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Corporate Social Responsibility and Diversity Management. Theoretical Approaches and Best Practices
(2017)
This book provides unique insights into how the idea of quota laws to get women on to corporate boards gained international momentum from its origins in Norway. Invaluable insights are gained through the stories of actors involved in shaping the discourse and practice on women of boards.
In exploring political contexts, the role of the advocacy movement, experiences of women directors themselves and latest research findings, the contributors provide a comprehensive overview of the rationales, processes and outcomes of formal approaches to gender diversity on boards. Drawing on insights from political, business and academic actors, the book discusses how and why the Norwegian law on gender equality on corporate boards is turning into a blueprint for action internationally.
Getting Women on to Corporate Boards will prove an invaluable resource for policy-makers, principle-setters, practitioners and students interested in the international lessons from Norway, as well as for current and potential female directors.
We present a scheme for cooling a vibrational mode of a magnetic molecular nanojunction by a spin-polarized charge current upon exploiting the interaction between its magnetic moment and the vibration. The spin-polarized charge current polarizes the magnetic moment of the nanoisland, thereby lowering its energy. A small but finite coupling between the vibration and the magnetic moment permits a direct exchange of energy such that vibrational energy can be transferred into the magnetic state. For positive bias voltages, this generates an effective cooling of the molecular vibrational mode. We determine parameter regimes for the cooling of the vibration to be optimal. Although the flowing charge current inevitably heats up the vibrational mode via Ohmic energy losses, we show that due to the magnetomechanical coupling, the vibrational energy (i.e, the effective phonon temperature) can be lowered below 50% of its initial value, when the two leads are polarized anti-parallel. In contrast to the cooling effect for positive bias voltages, net heating of the vibrational mode occurs for negative bias voltages. The cooling effect is enhanced for a stronger anti-parallel magnetic polarization of the leads, while the heating is stronger for a larger parallel polarization. Yet, dynamical cooling is also possible with parallel lead alignments when the two tunneling barriers are asymmetric.
Efficient tool to calculate two-dimensional optical spectra for photoactive molecular complexes
(2015)
We show that strong non-Markovian effects can be revealed by the steady-state two-dimensional (2D) photon echo spectra at asymptotic waiting times. For this, we use a simple dimer toy model that is strongly coupled to a harmonic bath with parameters typical for photoactive biomolecules. We calculate the 2D photon echo spectra employing both the numerically exact hierarchy equation of motion and the quasiadiabatic path integral approach and compare these results with approximate results from a time-nonlocal quantum master equation approach. While the latter correctly reproduces the exact population dynamics at long times, it fails at the same time to correctly describe the 2D photon echo spectra at long waiting times. The differences show that non-Markovian effects are much more important for the steady-state 2D photon echoes than for the equilibrium populations. Thus, accurate theoretical descriptions of the energy transfer dynamics in biomolecular complexes have to be based on numerically exact simulations of the environmental fluctuations when nonlinear response functions are analyzed.
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.
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.
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.
There is a strongly held belief that if companies can direct their marketing activities to improve customer attitudes and intentions, it will impact on purchase behaviors. Departing from complementary yet sometimes conflicting findings of the current literature, we intend to contribute to the literature by answering two related questions. First, we investigate drivers of loyalty intention over time, and by so doing try to better understand loyalty formation. Second, once we understand loyalty formation, we assess the impact of loyalty on different aspects of purchase behavior, considering temporal effects. Therefore, we develop a consumption-system model which assumes that perceptions, intention, and the impact of perceptions and intention on behavior in one period serve as anchors for the same constructs in a subsequent period, implying a pattern of repeated consumption over time.
Using 3SLS regression analysis, results of a large-scale study using survey data from a sample of 2,478 customers from two points in time and purchase data gathered over a 30-month period suggest interesting findings on the two aforementioned questions:
Considering the first question, we find strong support for customer equity drivers directly influencing loyalty. Moreover, we see evidence for loyalty formation as a consumption-system as equity drivers and loyalty intention of one period are significant predictors of the same constructs in the next period.
