## Wirtschaft und Informationstechnik Bocholt

We study the nonequilibrium dynamics of a quantum system under the influence of two noncommuting fluctuation sources, i.e., purely dephasing fluctuations and relaxational fluctuations. We find that increasing purely dephasing fluctuations suppress increasing relaxation in the quantum system. This effect is further enhanced when both fluctuation sources are fully correlated. These effects arise for medium to strong primary fluctuations already when the secondary fluctuations are weak due to their noncommuting coupling to the quantum system. Dephasing, in contrast, is increased by increasing any of the two fluctuations. Fully correlated fluctuations result in overdamping at much lower system-bath coupling than uncorrelated noncommuting fluctuations. In total, we observe that treating subdominant secondary environmental fluctuations perturbatively leads, as neglecting them, to erroneous conclusions.

This introduction to a special issue about concepts and facets of entrepreneurial diversity serves as a starting point for further discussion and research in this field. For this purpose, we provide information about the roots of the study of diversity and current trends in entrepreneurship research and present a frame for (researching) entrepreneurial diversity. Additionally, we briefly summarize the three papers selected for inclusion in this special issue. Together, they offer insights into the intersections of different diversity dimensions, personality as a deep dimension of team composition, and a general critical reflection on the conceptualization of entrepreneurial diversity. Taken together, the papers in this special issue present new findings and contribute to further advancing the long overdue research on and discussion about diversity in the field of entrepreneurship.

We study the impact of underdamped intramolecular vibrational modes on the efficiency of the excitation energy transfer in a dimer in which each state is coupled to its own underdamped vibrational mode and, in addition, to a continuous background of environmental modes. For this, we use the numerically exact hierarchy equation of motion approach. We determine the quantum yield and the transfer time in dependence of the vibronic coupling strength, and in dependence of the damping of the incoherent background. Moreover, we tune the vibrational frequencies out of resonance with the excitonic energy gap. We show that the quantum yield is enhanced by up to 10% when the vibrational frequency of the donor is larger than at the acceptor. The vibronic energy eigenstates of the acceptor acquire then an increased density of states, which leads to a higher occupation probability of the acceptor in thermal equilibrium. We can conclude that an underdamped vibrational mode which is weakly coupled to the dimer fuels a faster transfer of excitation energy, illustrating that long-lived vibrations can, in principle, enhance energy transfer, without involving long-lived electronic coherence.

We study a quantum two-level system under the influence of two independent baths, i.e., a sub-Ohmic pure dephasing bath and an Ohmic or sub-Ohmic relaxational bath. We show that cooling such a system invariably polarizes one of the two baths. A polarized relaxational bath creates an effective asymmetry. This asymmetry can be suppressed by additional dephasing noise. This being less effective, the more dominant low frequencies are in the dephasing noise. A polarized dephasing bath generates a large shift in the coherent oscillation frequency of the two-level system. This frequency shift is little affected by additional relaxational noise nor by the frequency distribution of the dephasing noise itself. As our model reflects a typical situation for superconducting phase qubits, our findings can help optimize cooling protocols for future quantum electronic devices.

Ultrafast Energy Transfer in Excitonically Coupled Molecules Induced by a Nonlocal Peierls Phonon
(2019)

Molecular vibration can influence exciton transfer via either a local (intramolecular) Holstein or a nonlocal (intermolecular) Peierls mode. We show that a strong vibronic coupling to a nonlocal mode dramatically speeds up the transfer by opening an additional transfer channel. This Peierls channel is rooted in the formation of a conical intersection of the excitonic potential energy surfaces. For increasing Peierls coupling, the electronically coherent transfer for weak coupling turns into an incoherent transfer of a localized exciton through the intersection for strong coupling. The interpretation in terms of a conical intersection intuitively explains recent experiments of ultrafast energy transfer in photosynthetic and photovoltaic molecular systems.

When a hydrophilic solute in water is suddenly turned into a hydrophobic species, for instance, by photoionization, a layer of hydrated water molecules forms around the solute on a time scale of a few picoseconds. We study the dynamic buildup of the hydration shell around a hydrophobic solute on the basis of a time-dependent dielectric continuum model. Information about the solvent is spectroscopically extracted from the relaxation dynamics of a test dipole inside a static Onsager sphere in the nonequilibrium solvent. The growth process is described phenomenologically within two approaches. First, we consider a time-dependent thickness of the hydration layer that grows from zero to a finite value over a finite time. Second, we assume a time-dependent complex permittivity within a finite layer region around the Onsager sphere. The layer is modeled as a continuous dielectric with a much slower fluctuation dynamics. We find a time-dependent frequency shift down to the blue of the resonant absorption of the dipole, together with a dynamically decreasing line width, as compared to bulk water. The blue shift reflects the work performed against the hydrogen-bonded network of the bulk solvent and is a directly measurable quantity. Our results are in agreement with an experiment on the hydrophobic solvation of iodine in water.

Quantum systems are typically subject to various environmental noise sources. Treating these environmental disturbances with a system-bath approach beyond weak coupling, one must refer to numerical methods as, for example, the numerically exact quasi-adiabatic path integral approach. This approach, however, cannot treat baths which couple to the system via operators, which do not commute. We extend the quasi-adiabatic path integral approach by determining the time discrete influence functional for such non-commuting fluctuations and by modifying the propagation scheme accordingly. We test the extended quasi-adiabatic path integral approach by determining the time evolution of a quantum two-level system coupled to two independent baths via non-commuting operators. We show that the convergent results can be obtained and agreement with the analytical weak coupling results is achieved in the respective limits.

We derive a Magnus expansion for a frequency chirped quantum two-level system. We obtain a time-independent effective Hamiltonian which generates a stroboscopic time evolution. At lowest order the according dynamics is identical to results from using a rotating wave approximation. We determine, furthermore, also the next higher-order corrections within our expansion scheme in correspondence to the Bloch-Siegert shifts for harmonically driven systems. Importantly, our scheme can be extended to more complicated systems, i.e., even many-body systems.