470 research outputs found
Optimization of electron pumping by harmonic mixing
For a symmetric bridge coupled to infinite leads, in the presence of a
dipole-coupled external ac-field with harmonic mixing, we solve the
Schr\"odinger equation in the time-domain using open boundary conditions as
well as in the energy-domain using Floquet scattering theory. As this potential
breaks parity and generalized parity, we find a non-vanishing average current.
We then optimize the relative amplitude ratio between the fundamental and the
second harmonic leading to a maximum in the pump current.Comment: 13 pages, 6 figures, accepted at Phys. Rev. B,
http://prb.aps.org/accepted/B/7b073O7dMc412f17647d3877ee3ac5c3e271dcb1
Application of the Mixed Time-averaging Semiclassical Initial Value Representation method to Complex Molecular Spectra
The recently introduced mixed time-averaging semiclassical initial value
representation molecular dynamics method for spectroscopic calculations [M.
Buchholz, F. Grossmann, and M. Ceotto, J. Chem. Phys. 144, 094102 (2016)] is
applied to systems with up to 61 dimensions, ruled by a condensed phase
Caldeira-Leggett model potential. By calculating the ground state as well as
the first few excited states of the system Morse oscillator, changes of both
the harmonic frequency and the anharmonicity are determined. The method
faithfully reproduces blueshift and redshift effects and the importance of the
counter term, as previously suggested by other methods. Differently from
previous methods, the present semiclassical method does not take advantage of
the specific form of the potential and it can represent a practical tool that
opens the route to direct ab initio semiclassical simulation of condensed phase
systems.Comment: 11 figure
Spectra of Harmonium in a magnetic field using an initial value representation of the semiclassical propagator
For two Coulombically interacting electrons in a quantum dot with harmonic
confinement and a constant magnetic field, we show that time-dependent
semiclassical calculations using the Herman-Kluk initial value representation
of the propagator lead to eigenvalues of the same accuracy as WKB calculations
with Langer correction. The latter are restricted to integrable systems,
however, whereas the time-dependent initial value approach allows for
applications to high-dimensional, possibly chaotic dynamics and is extendable
to arbitrary shapes of the potential.Comment: 11 pages, 1 figur
Apoptosis of moving, non-orthogonal basis functions in many-particle quantum dynamics
Due to the exponential increase of the numerical effort with the number of
degrees of freedom, moving basis functions have a long history in quantum
dynamics. In addition, spawning of new basis functions is routinely applied.
Here we advocate the opposite process: the programmed removal of motional
freedom of selected basis functions. This is a necessity for converged
numerical results with respect to the size of a non-orthogonal basis, because
generically two or more states approach each other too closely early on,
rendering unstable the matrix inversion, required to make the equations of
motion explicit. Applications to the sub-Ohmic spin-boson model as well as to
polaron dynamics in a Holstein molecular crystal model demonstrate the power of
the proposed methodology.Comment: 10 pages, 6 figure
Herman-Kluk propagator is free from zero-point energy leakage
Semiclassical techniques constitute a promising route to approximate quantum
dynamics based on classical trajectories starting from a quantum-mechanically
correct distribution. One of their main drawbacks is the so-called zero-point
energy (ZPE) leakage, that is artificial redistribution of energy from the
modes with high frequency and thus high ZPE to that with low frequency and ZPE
due to classical equipartition. Here, we show that an elaborate semiclassical
formalism based on the Herman-Kluk propagator is free from the ZPE leakage
despite utilizing purely classical propagation. This finding opens the road to
correct dynamical simulations of systems with a multitude of degrees of freedom
that cannot be treated fully quantum-mechanically due to the exponential
increase of the numerical effort.Comment: 6 pages 2 figure
Obtaining Maxwell's equations heuristically
Starting from the experimental fact that a moving charge experiences the
Lorentz force and applying the fundamental principles of simplicity (first
order derivatives only) and linearity (superposition principle), we show that
the structure of the microscopic Maxwell equations for the electromagnetic
fields can be deduced heuristically by using the transformation properties of
the fields under space inversion and time reversal. Using the experimental
facts of charge conservation and that electromagnetic waves propagate with the
speed of light together with Galileo invariance of the Lorentz force allows us
to introduce arbitrary electrodynamic units naturally.Comment: 11 page
Entanglement in the full state vector of boson sampling
The full state vector of boson sampling is generated by passing S single
photons through beam splitters of M modes. The initial Fock state is expressed
withgeneralized coherent states, and an exact application of the unitary
evolution becomes possible. Due to the favorable polynomial scaling in M , we
can investigate Renyi entanglement entropies for moderate particle and huge
mode numbers. We find (almost) Renyi index independent symmetric Page curves
with maximum entropy at equal partition. Furthermore, the maximum entropy as a
function of mode index saturates as a function of M in the collision-free
subspace case. The asymptotic value of the entropy increases linearly with S.
Furthermore, we show that the build-up of the entanglement leads to a cusp at
subsystem size equal to S in the asymmetric entanglement curve. The maximum
entanglement is reached surprisingly early before the mode population is
distributed over the whole system
Simplified Approach to the Mixed Time-averaging Semiclassical Initial Value Representation for the Calculation of Dense Vibrational Spectra
We present and test an approximate method for the semiclassical calculation
of vibrational spectra. The approach is based on the mixed time-averaging
semiclassical initial value representation method, which is simplified to a
form that contains a filter to remove contributions from approximately harmonic
environmental degrees of freedom. This filter comes at no additional numerical
cost, and it has no negative effect on the accuracy of peaks from the
anharmonic system of interest. The method is successfully tested for a model
Hamiltonian, and then applied to the study of the frequency shift of iodine in
a krypton matrix. Using a hierarchic model with up to 108 normal modes included
in the calculation, we show how the dynamical interaction between iodine and
krypton yields results for the lowest excited iodine peaks that reproduce
experimental findings to a high degree of accuracy
Semiclassical Approach to the Hydrogen-exchange Reaction- Reactive and Transition-state Dynamics
Scattering matrix elements and symmetric transition-state resonances for the collinear H 2 + H → H + H 2 reaction are obtained using a time-dependent approach. The correlation function between reactant channel wavepackets and product channel wavepackets is used to determine the S-matrix elements. In a similar fashion, autocorrelation functions are used to extract the positions and widths of transition-state resonances. The time propagation of the wavepackets is performed by the improved semiclassical frozen Gaussian method of Herman and Kluk, which is an initial value, uniformly converged method. The agreement between the quantum and semiclassical results is far better than that obtained previously for this system by other semiclassical methods
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