Addressing the second research question is less straightforward. We find a significant impact of loyalty intention only for purchase frequency, but not for future sales and average receipt. This suggests that in a retailing context, the amount spent depends to a larger extent on actual needs and not on loyalty intention. Loyalty intention seems to be a more appropriate lead indicator for the frequency of store visits. For most categories, repurchase intention will not necessarily be related to higher sales. On the contrary, higher future sales are more likely to depend on the retailer’s ability to cross- and up-sell to its customers. In all, we need to acknowledge that the strongest predictor of future behavior is, in fact, past behavior.
These results question some of the strongly held beliefs of relationship marketing and its impact on actual behavior. Effects might not be as simple as they appear at first, i.e., temporal interplay between constructs. Moreover, it seems that inertia is more important than some marketing research tends to acknowledge. We would therefore suggest a more detailed investigation of customers’ initial choice behavior. If, in fact, inertia is the driving force behind purchase behavior, companies need to augment their emphasis on increasing initial customer contact and, accordingly, on initial product trial. This is somewhat counter-intuitive from a relationship marketing perspective, because that stream of research largely suggests the advantage of retaining customers rather than acquiring new ones. While we are not denying the importance of customer retention, it seems that companies are already fairly successful in doing so – the strong inertia effect confirms that. Hence, customer retention might not be the best strategy to differentiate in the market. Perhaps companies can better differentiate by excelling in customer acquisition. This, however, would have a significant impact on how marketing budgets should be spent by companies trying to reach sustained success. It might be time for re-balancing customer acquisition and customer retention.
Gaining customer loyalty is an important goal of marketing, and loyalty programs are intended to help in reaching it. Research on loyalty programs suggests that customers differentiate between loyalty to a company and loyalty to a loyalty program, yet little is known about the consequences of these two types of loyalty. Therefore, our study intends to make two main contributions: (1) improving our understanding of the constructs “program loyalty” and “company loyalty”, (2) investigating the relative impact of the two types of loyalty on preference, intention, and purchase behavior for the case of a multi-firm loyalty program. Results indicate that company loyalty influences a customer’s choice to visit a particular provider and to prefer it over competitors, but it is not a strong predictor of purchase behavior. Conversely, program loyalty is a far more important driver of purchase behavior. This implies that company loyalty primarily attracts customers to a particular provider and program loyalty ensures that once inside the store, more money is spent.
Commonly, nanosystems are characterized by their response to time-dependent external fields in the presence of inevitable environmental fluctuations. The direct impact of the external driving on the environment is generally neglected. While this approach is satisfactory for macroscopic systems, on the nanoscale, an interaction of external fields with the environment is often unavoidable on principle. We extend the standard linear response theory of quantum dissipative systems to strongly driven baths. Significant modifications are found for two paradigm examples. First, we evaluate the polarizability of a molecule immersed in a strongly polarizable medium that responds to terahertz radiation. We find an increase of the molecular polarizability by about 30%. Second, we determine the response of a semiconductor quantum dot in close proximity to a metallic nanoparticle. Both are placed in a polarizable medium and exposed to electromagnetic irradiation. We show that the response of the quantum dot is qualitatively modified by the driven nanoparticle, including the generation of an additional channel of stimulated emission.
We propose a quantum-mechanical model to calculate the current through a single molecular junction immersed in a solvent and surrounded by a thin shell of bound water under an applied ac voltage. The solvent plus hydration shell are captured by a dielectric continuum model for which the resulting spectral density is determined. Here the dielectric properties, e.g., the Debye relaxation time and the dielectric constant, of the bulk solvent and the hydration shell as well as the shell thickness directly enter. We determine the charge current through the molecular junction under an ac voltage in the sequential tunneling regime where we solve a quantum master equation by a real-time diagrammatic technique. Interestingly, the Fourier components of the charge current show an exponential-like decline when the hydration shell thickness increases. Finally, we apply our findings to binary solvent mixtures with varying volume fractions and find that the current is highly sensitive to both the hydration shell thickness as well as the volume fraction of the solvent mixture, giving rise to possible applications as shell and concentration sensors on the molecular scale.
