Adiabatic tracking for photo- and magneto-association of Bose-Einstein condensates with Kerr nonlinearities

We develop the method of adiabatic tracking for photo- and magneto-association of Bose-Einstein atomic condensates with models that include Kerr type nonlinearities. We show that the inclusion of these terms can produce qualitatively important modifications in the adiabatic dynamics, like the appearance of bifurcations, in which the trajectory that is being tracked loses its stability. As a consequence the adiabatic theorem does not apply and the adiabatic transfer can be strongly degraded. This degradation can be compensated by using fields that are strong enough compared with the values of the Kerr terms. The main result is that, despite these potentially detrimental features, there is always a choice of the detuning that leads to an efficient adiabatic tracking, even for relatively weak fields

New powerful outburst of the unusual young star V1318 Cyg S (LkH{\alpha} 225)

Young double star V1318 Cyg, which is associated with a small isolated star-forming region around HAeBe star BD+40o4124, has very unusual photometric and spectral behavior. We present results of photometric and spectroscopic observations in the optical range. We carried out BVRI CCD photometric observations of V1318 Cyg from 2015 Sept. to 2017 July. For the same period we acquired medium- and low-resolution spectra. Observations were performed with the 2.6 m telescope. We analyze the historical light curve for V1318 Cyg and demonstrate that the southern component, V1318 Cyg S, after being rather bright in the 1970s (V$\approx$14 mag) started to lower its brightness and in 1990 became practically invisible in the optical. After its reappearance in the second half of the 1990s the star started to become very slowly brighter. Between 2006 and 2010 V1318 Cyg S started brightening more quickly, and in 2015 had become brighter by more than five magnitudes in visible light. Since this time V1318 Cyg S has remained at this maximum. Its spectrum shows little variability and consists of a mixture of emission and absorption lines, which has allowed for estimates of its spectral type as early Ae, with obvious evidence of matter outflow. We derive its current A(V)$\approx$ 7.2 and L = 750 L(sun) thus confirming that V1318 Cyg S should belong to the Herbig Ae stars, making it, along with BD+40o4124 and V1686 Cyg, the third luminous young star in the group. It is very probable that we observe V1318 Cyg S near the pole and that the inclination of its dense and slow ($\approx$ 100 km/s) outflow is low. The unusual variability and other features of V1318 Cyg S make it difficult to classify this star among known types of eruptive young stars. It could be an extreme, higher-mass example of an EXor, or an object of intermediate class between EXors and FUors, like V1647 Ori.Comment: 9 pages, 7 figure

Bistability and chaos at low-level of quanta

We study nonlinear phenomena of bistability and chaos at a level of few quanta. For this purpose we consider a single-mode dissipative oscillator with strong Kerr nonlinearity with respect to dissipation rate driven by a monochromatic force as well as by a train of Gaussian pulses. The quantum effects and decoherence in oscillatory mode are investigated on the framework of the purity of states and the Wigner functions calculated from the master equation. We demonstrate the quantum chaotic regime by means of a comparison between the contour plots of the Wigner functions and the strange attractors on the classical Poincar\'e section. Considering bistability at low-limit of quanta, we analyze what is the minimal level of excitation numbers at which the bistable regime of the system is displayed? We also discuss the formation of oscillatory chaotic regime by varying oscillatory excitation numbers at ranges of few quanta. We demonstrate quantum-interference phenomena that are assisted hysteresis-cycle behavior and quantum chaos for the oscillator driven by the train of Gaussian pulses as well as we establish the border of classical-quantum correspondence for chaotic regimes in the case of strong nonlinearities.Comment: 10 pages, 14 figure

Expansions of the solutions of the biconfluent Heun equation in terms of incomplete Beta and Gamma functions

Starting from equations obeyed by functions involving the first or the second derivatives of the biconfluent Heun function, we construct two expansions of the solutions of the biconfluent Heun equation in terms of incomplete Beta functions. The first series applies single Beta functions as expansion functions, while the second one involves a combination of two Beta functions. The coefficients of expansions obey four- and five-term recurrence relations, respectively. It is shown that the proposed technique is potent to produce series solutions in terms of other special functions. Two examples of such expansions in terms of the incomplete Gamma functions are presente

Dissipative Chaos in Quantum Distributions

We discuss some problems of dissipative chaos for open quantum systems in the framework of semiclassical and quantum distributions. For this goal, we propose a driven nonlinear oscillator with time-dependent coefficients, i.e. with time-dependent Kerr-nonlinearity and time-modulated driving field. This model showing both regular and chaotic dynamics in the classical limit is realized in several experimental schemes. Quantum dissipative chaos is analyzed on the base of numerical method of quantum trajectories. Three quantities are studied: the Wigner function of oscillatory mode from the point of view of quantum-assemble theory and both semiclassical Poincare section and quantum Poincare section calculated on a single quantum trajectory. The comparatively analysis of these distributions for various operational chaotic regimes of the models is performed, as well as scaling invariance in dissipative chaos and quantum interference effects assisted by chaos are discussed.Comment: 17 pages, 3 figures, proceeding of Modern Optics And Photonic

Quantum interference and sub-Poissonian statistics for time-modulated driven dissipative nonlinear oscillator

We show that quantum-interference phenomena can be realized for the dissipative nonlinear systems exhibiting hysteresis-cycle behavior and quantum chaos. Such results are obtained for a driven dissipative nonlinear oscillator with time-dependent parameters and take place for the regimes of long time intervals exceeding dissipation time and for macroscopic levels of oscillatory excitation numbers. Two schemas of time modulation: (i) periodic variation of the strength of the {\chi}(3) nonlinearity; (ii) periodic modulation of the amplitude of the driving force, are considered. These effects are obtained within the framework of phase-space quantum distributions. It is demonstrated that the Wigner functions of oscillatory mode in both bistable and chaotic regimes acquire negative values and interference patterns in parts of phase-space due to appropriately time-modulation of the oscillatory nonlinear dynamics. It is also shown that the time-modulation of the oscillatory parameters essentially improves the degree of sub-Poissonian statistics of excitation numbers

HFRR test method with stainless steel specimens for gasoline fuels

Reducing CO2 emission is a major challenge for the automotive industry. The different fuels (E10, E100, M15 etc.) that are used for gasoline systems not only influence the CO2 emission but also significantly influence the friction and wear behavior and subsequently the lifetime of powertrain components. The effect is much higher when biofuels are used. The characterization of tribological properties of gasoline fuels is necessary for a robust design which allows for permanent control of performance. The High Frequency Reciprocating Rig (HFRR) test concept according to ISO 12156 is the standard test method for evaluating the lubricity of diesel fuels. Up to now, no standard for gasoline fuels is known. The standardized HFRR test method uses 100Cr6 test specimens which are stable in contact with diesel fuel, but, unlike the stainless steel components used in gasoline fuel injection systems, is prone to corrosion in a gasoline environment typically containing a certain amount of water. This paper aims to develop a lubricity test method with stainless steel for gasoline fuels and reports first results for various fuel compositions