arXiv subjects

Ulrich Kleinekathoefer

Publications and source records attributed to Ulrich Kleinekathoefer.

15 recordsLinked to original sources

arXiv2019

Chebyshev Hierarchical Equations of Motion for Systems with Arbitrary Spectral Densities and Temperatures

The time evolution in open quantum systems, such as a molecular aggregate in contact with a thermal bath, still poses a complex and challenging problem. The influence of the thermal noise can be treated using a plethora of schemes, several of which decompose the corresponding correlation functions in terms of weighted sums of exponential functions. One such scheme is based on the hierarchical equations of motion (HEOM), which is built using only certain forms of bath correlation functions. In the case where the environment is described by a complex spectral density or is at a very low temperature, approaches utilizing the exponential decomposition become very inefficient. Here we utilize an alternative decomposition scheme for the bath correlation function based on Chebyshev polynomials and Bessel functions to derive a hierarchical equations of motion approach up to an arbitrary order in the environmental coupling. These hierarchical equations are similar in structure to the popular exponential HEOM scheme, but are formulated using the derivatives of the Bessel functions. The proposed scheme is tested up to the fourth order in perturbation theory for a two-level system and compared to benchmark calculations for the case of zero-temperature quantum Ohmic and super-Ohmic noise. Furthermore, the benefits and shortcomings of the present Chebyshev-based hierarchical equations are discussed.

physics.chem-ph↗

arXiv2007

Coherent destruction of the current through molecular wires using short laser pulses

A molecular wire coupled to two electron reservoirs is investigated within a tight-binding approach including spin and Coulomb interaction. Under the assumption of weak coupling to the electron reservoirs a quantum master equation can be derived for the electron transport through the wire. Motivated by the phenomenon of coherent destruction of tunneling for monochromatic laser fields, the influence of Gaussian laser pulses on the transport through the wires is studied. For situations in which the maximum amplitude of the electric field fulfills the conditions for the destructive quantum effect the average current through the system can be suppressed even for a wire consisting of only one site. Turning on the electron correlation does not destroy the suppression of the current by the laser.

cond-mat.mes-hall↗

arXiv2007

Coherent laser control of the current through molecular junctions

The electron tunneling through a molecular junction modeled by a single site weakly coupled to two leads is studied in the presence of a time-dependent external field using a master equation approach. In the case of small bias voltages and high carrier frequencies of the external field, we observe the phenomenon of coherent destruction of tunneling, i.e. the current through the molecular junction vanishes completely for certain parameters of the external field. In previous studies the tunneling within isolated and open multi-site systems was suppressed; it is shown here that the tunneling between a single site and electronic reservoirs, i.e. the leads, can be suppressed as well. For larger bias voltages the current does not vanish any more since further tunneling channels participate in the electron conduction and we also observe photon-assisted tunneling which leads to steps in the current-voltage characteristics. The described phenomena are demonstrated not only for monochromatic fields but also for laser pulses and therefore could be used for ultrafast optical switching of the current through molecular junctions.

cond-mat.mes-hall↗

arXiv2007

Switching the current through molecular wires

The influence of Gaussian laser pulses on the transport through molecular wires is investigated within a tight-binding model for spinless electrons including correlation. Motivated by the phenomenon of coherent destruction of tunneling for monochromatic laser fields, situations are studied in which the maximum amplitude of the electric field fulfills the conditions for the destructive quantum effect. It is shown that, as for monochromatic laser pulses, the average current through the wire can be suppressed. For parameters of the model, which do not show a net current without any optical field, a Gaussian laser pulse can establish a temporary current. In addition, the effect of electron correlation on the current is investigated.