Broadening the Target Group for Higher education in Germany: A Case Study on Diversity Management
(2011)
In some industrialized German areas, as in the Ruhr-Area, the percentage of students with migrant background in primary education has overcome the 50 percentage limit with an increasing share in future, the overwhelming part of them with family from Turkey. A large share of those students attains the admission qualification to higher education from “Berufskollegs”, schools which focus on the combination of vocational skills and theoretical education. This migrant potential can primarily be tapped for additional students by universities of applied sciences which are embedded into their regions and dedicated to teaching.
First, we show the approach to conceptualize culture and cultural specifics of migrants with Turkish background this project is based on.
Second, we give an overview on the main actions of the project, systematically presented as a process leading students through the institution (“input, throughput, output”).
Third, we frame the project by referring to principles of diversity management in general.
Diversity Management - an approach to use people of different ages as a resource in enterprises
(2003)
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.
We investigate how professional recruiters perceive and assess potential board director candidates. Based on a human capital perspective, individual characteristics will represent certain human capital resources, perceived as more or less useful for the firm. We focus on what characteristics are critical for a candidate to be perceived as appointable to a board. We are particularly interested in the role visible vs. more hidden aspects of human capital in these assessments. The aim of the study is to uncover central actors’ ideas and assumptions of what constitutes the ideal board director. This will add
knowledge as to how board compositions are created and
changed.
We conducted eight semi-structured, in-depth interviews with professional recruiters in Germany and Norway. The results show that formal competence is partly downplayed as selection criteria for board positions, while experience has a central role. Further, our results show that experiences have both a concrete and a symbolic side, where certain individual characteristics appear to represent an image of a successful director of a board. Further, our data show that symbolic capital, labeled “habitus”, is a crucial prerequisite for an individual to be appraised as an ideal candidate. The results indicate preferences for stability and predictability in recruitment processes, which may contribute to explain the persistently low
proportion of women on corporate boards.
This paper develops a framework for understanding the relationships between approaches to learning adopted by students in the context of higher education and the culture of the country they were brought up in. The paper, after examining the more widely used Kolb's learning styles, opts for another categorisation, namely the so called learning approaches developed by Entwistle and others (for example, Entwistle and Ramsden, 1983; Biggs, 1987; Entwistle, 1992; Tait, Entwistle and McCune, 1998; Biggs, Kember and Leung, 2001). Each of the main categories of learning approaches identified by his school, namely, deep, surface apathetic, and strategic are related to Hofstede's cultural dimensions, namely, power distance, individualism vs. collectivism, uncertainty avoidance, long vs. short time orientation and masculinity vs. femininity and a series of hypotheses developed that could be tested in cross cultural samples. This study would give practical hints on students moving out to study in different cultures (e.g. for higher education) and for teachers dealing with students from multiple cultures.
(PDF) Does culture influence learning styles in higher education?. Available from: https://www.researchgate.net/publication/254836756_Does_culture_influence_learning_styles_in_higher_education [accessed Jul 09 2018].
Dephasing in quantum systems is typically the result of their interaction with environmental degrees of freedom. We investigate within a spin-boson model the influence of a super-Ohmic environment on the dynamics of a quantum two-state system. A super-Ohmic environment thereby models typical bulk phonons which are a common disturbance for solid state quantum systems as, for example, nitrogen-vacancy centers. By applying the numerically exact quasiadiabatic path-integral approach we show that for strong system-bath coupling, pseudocoherent dynamics emerges, i.e., oscillatory dynamics at short times due to slaving of the quantum system to the bath dynamics. We extend the phase diagram known for sub-Ohmic and Ohmic environments into the super-Ohmic regime and observe a pronounced nonmonotonous behavior. Super-Ohmic purely dephasing fluctuations strongly suppress the amplitude of coherent dynamics at very short times with no subsequent further decay at later times. Nevertheless, they render the dynamics overdamped. The corresponding phase separation line shows also a nonmonotonous behavior, very similar to the pseudocoherent dynamics.
