15 research outputs found
Heavy atom quantum diffraction by scattering from surfaces
Typically one expects that when a heavy particle collides with a surface, the
scattered angular distribution will follow classical mechanics. The heavy mass
assures that the de Broglie wavelength of the incident particle in the
direction of the propagation of the particle (the parallel direction) will be
much shorter than the characteristic lattice length of the surface, thus
leading to a classical description. Recent work on molecular interferometry has
shown that by increasing the perpendicular coherence length, one may observe
interference of very heavy species passing through a grating. Here we show,
using quantum mechanical simulations, that the same effect will lead to quantum
diffraction of heavy particles colliding with a surface. We find that the
effect is robust with respect to the incident energy, the angle of incidence
and the mass of the particle. It may also be used to verify the quantum nature
of the surface and its fluctuations at very low temperatures.Comment: 9 pages, 3 figure
Dissipating the Langevin equation in the presence of an external stochastic potential
In the Langevin formalism, the delicate balance maintained between the
fluctuations in the system and their corresponding dissipation may be upset by
the presence of a secondary, space-dependent stochastic force, particularly in
the low friction regime. In prior work, the latter was dissipated
self-consistently through an additional uniform (mean-field) friction [Shepherd
and Hernandez, J. Chem. Phys., 115, 2430-2438 (2001).] An alternative approach
to ensure that equipartition is satisfied relies on the use of a
space-dependent friction while ignoring nonlocal correlations. The approach is
evaluated with respect to its ability to maintain constant temperature for two
simple one-dimensional, stochastic potentials of mean force wherein the
friction can be evaluated explicitly when there is no memory in the barriers.
The use of a space-dependent friction is capable of providing qualitatively
similar results to those obtained previously, but in extreme cases, deviations
from equipartition may be observed due to the neglect of the memory effects
present in the stochastic potentials.Comment: 9 pages, 5 figures, to appear in J. Chem. Phy
Coherent quantum transport in disordered systems I: The influence of dephasing on the transport properties and absorption spectra on one-dimensional systems
Excitonic transport in static disordered one dimensional systems is studied
in the presence of thermal fluctuations that are described by the
Haken-Strobl-Reineker model. For short times, non-diffusive behavior is
observed that can be characterized as the free-particle dynamics in the
Anderson localized system. Over longer time scales, the environment-induced
dephasing is sufficient to overcome the Anderson localization caused by the
disorder and allow for transport to occur which is always seen to be diffusive.
In the limiting regimes of weak and strong dephasing quantum master equations
are developed, and their respective scaling relations imply the existence of a
maximum in the diffusion constant as a function of the dephasing rate that is
confirmed numerically. In the weak dephasing regime, it is demonstrated that
the diffusion constant is proportional to the square of the localization length
which leads to a significant enhancement of the transport rate over the
classical prediction. Finally, the influence of noise and disorder on the
absorption spectrum is presented and its relationship to the transport
properties is discussed.Comment: 23 pages, 7 figure
A hybrid stochastic hierarchy equations of motion approach to treat the low temperature dynamics of non-Markovian open quantum systems
The hierarchical equations of motion technique has found widespread success
as a tool to generate the numerically exact dynamics of non-Markovian open
quantum systems. However, its application to low temperature environments
remains a serious challenge due to the need for a deep hierarchy that arises
from the Matsubara expansion of the bath correlation function. Here we present
a hybrid stochastic hierarchical equation of motion (sHEOM) approach that
alleviates this bottleneck and leads to a numerical cost that is nearly
independent of temperature. Additionally, the sHEOM method generally converges
with fewer hierarchy tiers allowing for the treatment of larger systems.
Benchmark calculations are presented on the dynamics of two level systems at
both high and low temperatures to demonstrate the efficacy of the approach.
Then the hybrid method is used to generate the exact dynamics of systems that
are nearly impossible to treat by the standard hierarchy. First, exact energy
transfer rates are calculated across a broad range of temperatures revealing
the deviations from the Forster rates. This is followed by computations of the
entanglement dynamics in a system of two qubits at low temperature spanning the
weak to strong system-bath coupling regimes.Comment: 20 pages, 6 figure
Quantum Diffusion on Molecular Tubes: Universal Scaling of the 1D to 2D Transition
The transport properties of disordered systems are known to depend critically
on dimensionality. We study the diffusion coefficient of a quantum particle
confined to a lattice on the surface of a tube, where it scales between the 1D
and 2D limits. It is found that the scaling relation is universal and
independent of the disorder and noise parameters, and the essential order
parameter is the ratio between the localization length in 2D and the
circumference of the tube. Phenomenological and quantitative expressions for
transport properties as functions of disorder and noise are obtained and
applied to real systems: In the natural chlorosomes found in light-harvesting
bacteria the exciton transfer dynamics is predicted to be in the 2D limit,
whereas a family of synthetic molecular aggregates is found to be in the
homogeneous limit and is independent of dimensionality.Comment: 10 pages, 6 figure
An exact equilibrium reduced density matrix formulation I: The influence of noise, disorder, and temperature on localization in excitonic systems
An exact method to compute the entire equilibrium reduced density matrix for
systems characterized by a system-bath Hamiltonian is presented. The approach
is based upon a stochastic unraveling of the influence functional that appears
in the imaginary time path integral formalism of quantum statistical mechanics.
