Classification of integrable super-systems using the SsTools environment

A classification problem is proposed for supersymmetric evolutionary PDE that satisfy the assumptions of nonlinearity and nondegeneracy. Four classes of nonlinear coupled boson-fermion systems are discovered under the homogeneity assumption |f|=|b|=|D_t|=1/2. The syntax of the Reduce package SsTools, which was used for intermediate computations, and the applicability of its procedures to the calculus of super-PDE are described.Comment: MSC 35Q53,37K05,37K10,81T40; PACS 02.30.Ik,02.70.Wz,12.60.Jv; Comput. Phys. Commun. (2007), 26 pages (accepted

Supersymmetric Representations and Integrable Fermionic Extensions of the Burgers and Boussinesq Equations

We construct new integrable coupled systems of N = 1 supersymmetric equations and present integrable fermionic extensions of the Burgers and Boussinesq equations. Existence of infinitely many higher symmetries is demonstrated by the presence of recursion operators. Various algebraic methods are applied to the analysis of symmetries, conservation laws, recursion operators, and Hamiltonian structures. A fermionic extension of the Burgers equation is related with the Burgers flows on associative algebras. A Gardner's deformation is found for the bosonic super-field dispersionless Boussinesq equation, and unusual properties of a recursion operator for its Hamiltonian symmetries are described. Also, we construct a three-parametric supersymmetric system that incorporates the Boussinesq equation with dispersion and dissipation but never retracts to it for any values of the parameters

Spin decay and quantum parallelism

We study the time evolution of a single spin coupled inhomogeneously to a spin environment. Such a system is realized by a single electron spin bound in a semiconductor nanostructure and interacting with surrounding nuclear spins. We find striking dependencies on the type of the initial state of the nuclear spin system. Simple product states show a profoundly different behavior than randomly correlated states whose time evolution provides an illustrative example of quantum parallelism and entanglement in a decoherence phenomenon.Comment: 6 pages, 4 figures included, version to appear in Phys. Rev.

Electron spin evolution induced by interaction with nuclei in a quantum dot

We study the decoherence of a single electron spin in an isolated quantum dot induced by hyperfine interaction with nuclei for times smaller than the nuclear spin relaxation time. The decay is caused by the spatial variation of the electron envelope wave function within the dot, leading to a non-uniform hyperfine coupling $A$. We show that the usual treatment of the problem based on the Markovian approximation is impossible because the correlation time for the nuclear magnetic field seen by the electron spin is itself determined by the flip-flop processes. The decay of the electron spin correlation function is not exponential but rather power (inverse logarithm) law-like. For polarized nuclei we find an exact solution and show that the precession amplitude and the decay behavior can be tuned by the magnetic field. The decay time is given by $\hbar N/A$, where $N$ is the number of nuclei inside the dot. The amplitude of precession, reached as a result of the decay, is finite. We show that there is a striking difference between the decoherence time for a single dot and the dephasing time for an ensemble of dots.Comment: Revtex, 11 pages, 5 figure

On distribution of number of trades in different time windows in the stock market

Properties of distributions of the number of trades in different intraday time intervals for five stocks traded in MICEX are studied. The dependence of the mean number of trades on the capital turnover is analyzed. Correlation analysis using factorial and $H_q$ moments demonstrates the multifractal nature of these distributions as well as some peculiar changes in the correlation pattern. Guided by the analogy with the analysis of particle multiplicity distributions in multiparticle production at high energies, an evolution equation relating changes in capital turnover and a number of trades is proposed. We argue that such equation can describe the observed features of the distribution of the number of trades in the stock market.Comment: LaTeX, 6 figure

Spin Accumulation in Quantum Wires with Strong Rashba Spin-Orbit Coupling

We present analytical and numerical results for the effect of Rashba spin-orbit coupling on band structure, transport, and interaction effects in quantum wires when the spin precession length is comparable to the wire width. In contrast to the weak-coupling case, no common spin-quantization axis can be defined for eigenstates within a single-electron band. The situation with only the lowest spin-split subbands occupied is particularly interesting because electrons close to Fermi points of the same chirality can have approximately parallel spins. We discuss consequences for spin-dependent transport and effective Tomonaga-Luttinger descriptions of interactions in the quantum wire.Comment: 4 pages, 4 figures, expanded discussion of spin accumulatio

Optimal Fractionation of Products of Refining Straight-run Gasoline on Zeolite Catalyst with Account of its Deactivation

Flowsheet of industrial refining straight-run gasoline on zeolite catalyst includes the necessary stage of fractionation of conversion products to produce commercial gasoline, gas and heavy residue. Changes in qualitative and quantitative compositions of the catalytic conversion products under catalyst deactivation require current parametrical optimization of this stage. Objective functions that take into account catalyst deactivation and the constrains depending on the requirements for product quality and equipment specifications were developed. Optimal conditions were found to differ significantly from those designed for fresh catalyst

Recent Experimental Tests of Special Relativity

We review our recent Michelson-Morley (MM) and Kennedy-Thorndike (KT) experiment, which tests Lorentz invariance in the photon sector, and report first results of our ongoing atomic clock test of Lorentz invariance in the matter sector. The MM-KT experiment compares a cryogenic microwave resonator to a hydrogen maser, and has set the most stringent limit on a number of parameters in alternative theories to special relativity. We also report first results of a test of Lorentz invariance in the SME (Standard Model Extension) matter sector, using Zeeman transitions in a laser cooled Cs atomic fountain clock. We describe the experiment together with the theoretical model and analysis. Recent experimental results are presented and we give a first estimate of components of the $\tilde{c}^p$ parameters of the SME matter sector. A full analysis of systematic effects is still in progress, and will be the subject of a future publication together with our final results. If confirmed, the present limits would correspond to first ever measurements of some $\tilde{c}^p$ components, and improvements by 11 and 14 orders of magnitude on others.Comment: 29 pages. Contribution to Springer Lecture Notes, "Special Relativity - Will it survive the next 100 years ?", Proceedings, Potsdam, 200

Moduli-Space Dynamics of Noncommutative Abelian Sigma-Model Solitons

In the noncommutative (Moyal) plane, we relate exact U(1) sigma-model solitons to generic scalar-field solitons for an infinitely stiff potential. The static k-lump moduli space C^k/S_k features a natural K"ahler metric induced from an embedding Grassmannian. The moduli-space dynamics is blind against adding a WZW-like term to the sigma-model action and thus also applies to the integrable U(1) Ward model. For the latter's two-soliton motion we compare the exact field configurations with their supposed moduli-space approximations. Surprisingly, the two do not match, which questions the adiabatic method for noncommutative solitons.Comment: 1+15 pages, 2 figures; v2: reference added, to appear in JHE

Bell's inequalities for states with positive partial transpose

We study violations of n particle Bell inequalities (as developed by Mermin and Klyshko) under the assumption that suitable partial transposes of the density operator are positive. If all transposes with respect to a partition of the system into p subsystems are positive, the best upper bound on the violation is 2^((n-p)/2). In particular, if the partial transposes with respect to all subsystems are positive, the inequalities are satisfied. This is supporting evidence for a recent conjecture by Peres that positivity of partial transposes could be equivalent to existence of local classical models.Comment: 4 pages, REVTe