Electron–phonon coupling underlies many physical phenomena, but its microscopic origins are nuanced. This Review derives the spin–phonon interactions in molecules from first principles, and describes an implementation for molecular spin dynamics calculations.
In this paper we consider the stabilization problem of a clamped beam with torque and force actuation on a mass in the other side of the beam. We show how to derive the model starting from the Principle of Least Action and we rewrite it as the interconnection between a 1 dimensional distributed parameter port-Hamiltonian system and a finite dimensional port-Hamiltonian system. Therefore, we propose a control law that allow to exponentially stabilise the origin of the closedloop system. In this preliminary paper we only sketch the theoretical proofs, but we give the procedure to compute the exponential bound of the system's state. Finally, we provide some numerical simulations testing the closed-loop behaviour with different choices of the control parameters.
We perform magnetization sweeps on the high-performing
single-molecule
magnet [Dy(Cpttt)2][B(C6F5)4] (Cpttt = C5H2
t
Bu3-1,2,4;
t
Bu = C(CH3)3) to determine the quantum tunneling gap of the ground-state avoided
crossing at zero-field, finding a value on the order of 10–7 cm–1. In addition to the pure crystalline material,
we also measure the tunnel splitting of [Dy(Cpttt)2][B(C6F5)4] dissolved in
dichloromethane (DCM) and 1,2-difluorobenzene (DFB). We find that
concentrations of 200 or 100 mM [Dy(Cpttt)2][B(C6F5)4] in these solvents increases the
size of the tunneling gap compared to the pure sample, despite a similarity
in the strength of the dipolar fields, indicating that either a structural
or vibrational change due to the environment increases quantum tunneling
rates.
Molecular materials are poised to play a significant role in the development future opto-electronic and quantum technologies. A crucial aspect of these areas is the role of spin-phonon coupling and how it facilitates energy-transfer processes such as intersystem crossing, quantum decoherence, and magnetic relaxation. Thus, it is of significant interest to be able to accurately calculate molecular spin-phonon coupling and spin dynamics in the condensed phase. Here we examine the various approximations inherent in spin-phonon coupling and spin dynamics calculations on molecular solids by performing a case study on a single-molecule magnet. Three key results are: i) finite crystalline slab calculations should be avoided; ii) the phonon spectrum in reciprocal space should be sampled as densely as possible; and iii) phonon linewidths, as calculated by periodic density-functional theory, are likely overestimated at low temperature, but are not essential to obtain accurate magnetic relaxation rates provided point ii is adhered to. Calculations using this approach are facilitated by the open-source packages we have developed, which enable cost-effective and accurate spin-phonon coupling calculations on molecular solids with quantitative accuracy.
This paper proposes a modular and control oriented model of a double flexiblelink manipulator stems from the modelling of a spatial flexible robot. The model consists of the power preserving interconnection between two infinite dimensional systems describing the beam's motion and deformation with a finite dimensional nonlinear system describing the dynamics of the actuated rotating joints. To derive the model, Timoshenko's assumptions are made for the flexible beams. Using Hamilton's principle, the dynamic equations of the system are derived and then written in the Port-Hamiltonian (PH) framework through a proper choice of the state variables. These so called energy variables allow to write the total energy as a quadratic form with respect to a state dependent energy matrix. The resulting model is shown to be a passive system, a convenient property for control design purposes.
In this paper we consider the stabilization problem of a beam clamped on a moving inertia actuated by an external torque and force. The beam is modelled as a distributed parameter port-Hamiltonian system (PDEs), while the inertia as a finite dimensional port-Hamiltonian system (ODEs). The control inputs correspond to a torque applied by a rotating motor and a force applied by a linear motor. In this paper we propose the use of a strong dissipation term in the control law, consisting of the time derivative of the restoring force at the clamping point. After a change of variables, the closed loop system shows dissipation at the boundaries of the PDEs. In this preliminary work we show that the closed loop operator is the generator of a contraction C 0 -semigroup in a special weighted space, with norm equivalent to the standard one. Further, we prove the asymptotic stability of the closed loop system and we show the effectiveness of the proposed control law in comparison with a PD controller with the help of numerical simulations.
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