Seiberg–Witten theory as a Fermi gas

We explore a new connection between Seiberg–Witten theory and quantum statistical systems by relating the dual partition function of SU(2) Super Yang–Mills theory in a self-dual \(\Omega \) background to the spectral determinant of an ideal Fermi gas. We show that the spectrum of this gas is encoded in the zeroes of the Painlevé \(\mathrm{III}_3\) \(\tau \) function. In addition, we find that the Nekrasov partition function on this background can be expressed as an O(2) matrix model. Our construction arises as a four-dimensional limit of a recently proposed conjecture relating topological strings and spectral theory. In this limit, we provide a mathematical proof of the conjecture for the local \({\mathbb P}^1 \times {\mathbb P}^1\) geometry.     

Theory of discharge sectionalized along a gas flow

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Fluctuations in a lévy flight gas

We consider the density fluctuations of an ideal Brownian gas of particles performing Lévy flìghts characterized by the indexf. We find that the fluctuations scale as N(t) t^H, where the Hurst exponentH locks onto the universal value 1/4 for Lévy flights with a finite root-mean-square range (f>2). For Lévy flights with a finite mean range but infinite root-mean-square range (1相似文献   

Thermodynamics of a quantum gas and a two-particle Green’S function

It has been shown with the use of the virial theorem and the equation of motion for the single-particle Green’s function that the thermodynamic properties of a single-component quantum gas beyond the perturbation theory are fully determined by the two-particle Green’s function Moscow Power Engineering Institute.     

Castaing’s instability in a trapped ultra-cold gas

We consider a trapped ultra-cold gas of (non-condensed) bosons with two internal states (described by a pseudo spin) and study the stability of a longitudinal pseudo spin polarization gradient. For this purpose, we numerically solve a kinetic equation corresponding to a situation close to the experiment at JILA [1]. It shows the presence of Castaings instability of transverse spin polarization fluctuations at long wavelengths. This phenomenon could be used to create spontaneous transverse spin waves.Received: 1st October 2002, Published online: 15 July 2003PACS: 03.75.Nt Other Bose-Einstein condensation phenomena - 51.10.+y Kinetic and transport theory of gases - 75.30.Ds Spin wavesO. Prévoté: Present address: Université de Cergy-Pontoise, Département de Physique, 5 mall Gay Lussac, Neuville-sur-Oise, 95031 Cergy-Pontoise, France.     

Bose–Einstein condensation of a relativistic Bose gas in a harmonic potential

Using semiclassical method, Bose–Einstein condensation (BEC) of a relativistic ideal Bose gas (RIBG) with and without antibosons in the three-dimensional (3D) harmonic potential is investigated. Analytical expressions for the BEC transition temperature, condensate fraction, specific heat and entropy of the system are obtained. Relativistic effects on the properties of the system are discussed and it is found that the relativistic effect decreases the transition temperature T_c but enlarges the gap of specific heat at T_c. We also study the influence of antibosons on a RIBG. Comparing with the system without antibosons, the system with antibosons has a higher transition temperature and a lower Helmholtz free energy. It implies that the system with antibosons is more stable.     

Dynamics of a cold quantum gas in a δ-split one-dimensional potential well

Dynamics of a wave function in a non-symmetrically split (spatially asymmetric) doublewell potential is considered. We study the dependence of the probability of well-to-well transitions on the degree of spatial asymmetry of well sizes and show that the quantum tunneling between the wells is significantly suppressed by this asymmetry. Practically complete suppression occurs at five-ten percent asymmetry. This is close to the threshold of sensitivity of contemporary experimental schemes for creating two-well potentials. We predict the phenomenon of resonance in quantum tunneling of considered states. We have also shown that an incoherently prepared superposition state tunnels in a double-well potential almost in the same way as a perfectly coherent state.     

Rashba–Dresselhaus double refraction in a two-dimensional electron gas

We investigate the ballistic transport properties of an electron traversing through a two-dimensional electron gas with the Rashba and Dresselhaus spin–orbit coupling (R–D SOC) coexistent. A nonzero incident angle is considered. The relation between the transmission and the incident angle, the interfacial scattering strength, the length of the SOC region and the SOC intensity are revealed. The transmission strength decays when the incident angle is larger than a critical angle. The transport spin polarization is remarkably modulated by the coaction of the two types of SOC.     