cond-mat.mes-hall↗

arXiv2007

Optimal control of molecular electronics by femtosecond laser pulses

Combining the features of molecular wires and femtosecond laser pulses gives the unique opportunity to optically switch electron currents in molecular devices with very high speed. Based on a weak-coupling approximation between wire and leads a quantum master equation for the population dynamics and the electric current through the molecular wire has been developed which allows for arbitrary time-dependent laser fields interacting with the wire. This formalism is combined with the theory of optimal control. For a tight-binding approximation of the wire we show how to compute the laser pulses to switch the current through the wire on and off. With this approach the desired pattern of the current in time can be chosen in an almost arbitrary fashion.

cond-mat.mes-hall↗

arXiv2005

The influence of ultra-fast laser pulses on electron transfer in molecular wires studied by a non-Markovian density matrix approach

New features of molecular wires can be observed when they are irradiated by laser fields. These effects can be achieved by periodically oscillating fields but also by short laser pulses. The theoretical foundation used for these investigations is a density matrix formalism where the full system is partitioned into a relevant part and a thermal fermionic bath. The derivation of a quantum master equation, either based on a time-convolutionless or time-convolution projection-operator approach, incorporates the interaction with time-dependent laser fields non-perturbatively and is valid at low temperatures for weak system-bath coupling. From the population dynamics the electrical current through the molecular wire is determined. This theory including further extensions is used for the determination of electron transport through molecular wires. As examples, we show computations of coherent destruction of tunneling in asymmetric periodically driven quantum systems, alternating currents and the suppression of the directed current by using a short laser pulse.

cond-mat.mes-hall↗

arXiv2003

Stochastic unraveling of Redfield master equations and its application to electron transfer problems

A method for stochastic unraveling of general time-local quantum master equations (QMEs) is proposed. The present kind of jump algorithm allows a numerically efficient treatment of QMEs which are not in Lindblad form, i.e. are not positive semidefinite by definition. The unraveling can be achieved by allowing for trajectories with negative weights. Such a property is necessary, e.g. to unravel the Redfield QME and to treat various related problems with high numerical efficiency. The method is successfully tested on the damped harmonic oscillator and on electron transfer models including one and two reaction coordinates. The obtained results are compared to those from a direct propagation of the reduced density matrix (RDM) as well as from the standard quantum jump method. Comparison of the numerical efficiency is performed considering both the population dynamics and the RDM in the Wigner phase space representation.

physics.chem-ph↗

arXiv2002

Stochastic unraveling of time-local quantum master equations beyond the Lindblad class

A new method for stochastic unraveling of general time-local quantum master equations (QME) which involve the reduced density operator at time t only is proposed. The present kind of jump algorithm enables a numerically efficient treatment of QMEs which are not of Lindblad form. So it opens new large fields of application for stochastic methods. The unraveling can be achieved by allowing for trajectories with negative weight. We present results for the quantum Brownian motion and the Redfield QMEs as test examples. The algorithm can also unravel non-Markovian QMEs when they are in a time-local form like in the time-convolutionless formalism.

quant-ph↗

arXiv2001

Exciton scattering in light-harvesting systems of purple bacteria

Using the reduced density matrix formalism the exciton scattering in light-harvesting systems of purple bacteria is calculated. The static disorder (fluctuations of the site energies) as well as the dynamic disorder (dissipation) is taken into account in this work. Circular aggregates with 18 pigments are studied to model the B850 ring of bacteriochlorophylls with LH2 complexes. It can be shown that the influence of dissipation may not be neglected in the simulation of the time-dependent anisotropy of fluorescence. Also an elliptical deformation of the ring could be essential.

physics.chem-ph↗

arXiv2001

A density matrix approach to photoinduced electron injection

Electron injection from an adsorbed molecule to the substrate (heterogeneous electron transfer) is studied. One reaction coordinate is used to model this process. The surface phonons and/or the electron-hole pairs together with the internal degrees of freedom of the adsorbed molecule as well as possibly a liquid surrounding the molecule provide a dissipative environment, which may lead to dephasing, relaxation, and sometimes excitation of the relevant system. In the process studied the adsorbed molecule is excited by a light pulse. This is followed by an electron transfer from the excited donor state to the quasi-continuum of the substrate. It is assumed that the substrate is a semiconductor. The effects of dissipation on electron injection are investigated.