We study the dynamics of a quantum two-state system driven through an avoided crossing under the influence of a super-Ohmic environment. We determine the Landau–Zener probability employing the numerical exact quasi-adiabatic path integral and a Markovian weak coupling approach. Increasing the driving time in the numerical protocol, we find converged results which shows that super-Ohmic environments only influence the Landau Zener probability within a finite crossing time window. This crossing time is qualitatively determined by the environmental cut-off energy. At weak coupling, we show that the Markovian weak coupling approach provides an accurate description. Since pure dephasing of a super-Ohmic bath is non-Markovian, this highlights that pure dephasing hardly influences the Landau–Zener probability. The finite crossing time window, thus, results from the suppression of relaxation once the energy splitting exceeds the environmental cut-off energy.
We propose a quantum-mechanical model to calculate the nonlinear differential conductance of a single molecular junction immersed in a solvent, either in pure form or as a binary mixture with varying volume fraction. The solvent mixture is captured by a dielectric continuum model for which the resulting spectral density is determined within the Gladstone-Dale approach. The conductance of the molecular junction is calculated by a real-time diagrammatic technique. We find a strong variation of the conductance maximum for varying volume fraction of the solvent mixture. Importantly, the calculated molecular nonlinear conductance shows a very good agreement with experimentally measured data for common molecular junctions in various polar solvent mixtures.
The two-state two-path model is introduced as a minimized model to describe the quantum dynamics of an electronic wave packet in the vicinity of a conical intersection. It involves two electronic potential energy surfaces each of which hosts a pair of quasi-classical trajectories over which the wave packet is assumed to be delocalized. When both trajectories evolve dynamically either diabatically or adiabatically, the full wave packet dynamics shows only features of the dynamics around avoided level crossings in the vicinity of the conical intersection. When one trajectory evolves adiabatically whereas the other trajectory follows a diabatic evolution, quantum mechanical interference of the wave packet components on each path generates Stueckelberg oscillations in the transition probability. These are surprisingly robust against a dissipative environment and, thus, should be a marker for conical intersections.
The two-state two-path model is introduced as a minimized model to describe the quantum dynamics of an electronic wave packet in the vicinity of a conical intersection. It involves two electronic potential energy surfaces each of which hosts a pair of quasi-classical trajectories over which the wave packet is assumed to be delocalized. When both trajectories evolve dynamically either diabatically or adiabatically, the full wave packet dynamics shows only features of the dynamics around avoided level crossings in the vicinity of the conical intersection. When one trajectory evolves adiabatically whereas the other trajectory follows a diabatic evolution, quantum mechanical interference of the wave packet components on each path generates Stueckelberg oscillations in the transition probability. These are surprisingly robust against a dissipative environment and, thus, should be a marker for conical intersections.
Environmental rocking ratchet: Environmental rectification by a harmonically driven avoided crossing
(2017)
We propose a rocking ratchet designed as a symmetric quantum two-state system driven by a single periodic harmonic force and influenced symmetrically by thermal fluctuations. We show that the necessary broken symmetry can dynamically be achieved by a thermal environment that couples to the energy difference between the two states and the tunnel coupling between them. The quantum two-state system is driven by the harmonic periodic drive through its avoided crossing. The correspondingly driven dissipative quantum dynamics results on average in a finite population difference between both states. This then causes directed particle transport.
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.
Tunneling two-level systems (TLSs) are ubiquitous in amorphous solids, and form a major source of noise in systems such as nano-mechanical oscillators, single electron transistors, and superconducting qubits. Occurance of defect tunneling despite their coupling to phonons is viewed as a hallmark of weak defect-phonon coupling. This is since strong coupling to phonons results in significant phonon dressing and suppresses tunneling in two-level tunneling defects effectively. Here we determine the dynamics of a tunneling defect in a crystal strongly coupled to phonons incorporating the full 3D geometry in our description. Wefind that inversion symmetric tunneling is not dressed by phonons whereas other tunneling pathways are dressed by phonons and, thus, are suppressed by strong defect-phonon coupling. We provide the linear acoustic and dielectric response functions for a tunneling defect in a crystal for strong defect-phonon coupling. This allows direct experimental determination of the defect-phonon coupling. The singling out of inversion-symmetric tunneling states in single tunneling defects is complementary to their dominance of the low energy excitations in strongly disordered solids as a result of inter-defect interactions for large defect concentrations. This suggests that inversion symmetric TLSs play a unique role in the low energy properties of disordered solids.
