non-steroidal anti-inflammatory drugs (NSAIDs) on human tendon. Explants of human digital flexor and patella tendons were cultured in medium containing pharmacological concentrations of NSAIDs. Cell proliferation was measured by incorporation of 3H-thymidine and glycosaminoglycan synthesis was measured by incorporation of 35S-Sulphate. Diclofenac and aceclofenac had no significant effect either on tendon cell proliferation or glycosaminoglycan synthesis. Indomethacin and naproxen inhibited cell proliferation in patella tendons and inhibited glycosaminoglycan synthesis in both digital flexor and patella tendons. If applicable to the in vivo situation, these NSAIDs should be used with caution in the treatment of pain after tendon injury and surgery

Computation of inflationary cosmological perturbations in chaotic inflationary scenarios using the phase-integral method

The phase-integral approximation devised by Fr\"oman and Fr\"oman, is used for computing cosmological perturbations in the quadratic chaotic inflationary model. The phase-integral formulas for the scalar and tensor power spectra are explicitly obtained up to fifth order of the phase-integral approximation. We show that, the phase integral gives a very good approximation for the shape of the power spectra associated with scalar and tensor perturbations as well as the spectral indices. We find that the accuracy of the phase-integral approximation compares favorably with the numerical results and those obtained using the slow-roll and uniform approximation methods.Comment: 21 pages, RevTex, to appear in Phys. Rev

On the Aggregation of Inertial Particles in Random Flows

We describe a criterion for particles suspended in a randomly moving fluid to aggregate. Aggregation occurs when the expectation value of a random variable is negative. This random variable evolves under a stochastic differential equation. We analyse this equation in detail in the limit where the correlation time of the velocity field of the fluid is very short, such that the stochastic differential equation is a Langevin equation.Comment: 16 pages, 2 figure

Cosmological particle production and the precision of the WKB approximation

Particle production by slow-changing gravitational fields is usually described using quantum field theory in curved spacetime. Calculations require a definition of the vacuum state, which can be given using the adiabatic (WKB) approximation. I investigate the best attainable precision of the resulting approximate definition of the particle number. The standard WKB ansatz yields a divergent asymptotic series in the adiabatic parameter. I derive a novel formula for the optimal number of terms in that series and demonstrate that the error of the optimally truncated WKB series is exponentially small. This precision is still insufficient to describe particle production from vacuum, which is typically also exponentially small. An adequately precise approximation can be found by improving the WKB ansatz through perturbation theory. I show quantitatively that the fundamentally unavoidable imprecision in the definition of particle number in a time-dependent background is equal to the particle production expected to occur during that epoch. The results are illustrated by analytic and numerical examples.Comment: 14 pages, RevTeX, 5 figures; minor changes, a clarification in Sec. II