On the ubiquity of Beutler-Fano profiles: from scattering to dissipative processes

Fano models - consisting of a Hamiltonian with discrete-continuous spectrum - are one of the basic toy models in spectroscopy. They have been succesfull in explaining the lineshape of experiments in atomic physics and condensed matter. These models however have largely been out of the scope of dissipative dynamics, with ony a handful of works considering the effect of a thermal bath. Yet in nanostructures and condensed matter systems, dissipation strongly modulates the dynamics. In this article, we present an overview of the theoretical works dealing with Fano interferences coupled to a thermal bath and compare them to the scattering formalism. We provide the solution to any discrete-continuous Hamiltonian structure within the wideband approximation coupled to a Markovian bath. In doing so, we update the toy models that have been available for unitary evolution since the 1960s. We find that the Fano lineshape is preserved as long as we allow a rescaling of the parameters, and an additional Lorentzian contribution that reflects the destruction of the interference by dephasings. We discuss the pertinence of each approach - dissipative and unitary - to different experimental setups: scattering, transport and spectroscopy of dissipative systems. We finish by discussing the current limitations of the theories due to the wideband approximation and the memory effects of the bath.Comment: Expanded bibliography, minor typos correcte

School Food Environments and Policies in U.S. Public Schools

Examines food environments in elementary, middle, and high schools based on seventeen factors, including foods and beverages offered, the availability of vending machines, and how they vary by grade level, location, and other school characteristics

Analytical Results for a Single-Unit System Subject To Markovian Wear and Shocks

This thesis develops and analyzers a mathematical model for the reliability measures of a single-unit system subject to continuous wear due to its operating environment and randomly occurring shocks that inflict a random amount of damage to the unit. Assuming a Markovian operating environment and shock arrival mechanism, Laplace-Stieltjes transform expressions are obtained for the failure time distribution and all of its moments. Moreover, an analytical expression is derived for the long-run availability of the single-unit system when it is subject to an inspect-and-replace maintenance policy. The analytical results are illustrated, and their results compared with those of Monte Carlo-simulated failure data. The numerical results indicate that the reliability measures may be accurately computed via numerical inversion of the transform expressions in a straightforward manner when the input parameters are known a priori. In stark contrast to the simulation model which requires several hours to obtain the reliability measures, the analytical procedure computes the same measures in only a few seconds

Classification of Dark States in Multi-level Dissipative Systems

Dark states are eigenstates or steady-states of a system that are decoupled from the radiation. Their use, along with associated techniques such as Stimulated Raman Adiabatic Passage, has extended from atomic physics where it is an essential cooling mechanism, to more recent versions in condensed phase where it can increase the coherence times of qubits. These states are often discussed in the context of unitary evolution and found with elegant methods exploiting symmetries, or via the Bruce-Shore transformation. However, the link with dissipative systems is not always transparent, and distinctions between classes of CPT are not always clear. We present a detailed overview of the arguments to find stationary dark states in dissipative systems, and examine their dependence on the Hamiltonian parameters, their multiplicity and purity. We find a class of dark states that depends not only on the detunings of the lasers but also on their relative intensities. We illustrate the criteria with the more complex physical system of the hyperfine transitions of $^{87}$Rb and show how a knowledge of the dark state manifold can inform the preparation of pure states.Comment: additional example

Continuum model for chiral induced spin selectivity in helical molecules

A minimal model is exactly solved for electron spin transport on a helix. Electron transport is assumed to be supported by well oriented $p_z$ type orbitals on base molecules forming a staircase of definite chirality. In a tight binding interpretation, the SOC opens up an effective $\pi_z-\pi_z$ coupling via interbase $p_{x,y}-p_z$ hopping, introducing spin coupled transport. The resulting continuum model spectrum shows two Kramers doublet transport channels with a gap proportional to the SOC. Each doubly degenerate channel satisfies time reversal symmetry, nevertheless, a bias chooses a transport direction and thus selects for spin orientation. The model predicts which spin orientation is selected depending on chirality and bias, changes in spin preference as a function of input Fermi level and scattering suppression protected by the SO gap. We compute the spin current with a definite helicity and find it to be proportional to the torsion of the chiral structure and the non-adiabatic Aharonov- Anandan phase. To describe room temperature transport we assume that the total transmission is the result of a product of coherent steps limited by the coherence length

Training Law Students to Be International Transactional Lawyers - Using an Extended Simulation to Educate Law Students About Business Transactions

The article describes an innovative approach to educating law students about the legal issues and the role of lawyers in negotiating international business transactions. It is based on our experiences in developing and teaching a course that is built around a semester-long simulation exercise and taught in counterpart classes at two law schools. The students in these classes represent the opposing parties and negotiate a cross-border business transaction involving a joint venture agreement, a licensing agreement and a long-term supply contract. The students, who attend either the American University Washington College of Law or the Centre for Energy Mineral and Petroleum Law and Policy at the Dundee University in Scotland, utilize written communications, video-conferencing and teleconferencing in their negotiations. In the paper we discuss the value the course adds to the education of our students, the challenges and pleasures of teaching the course, the response of students to the innovative approach to teaching, and ways in which the course could be adapted and enriched

Fano-Liouville Spectral Signatures in Open Quantum Systems

The scattering amplitude from a set of discrete states coupled to a continuum became known as the Fano profile, characteristic for its asymmetric lineshape and originally investigated in the context of photoionization. The generality of the model, and the proliferation of engineered nanostructures with confined states gives immense success to the Fano lineshape, which is invoked whenever an asymmetric lineshape is encountered. However, many of these systems do not conform to the initial model worked out by Fano in that i) they are subject to dissipative processes and ii) the observables are not entirely analogous to the ones measured in the original photoionization experiments. In this letter, we work out the full optical response of a Fano model with dissipation. We find that the exact result for absorption, Raman, Rayleigh and fluorescence emission is a modified Fano profile where the typical lineshape has an additional Lorentzian contribution. Expressions to extract model parameters from a set of relevant observables are given.Comment: corrected typo

Training Law Students to be International Transactional Lawyers-Using An Extended Simulation to Educate Law Students About Business Transactions

The article describes an innovative approach to educating law students about the legal issues and the role of lawyers in negotiating international business transactions. It is based on our experiences in developing and teaching a course that is built around a semester-long simulation exercise and taught in counterpart classes at two law schools. The students in these classes represent the opposing parties and negotiate a cross-border business transaction involving a joint venture agreement, a licensing agreement and a long-term supply contract. The students, who attend either the American University Washington College of Law or the Centre for Energy Mineral and Petroleum Law and Policy at the Dundee University in Scotland, utilize written communications, video-conferencing and teleconferencing in their negotiations. In the paper we discuss the value the course adds to the education of our students, the challenges and pleasures of teaching the course, the response of students to the innovative approach to teaching, and ways in which the course could be adapted and enriched