Exploration of the Townsend regime by discharge light emission in a gas discharge deviceExploration of the Townsend regime by discharge light emission in a gas discharge deviceExploration of the Townsend regime by discharge light emission in a gas discharge deviceExploration of the Townsend regime by discharge light emission in a gas discharge deviceExploration of the Townsend regime by discharge light emission in a gas discharge device

The Townsend discharge mechanism has been explored in a planar microelectronic gas discharge device （MGDD） with different applied voltages U and interelectrode distance d under various pressures in air. The anode and the cathode of the MGDD are formed by a transparent SnO2 covered glass and a GaAs semiconductor, respectively. In the experiments, the discharge is found to be unstable just below the breakdown voltage Ub, whereas the discharge passes through a homo- geneous stable Townsend mode beyond the breakdown voltage. The measurements are made by an electrical circuit and a CCD camera by recording the currents and light emission （LE） intensities. The intensity profiles, which are converted from the 3D light emission images along the semiconductor diameter, have been analysed for different system parameters. Dif- ferent instantaneous conductivity ~t regimes are found below and beyond the Townsend region. These regimes govern the current and spatio-temporal LE stabilities in the plasma system. It has been proven that the stable LE region increases up to 550 Torr as a function of pressure for small d. If the active area of the semiconductor becomes larger and the interlectrode distance d becomes smaller, the stable LE region stays nearly constant with pressure.     

Laminar-turbulent transition in Hagen–Poiseuille flow of a real gas

The effect of gas non-ideality on the laminar-turbulent transition is studied experimentally as the flow in a long circular tube at room temperature. The gases SF₆ and Ar, differing significantly in the value of the second virial coefficient, were chosen for this study. Experiments were carried out by varying the pressure at the tube inlet (the maximum pressure of 10⁵ Pa) and at the tube outlet up to the chock flow (formation of a supersonic flow at the outlet). The difference between the critical Reynolds numbers in the flow of SF₆ and Ar was found. The largest difference was observed for the maximum pressures; with a decrease in pressure, the critical Reynolds numbers become closer. The conclusion is an effect of the non-ideal character of gas exists on the laminar-turbulent transition in Hagen–Poiseuille flow. Some experiments were suggested to confirm this conclusion.     

Acoustic–excitonic effects in a two-dimensional gas of dipolar excitons

The theory of the interaction of a two-dimensional gas of indirect dipolar excitons with Rayleigh surface elastic waves has been developed. The absorption and renormalization of the phase velocity of a surface wave, as well as the drag of excitons by the surface acoustic wave and the generation of bulk acoustic waves by a twodimensional gas of dipolar excitons irradiated by external electromagnetic radiation, have been considered. These effects have been studied both in a normal phase at high temperatures and in a condensed phase of the exciton gas. The calculations have been performed in the ballistic and diffusion limits for both phases.     

Sound waves in a liquid with polydisperse vapor–gas bubbles

A mathematical model is presented for the propagation of plane, spherical, and cylindrical sound waves in a liquid containing polydisperse vapor–gas bubbles with allowance for phase transitions. A system of integro-differential equations is constructed to describe perturbed motion of a two-phase mixture, and a dispersion relation is derived. An expression for equilibrium sound velocity is obtained for a gas–liquid or vapor–liquid mixture. The theoretical results agree well with the known experimental data. The dispersion curves obtained for the phase velocity and the attenuation coefficient in a mixture of water with vapor–gas bubbles are compared for various values of vapor concentration in the bubbles and various bubble distributions in size. The evolution of pressure pulses of plane and cylindrical waves is demonstrated for different values of the initial vapor concentration in bubbles. The calculated frequency dependence of the phase sound velocity in a mixture of water with vapor bubbles is compared with experimental data.     