Neuroscientists want to inspect the data their simulations are producing while these are still running. This will on the one hand save them time waiting for results and therefore insight. On the other, it will allow for more efficient use of CPU time if the simulations are being run on supercomputers. If they had access to the data being generated, neuroscientists could monitor it and take counter-actions, e.g., parameter adjustments, should the simulation deviate too much from in-vivo observations or get stuck.
As a first step toward this goal, we devise an in situ pipeline tailored to the neuroscientific use case. It is capable of recording and transferring simulation data to an analysis/visualization process, while the simulation is still running. The developed libraries are made publicly available as open source projects. We provide a proof-of-concept integration, coupling the neuronal simulator NEST to basic 2D and 3D visualization.
A quantum two-level system immersed in a sub-Ohmic bath experiences enhanced low-frequency quantum statistical fluctuations which render the nonequilibrium quantum dynamics highly non-Markovian. Upon using the numerically exact time-evolving matrix product operator approach, we investigate the phase diagram of the polarization dynamics. In addition to the known phases of damped coherent oscillatory dynamics and overdamped decay, we identify a new third region in the phase diagram for strong coupling showing an aperiodic behavior. We determine the corresponding phase boundaries. The dynamics of the quantum two-state system herein is not coherent by itself but slaved to the oscillatory bath dynamics.
Environmental noise leads to dephasing and relaxation in a quantum system. Often, a rigorous treatment of multiple noise sources within a system-bath approach is not possible. We discuss the influence of environmental fluctuations on a quantum system whose dynamics is dephasing already due to a phenomenologically treated additional noise source. For this situation, we develop a path-integral approach, which allows us to treat the system-environment coupling in a numerically exact way, and additionally we extend standard perturbative approaches. We observe strong deviations between the numerically exact and the perturbative results even for weak system-bath coupling. This shows that standard perturbative approaches fail for additional, even weak, system-bath couplings if the system dynamics is already dissipative.
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 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.
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.
Analysis of future development opportunities for OIS (Office Information Systems) methods and tools.
(1992)
When an open quantum system is driven by an external time-dependent force, the coupling of the driving to the central system is usually included, whereas the impact of the driving field on the bath is neglected. We investigate the effect of a quantum bath of linearly driven harmonic oscillators on the relaxation dynamics of a quantum two-level system which is not directly driven. In particular, we calculate the frequency-dependent response of the system when the bath is subject to Dirac and Gaussian driving pulses. We show that a time-retarded effective force on the system is induced by the driven bath which depends on the full history of the perturbation and the spectral characteristics of the underlying bath. In particular, when a structured Ohmic bath with a pronounced Lorentzian peak is considered, the dynamical response of the system to a driven bath is qualitatively different than that of the undriven bath. Specifically, additional resonances appear which can be directly associated with a Jaynes-Cummings-like effective energy spectrum.
Recent experimental results showing atypical nonlinear absorption and marked deviations from well known universality in the low temperature acoustic and dielectric losses in amorphous solids prove the need for improving the understanding of the nature of two-level systems (TLSs) in these materials. Here we suggest the study of TLSs focused on their properties which are nonuniversal. Our theoretical analysis shows that the standard tunneling model and the recently suggested two-TLS model provide markedly different predictions for the experimental outcome of these studies. Our results may be directly tested in disordered lattices, e.g KBr:CN, where there is ample theoretical support for the validity of the two-TLS model, as well as in amorphous solids. Verification of our results in the latter will significantly enhance understanding of the nature of TLSs in amorphous solids, and the ability to manipulate them and reduce their destructive effect in various cutting edge applications including superconducting qubits.