241 research outputs found
Rigorous derivation of coherent resonant tunneling time and velocity in finite periodic systems
The velocity 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 we apply the natural definition
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 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 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
A universal method of extraction of the complex dielectric function
from
experimentally accessible optical quantities is developed. The central idea is
that is parameterized independently at each node of a
properly chosen anchor frequency mesh, while is
dynamically coupled to 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
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 generated by and . It is based
on the close relationship of 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 ) 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 and are real or complex matrices.Comment: 30 page
Ab initio study of alanine polypeptide chains twisting
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
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
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
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 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
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
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
Two different sufficient conditions are given for the convergence of the
Magnus expansion arising in the study of the linear differential equation . The first one provides a bound on the convergence domain based on the
norm of the operator . The second condition links the convergence of the
expansion with the structure of the spectrum of , 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
- …