134 nm vacuum ultraviolet emission using an Ar/Kr gas mixture excited by a quasi-continuous-wave gas jet discharge

We have developed a vacuum ultraviolet (VUV) lamp at 134 nm with a quasi-point emission geometry using a quasi-continuous-wave (cw) gas jet discharge of an Ar/Kr gas mixture. We have unambiguously identified a new emission continuum centered at 134 nm as a transition of Ar-Kr hetero-nuclear excimers (ArKr^*). The VUV emission power of the 134 nm continuum was 10 mW at 21 atm of the total Ar/Kr stagnation gas pressure, at a Kr concentration of 0.1%. Characteristic energy transfer between atoms and dimers plays an important role for the efficient production of ArKr^* in such a gas jet discharge. Received: 15 June 2000 / Revised version: 31 July 2000 / Published online: 22 November 2000     

Adsorption thermodynamics of a lattice–gas model with non-additive lateral interactions

In the present paper, we study the adsorption thermodynamics of a lattice–gas model with non-additive interactions between adsorbed particles. We have assumed that the energy which links a certain atom with any of its nearest neighbors strongly depends on the state of occupancy in the first coordination sphere of that adatom. By means of Monte Carlo simulations in the grand canonical ensemble the adsorption isotherms, isothermal susceptibility (or equivalently the mean square density fluctuations of adparticles), and isosteric heat of adsorption were calculated and their striking behavior was analyzed and discussed in terms of the low temperature phases formed in the system.     

Effect of gas pressure on ionization of ambient gas

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Validation of a lattice Boltzmann model for gas–solid reactions with experiments

A lattice Boltzmann method is used to model gas–solid reactions where the composition of both the gas and solid phase changes with time, while the boundary between phases remains fixed. The flow of the bulk gas phase is treated using a multiple relaxation time MRT D3Q19 model; the dilute reactant is treated as a passive scalar using a single relaxation time BGK D3Q7 model with distinct inter- and intraparticle diffusivities. A first-order reaction is incorporated by modifying the method of Sullivan et al. [13] to include the conversion of a solid reactant. The detailed computational model is able to capture the multiscale physics encountered in reactor systems. Specifically, the model reproduced steady state analytical solutions for the reaction of a porous catalyst sphere (pore scale) and empirical solutions for mass transfer to the surface of a sphere at Re = 10 (particle scale). Excellent quantitative agreement between the model and experiments for the transient reduction of a single, porous sphere of Fe₂O₃ to Fe₃O₄ in CO at 1023 K and 10⁵ Pa is demonstrated. Model solutions for the reduction of a packed bed of Fe₂O₃ (reactor scale) at identical conditions approached those of experiments after 25 s, but required prohibitively long processor times. The presented lattice Boltzmann model resolved successfully mass transport at the pore, particle and reactor scales and highlights the relevance of LB methods for modelling convection, diffusion and reaction physics.     

Potential of an insulated electrode in a high-energy electron flow under a gas pressure of 0.1–1.0 Pa

We analyze the variation of the floating potential of an insulated metallic electrode in a flow of electrons with an energy of up to 300 eV under a gas pressure of 0.1–1.0 Pa at a current density lower than 0.1 A/cm². It is shown that the dependence of the floating potential on the initial electron energy is non-monotonic; this fact is explained by the variation of the ratio of the ion current density to the density of fast electron current in the plasma. The balance of the electron and ion currents on the surface of an insulated electrode is ensured by the cutoff of the low-energy part of the electron flow at the level determined by the magnitude of the floating potential. The maximal value of the floating potential increases upon a decrease in the gas pressure; this is due to a decrease in the ion current density. The interval of energy variation in which the floating potential decreases from the maximal value (50–250 eV) to 5–6 eV increases with the electron current density and the gas pressure. The electrode material and the type of the gas do not noticeably affect the variation of the floating potential.     

λ=2537 Å line from a low-pressure mercury discharge lamp emission profile and line absorption by a gas containing a mercury vapor

By measuring the emission-line intensity of Hgi =2537 Å (6³ P6¹ S) from a low-pressure mercurcury lamp, we have determined the dependence of the upper-level population on the discharge current and the mercury vapor density. From the radial profile of the intensity the spatial distribution function of the population has been determined to be the zero-th order decay mode for the trapped radiation. Line absorption by mercury vapor in a cell has been measured with various mercury densities and Lorentzian widths. The results are consistent with the upper-level population distribution as determined above. On the basis of these findings we calculate the emission-line profile and its change during the absorption in the absorption cell. The amount of absorption at an arbitrary depth of the absorption cell is calculated, and the optimum cold-spot temperature of the lamp of 40–50°C is suggested for the maximum absorption under the typical condition of the photo-CVD experiment.