This method is then applied to study the effects of thermal noise, static
disorder, and temperature on the coherence length in excitonic systems. As
representative examples of biased and unbiased systems, attention is focused on
the well-characterized light harvesting complexes of FMO and LH2, respectively.
Due to the bias, FMO is completely localized in the site basis at low
temperatures, whereas LH2 is completely delocalized. In the latter, the
presence of static disorder leads to a plateau in the coherence length at low
temperature that becomes increasingly pronounced with increasing strength of
the disorder. The introduction of noise, however, precludes this effect. In
biased systems, it is shown that the environment may increase the coherence
length, but only decrease that of unbiased systems. Finally it is emphasized
that for typical values of the environmental parameters in light harvesting
systems, the system and bath are entangled at equilibrium in the single
excitation manifold. That is, the density matrix cannot be described as a
product state as is often assumed, even at room temperature. The reduced
density matrix of LH2 is shown to be in precise agreement with the steady state
limit of previous exact quantum dynamics calculations.Comment: 37 pages, 12 figures. To appear in Phys. Rev.
Error analysis of free probability approximations to the density of states of disordered systems
Theoretical studies of localization, anomalous diffusion and ergodicity
breaking require solving the electronic structure of disordered systems. We use
free probability to approximate the ensemble- averaged density of states
without exact diagonalization. We present an error analysis that quantifies the
accuracy using a generalized moment expansion, allowing us to distinguish
between different approximations. We identify an approximation that is accurate
to the eighth moment across all noise strengths, and contrast this with the
perturbation theory and isotropic entanglement theory.Comment: 5 pages, 3 figures, submitted to Phys. Rev. Let
Friction-induced energy-loss rainbows in atom surface scattering
The rainbow is due to extrema of the angular deflection function of light impinging on water drops. Generically, extrema of suitably defined deflection functions lead to rainbows. These include angular and rotational rainbows in surface scattering and more. Here we introduce the concept of an >energy-loss deflection function> for scattering of particles from a periodic surface whose extrema lead to a new form-the >energy-loss rainbow> which appears as multiple maxima in the final energy distribution of the scattered particle. Energy-loss rainbows are caused by frictional phonon effects which induce structure in the energy-loss distribution instead of >washing it out.> We provide evidence that they have been observed in Ne scattering on self-assembled monolayers. © 2010 The American Physical Society.This work was supported by grants from the Israel Science Foundation, the Albert Einstein Minerva Center at the Weizmann Institute of Science, and the Ministry of Science and Innovation of Spain through project FIS2007- 62006.Peer Reviewe
Identifying reactive trajectories using a moving transition state
© 2006 American Institute of Physics. The electronic version of this article is the complete one and can be found at: http://dx.doi.org/10.1063/1.2206587DOI: 10.1063/1.2206587A time-dependent no-recrossing dividing surface is shown to lead to a new criterion for identifying reactive trajectories well before they are evolved to infinite time. Numerical dynamics simulations of a dissipative anharmonic two-dimensional system confirm the efficiency of this approach. The results are compared to the standard fixed transition state dividing surface that is well-known to suffer from recrossings and therefore requires trajectories to be evolved over a long time interval before they can reliably be classified as reactive or nonreactive. The moving dividing surface can be used to identify reactive trajectories in harmonic or moderately anharmonic systems with considerably lower numerical effort or even without any simulation at all
Dihedral-Angle Information Entropy as a Gauge of Secondary Structure Propensity
Protein structural information can be uncovered using an information-theory-based entropy and auxiliary functions by taking advantage of high-quality correlation plots between the dihedral angles around a residue and those between sequential residues. A standard information entropy for a primary sequence has been defined using the values of the probabilities of the most likely dihedral angles along the sequence. The distribution of entropy differences relative to the standard for each protein in a reference set—a sublibrary of the Protein Data Bank at the 90% sequence redundancy level—appears to be nearly Gaussian. It gives rise to an auxiliary checking function whose value signals the extent to which the dihedral angle propensities differ from typical structures. Such deviations can arise either because of incorrect dihedral angle assignments or secondary structural propensities that are atypical of the structures in the reference set. This auxiliary checking function can be readily calculated at the public website, http://www.d2check.gatech.edu. Its utility is demonstrated here in an analysis displaying differences between experimentally and theoretically derived structures, and in the analysis of structures derived by homology modeling. A comparison of the new measure, D(2)Check, to other checking functions based on backbone conformation—namely, PROCHECK and WHAT_CHECK—is also provided