Quantum Manifestations of Classical Stochasticity in the Mixed State

We investigate the QMCS in structure of the eigenfunctions, corresponding to mixed type classical dynamics in smooth potential of the surface quadrupole oscillations of a charged liquid drop. Regions of different regimes of classical motion are strictly separated in the configuration space, allowing direct observation of the correlations between the wave function structure and type of the classical motion by comparison of the parts of the eigenfunction, corresponding to different local minima.Comment: 4 pages, 3 figure

Symbolic dynamics for the NN-centre problem at negative energies

We consider the planar $N$-centre problem, with homogeneous potentials of degree -\a<0, \a \in [1,2). We prove the existence of infinitely many collisions-free periodic solutions with negative and small energy, for any distribution of the centres inside a compact set. The proof is based upon topological, variational and geometric arguments. The existence result allows to characterize the associated dynamical system with a symbolic dynamics, where the symbols are the partitions of the $N$ centres in two non-empty sets

Application Mathematic Methods of Nonlinear Dynamic by Development of Methodic Qualitative Determination of Nitrogen-Containing Organic Compounds. 4. Optimization of Terms of Amperometric Determination Quantitative Maintenance of Phosphotides (Lecithin and Kephalin) in Industrial Products

Із використанням методів математичного моделювання [3] розроблено спосіб кількісного визначення фосфоліпідів методом амперометричного титрування 12-молібдофосфатною гетерополікислотою, який дає можливість експресно і з достатньою чутливістю визначати вміст лецитину та кефаліну в промисловій продукції. With the use of methods of mathematical modeling [3] the method of quantitative determination of phosphotides is worked out by the method of amperometric titration 12-molybdophosphoric heteropolyacid, allowing quickly and with a sufficient sensitiveness to define maintenance of lecithin and kephalin in industrial products

How close can one approach the Dirac point in graphene experimentally?

The above question is frequently asked by theorists who are interested in graphene as a model system, especially in context of relativistic quantum physics. We offer an experimental answer by describing electron transport in suspended devices with carrier mobilities of several 10^6 cm^2V^-1s^-1 and with the onset of Landau quantization occurring in fields below 5 mT. The observed charge inhomogeneity is as low as \approx10^8 cm^-2, allowing a neutral state with a few charge carriers per entire micron-scale device. Above liquid helium temperatures, the electronic properties of such devices are intrinsic, being governed by thermal excitations only. This yields that the Dirac point can be approached within 1 meV, a limit currently set by the remaining charge inhomogeneity. No sign of an insulating state is observed down to 1 K, which establishes the upper limit on a possible bandgap