Time evolution of an entangled initial state in coupled quantum dots with Coulomb correlations
We proved that for arbitrary mixed state the concurrence and the entanglement are determined by the average value of electron’s pair correlation functions particular combinations. We analyzed the dynamics of the initial two-electronic state in two interacting single-level quantum dots (QDs) with Coulomb correlations, weakly tunnel coupled with an electronic reservoir. We obtained correlation functions of all orders for electrons in the QDs by decoupling high-order correlations between localized and band electrons in the reservoir. Analysis of the pair correlation functions time evolution allows to follow the changes of the concurrence and the entanglement during the relaxation and transient processes. We investigated dependence of the concurrence on the value of Coulomb interaction and energy levels spacing and found its monotonic behavior. The most interesting physical effect is that more entangled state than the initial one can be formed during the charge relaxation due to the Coulomb correlations. We also demonstrated that behavior of the two-electronic entangled state pair correlation functions in coupled QDs points to the fulfillment of the Hund’s rule for the strong Coulomb interaction. We revealed the appearance of dynamical inverse occupation of the QDs energy levels during the relaxation processes. Our results open up further perspectives in solid state quantum information based on the controllable dynamics of the entangled electronic states.
We present a general methodology for evaluating structure factors defining the orientation dependence of tunneling ionization rates of molecules, which is a key process in strong-field physics. The method is implemented at the Hartree-Fock level of electronic structure theory and is based on an integralequation approach to the weak-field asymptotic theory of tunneling ionization, which expresses the structure factor in terms of an integral involving the ionizing orbital and a known analytical function. The evaluation of the required integrals is done by three-dimensional quadrature which allows calculations using conventional quantum chemistry software packages. This extends the applications of the weak-field asymptotic theory to polyatomic molecules of almost arbitrary size. The method is tested by comparison with previous results and illustrated by calculating structure factors for the two degenerate highest occupied molecular orbitals (HOMOs) of benzene and for the HOMO and HOMO-1 of naphthalene
The fractal globule state is a popular model for describing chromatin packing in eukaryotic nuclei. Here we provide a scaling theory and dissipative particle dynamics computer simulation for the thermal motion of monomers in the fractal globule state. Simulations starting from different entanglement-free initial states show good convergence which provides evidence supporting the existence of a unique metastable fractal globule state. We show monomer motion in this state to be subdiffusive described by X2(t) ∼tαF with αF close to 0.4. This result is in good agreement with existing experimental data on the chromatin dynamics, which makes an additional argument in support of the fractal globule model of chromatin packing. © 2015 American Physical Society.
This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.
A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traﬃc is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the ﬁnal node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a ﬁnite-dimensional system of diﬀerential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of diﬀerential equations to a class of quasi-solutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasi-solutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.
Let k be a field of characteristic zero, let G be a connected reductive algebraic group over k and let g be its Lie algebra. Let k(G), respectively, k(g), be the field of k- rational functions on G, respectively, g. The conjugation action of G on itself induces the adjoint action of G on g. We investigate the question whether or not the field extensions k(G)/k(G)^G and k(g)/k(g)^G are purely transcendental. We show that the answer is the same for k(G)/k(G)^G and k(g)/k(g)^G, and reduce the problem to the case where G is simple. For simple groups we show that the answer is positive if G is split of type A_n or C_n, and negative for groups of other types, except possibly G_2. A key ingredient in the proof of the negative result is a recent formula for the unramified Brauer group of a homogeneous space with connected stabilizers. As a byproduct of our investigation we give an affirmative answer to a question of Grothendieck about the existence of a rational section of the categorical quotient morphism for the conjugating action of G on itself.
Let G be a connected semisimple algebraic group over an algebraically closed field k. In 1965 Steinberg proved that if G is simply connected, then in G there exists a closed irreducible cross-section of the set of closures of regular conjugacy classes. We prove that in arbitrary G such a cross-section exists if and only if the universal covering isogeny Ĝ → G is bijective; this answers Grothendieck's question cited in the epigraph. In particular, for char k = 0, the converse to Steinberg's theorem holds. The existence of a cross-section in G implies, at least for char k = 0, that the algebra k[G]G of class functions on G is generated by rk G elements. We describe, for arbitrary G, a minimal generating set of k[G]G and that of the representation ring of G and answer two Grothendieck's questions on constructing generating sets of k[G]G. We prove the existence of a rational (i.e., local) section of the quotient morphism for arbitrary G and the existence of a rational cross-section in G (for char k = 0, this has been proved earlier); this answers the other question cited in the epigraph. We also prove that the existence of a rational section is equivalent to the existence of a rational W-equivariant map T- - - >G/T where T is a maximal torus of G and W the Weyl group.