241 research outputs found

    Rigorous derivation of coherent resonant tunneling time and velocity in finite periodic systems

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    The velocity vresv_{res} of resonant tunneling electrons in finite periodic structures is analytically calculated in two ways. The first method is based on the fact that a transmission of unity leads to a coincidence of all still competing tunneling time definitions. Thus, having an indisputable resonant tunneling time Ď„res,\tau_{res}, we apply the natural definition vres=L/Ď„resv_{res}=L/\tau_{res} to calculate the velocity. For the second method we combine Bloch's theorem with the transfer matrix approach to decompose the wave function into two Bloch waves. Then the expectation value of the velocity is calculated. Both different approaches lead to the same result, showing their physical equivalence. The obtained resonant tunneling velocity vresv_{res} is smaller or equal to the group velocity times the magnitude of the complex transmission amplitude of the unit cell. Only at energies where the unit cell of the periodic structure has a transmission of unity vresv_{res} equals the group velocity. Numerical calculations for a GaAs/AlGaAs superlattice are performed. For typical parameters the resonant velocity is below one third of the group velocity.Comment: 12 pages, 3 figures, LaTe

    Kramers-Kronig constrained variational analysis of optical spectra

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    A universal method of extraction of the complex dielectric function ϵ(ω)=ϵ1(ω)+iϵ2(ω)\epsilon(\omega)=\epsilon_{1}(\omega)+i\epsilon_{2}(\omega) from experimentally accessible optical quantities is developed. The central idea is that ϵ2(ω)\epsilon_{2}(\omega) is parameterized independently at each node of a properly chosen anchor frequency mesh, while ϵ1(ω)\epsilon_{1}(\omega) is dynamically coupled to ϵ2(ω)\epsilon_{2}(\omega) by the Kramers-Kronig (KK) transformation. This approach can be regarded as a limiting case of the multi-oscillator fitting of spectra, when the number of oscillators is of the order of the number of experimental points. In the case of the normal-incidence reflectivity from a semi-infinite isotropic sample the new method gives essentially the same result as the conventional KK transformation of reflectivity. In contrast to the conventional approaches, the proposed technique is applicable, without readaptation, to virtually all types of linear-response optical measurements, or arbitrary combinations of measurements, such as reflectivity, transmission, ellipsometry {\it etc.}, done on different types of samples, including thin films and anisotropic crystals.Comment: 10 pages, 7 figure

    An efficient algorithm for computing the Baker-Campbell-Hausdorff series and some of its applications

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    We provide a new algorithm for generating the Baker--Campbell--Hausdorff (BCH) series Z = \log(\e^X \e^Y) in an arbitrary generalized Hall basis of the free Lie algebra L(X,Y)\mathcal{L}(X,Y) generated by XX and YY. It is based on the close relationship of L(X,Y)\mathcal{L}(X,Y) with a Lie algebraic structure of labeled rooted trees. With this algorithm, the computation of the BCH series up to degree 20 (111013 independent elements in L(X,Y)\mathcal{L}(X,Y)) takes less than 15 minutes on a personal computer and requires 1.5 GBytes of memory. We also address the issue of the convergence of the series, providing an optimal convergence domain when XX and YY are real or complex matrices.Comment: 30 page

    Ab initio study of alanine polypeptide chains twisting

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    We have investigated the potential energy surfaces for alanine chains consisting of three and six amino acids. For these molecules we have calculated potential energy surfaces as a function of the Ramachandran angles Phi and Psi, which are widely used for the characterization of the polypeptide chains. These particular degrees of freedom are essential for the characterization of proteins folding process. Calculations have been carried out within ab initio theoretical framework based on the density functional theory and accounting for all the electrons in the system. We have determined stable conformations and calculated the energy barriers for transitions between them. Using a thermodynamic approach, we have estimated the times of characteristic transitions between these conformations. The results of our calculations have been compared with those obtained by other theoretical methods and with the available experimental data extracted from the Protein Data Base. This comparison demonstrates a reasonable correspondence of the most prominent minima on the calculated potential energy surfaces to the experimentally measured angles Phi and Psi for alanine chains appearing in native proteins. We have also investigated the influence of the secondary structure of polypeptide chains on the formation of the potential energy landscape. This analysis has been performed for the sheet and the helix conformations of chains of six amino acids.Comment: 24 pages, 10 figure