physics.chem-ph↗

arXiv2001

Influence of Static and Dynamic Disorder on the Anisotropy of Emission in the Ring Antenna Subunits of Purple Bacteria Photosynthetic Systems

Using the reduced density matrix formalism the time dependence of the exciton scattering in light-harvesting ring systems of purple bacteria is calculated. In contrast to the work of Kumble and Hochstrasser (J. Chem. Phys. 109 (1998) 855) static disorder (fluctuations of the site energies) as well as dynamic disorder (dissipation) is taken into account. For the description of dissipation we use Redfield theory in exciton eigenstates without secular approximation. This is shown to be equivalent to the Markovian limit of Capek's theory in local states. Circular aggregates with 18 pigments are studied to model the B850 ring of bacteriochlorophyls within LH2 complexes. It can be demonstrated that the dissipation is important for the time-dependent anisotropy of the fluorescence. Smaller values of static disorder are sufficient to produce the same decay rates in the anisotropy in comparison with the results by Kumble and Hochstrasser.

physics.chem-ph↗

arXiv2000

Perturbative treatment of intercenter coupling in Redfield theory

The quantum dynamics of coupled subsystems connected to a thermal bath is studied. In some of the earlier work the effect of intercenter coupling on the dissipative part was neglected. This is equivalent to a zeroth-order perturbative expansion of the damping term with respect to the intercenter coupling. It is shown numerically for two coupled harmonic oscillators that this treatment can lead to artifacts and a completely wrong description, for example, of a charge transfer processes even for very weak intercenter coupling. Here we perform a first-order treatment and show that these artifacts disappear. In addition, we demonstrate that the thermodynamic equilibrium population is almost reached even for strong intercenter coupling strength.

physics.chem-ph↗

arXiv2000

Generalized Heitler-London Theory for H_3: A Comparison of the Surface Integral Method with Perturbation Theory

The generalized Heitler-London (GHL) theory provides a straightforward way to express the potential energy surface of H_3 in terms of Coulomb and exchange energies which can be calculated either by perturbation theory or using the surface integral method (SIM). By applying the Rayleigh-Schroedinger perturbation theory, GHL theory for the quartet spin state of H_3 is shown to yield results equivalent to the symmetrized Rayleigh-Schroedinger version of symmetry adapted perturbation theory (SAPT). This equivalence allows a comparison with the corresponding results obtained by the surface integral method. The surface integral result calculated with a product of atomic wave functions is found to have certain advantages over the perturbation approach.

physics.chem-ph↗

arXiv2000

Efficiency of different numerical methods for solving Redfield equations

The numerical efficiency of different schemes for solving the Liouville-von Neumann equation within multilevel Redfield theory has been studied. Among the tested algorithms are the well-known Runge-Kutta scheme in two different implementations as well as methods especially developed for time propagation: the Short Iterative Arnoldi, Chebyshev and Newtonian propagators. In addition, an implementation of a symplectic integrator has been studied. For a simple example of a two-center electron transfer system we discuss some aspects of the efficiency of these methods to integrate the equations of motion. Overall for time-independent potentials the Newtonian method is recommended. For time-dependent potentials implementations of the Runge-Kutta algorithm are very efficient.

physics.chem-ph↗

arXiv2000

Photo-induced intermolecular charge transfer in porphyrin complexes

Optical excitation of the sequential supermolecule H_2P-ZnP-Q induces an electron transfer from the free-base porphyrin (H_2P) to the quinone (Q) via the zinc porphyrin (ZnP). This process is modeled by equations of motion for the reduced density matrix which are solved numerically and approximately analytically. These two solutions agree very well in a great region of parameter space. It is shown that for the majority of solvents the electron transfer occurs with the superexchange mechanism.

physics.chem-ph↗