    Scar functions in the Bunimovich Stadium billiard

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    In the context of the semiclassical theory of short periodic orbits, scar functions play a crucial role. These wavefunctions live in the neighbourhood of the trajectories, resembling the hyperbolic structure of the phase space in their immediate vicinity. This property makes them extremely suitable for investigating chaotic eigenfunctions. On the other hand, for all practical purposes reductions to Poincare sections become essential. Here we give a detailed explanation of resonances and scar functions construction in the Bunimovich stadium billiard and the corresponding reduction to the boundary. Moreover, we develop a method that takes into account the departure of the unstable and stable manifolds from the linear regime. This new feature extends the validity of the expressions.Comment: 21 pages, 10 figure

    Modes of Oscillation in Radiofrequency Paul Traps

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    We examine the time-dependent dynamics of ion crystals in radiofrequency traps. The problem of stable trapping of general three-dimensional crystals is considered and the validity of the pseudopotential approximation is discussed. We derive analytically the micromotion amplitude of the ions, rigorously proving well-known experimental observations. We use a method of infinite determinants to find the modes which diagonalize the linearized time-dependent dynamical problem. This allows obtaining explicitly the ('Floquet-Lyapunov') transformation to coordinates of decoupled linear oscillators. We demonstrate the utility of the method by analyzing the modes of a small `peculiar' crystal in a linear Paul trap. The calculations can be readily generalized to multispecies ion crystals in general multipole traps, and time-dependent quantum wavefunctions of ion oscillations in such traps can be obtained.Comment: 24 pages, 3 figures, v2 adds citations and small correction

    Berry phases for the nonlocal Gross-Pitaevskii equation with a quadratic potential

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    A countable set of asymptotic space -- localized solutions is constructed by the complex germ method in the adiabatic approximation for the nonstationary Gross -- Pitaevskii equation with nonlocal nonlinearity and a quadratic potential. The asymptotic parameter is 1/T, where T≫1T\gg1 is the adiabatic evolution time. A generalization of the Berry phase of the linear Schr\"odinger equation is formulated for the Gross-Pitaevskii equation. For the solutions constructed, the Berry phases are found in explicit form.Comment: 13 pages, no figure

    Molecular dynamics study of accelerated ion-induced shock waves in biological media

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    We present a molecular dynamics study of the effects of carbon- and iron-ion induced shock waves in DNA duplexes in liquid water. We use the CHARMM force field implemented within the MBN Explorer simulation package to optimize and equilibrate DNA duplexes in liquid water boxes of different sizes and shapes. The translational and vibrational degrees of freedom of water molecules are excited according to the energy deposited by the ions and the subsequent shock waves in liquid water are simulated. The pressure waves generated are studied and compared with an analytical hydrodynamics model which serves as a benchmark for evaluating the suitability of the simulation boxes. The energy deposition in the DNA backbone bonds is also monitored as an estimation of biological damage, something which is not possible with the analytical model

    Dynamic Phase Transition in a Time-Dependent Ginzburg-Landau Model in an Oscillating Field

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    The Ginzburg-Landau model below its critical temperature in a temporally oscillating external field is studied both theoretically and numerically. As the frequency or the amplitude of the external force is changed, a nonequilibrium phase transition is observed. This transition separates spatially uniform, symmetry-restoring oscillations from symmetry-breaking oscillations. Near the transition a perturbation theory is developed, and a switching phenomenon is found in the symmetry-broken phase. Our results confirm the equivalence of the present transition to that found in Monte Carlo simulations of kinetic Ising systems in oscillating fields, demonstrating that the nonequilibrium phase transition in both cases belongs to the universality class of the equilibrium Ising model in zero field. This conclusion is in agreement with symmetry arguments [G. Grinstein, C. Jayaprakash, and Y. He, Phys. Rev. Lett. 55, 2527 (1985)] and recent numerical results [G. Korniss, C.J. White, P. A. Rikvold, and M. A. Novotny, Phys. Rev. E (submitted)]. Furthermore, a theoretical result for the structure function of the local magnetization with thermal noise, based on the Ornstein-Zernike approximation, agrees well with numerical results in one dimension.Comment: 16 pp. RevTex, 9 embedded ps figure

    Sufficient conditions for the convergence of the Magnus expansion

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    Two different sufficient conditions are given for the convergence of the Magnus expansion arising in the study of the linear differential equation Y′=A(t)YY' = A(t) Y. The first one provides a bound on the convergence domain based on the norm of the operator A(t)A(t). The second condition links the convergence of the expansion with the structure of the spectrum of Y(t)Y(t), thus yielding a more precise characterization. Several examples are proposed to illustrate the main issues involved and the information on the convergence domain provided by both conditions.Comment: 20 page
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