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This paper investigates the macroeconomic dynamics of consumption and real interest rates when there are constraints on debt finance, used both for insurance against income shocks and transferability of resources over time. We amend a standard continuous-time deterministic model, with patient and impatient household sectors, introducing sector level income shocks. Shocks that push the impatient sector towards its leverage limit increase precautionary saving and result in a substantial but transient decline of the real interest rate relative to the deterministic benchmark. We discuss the resulting dynamics of consumption, leverage and interest rates, and implications for macroeconomic modelling and policy.

By considering the direction of charge carriers and the conservation of probablity current the transmission properties of graphene Zener tunnelling nano-devices were obtained. The scattering properties were then used with an adaptation of the Landauer formalism to calculate an analytical expression for current and conductance. The numerical results of the IV characteristics were then briefly discussed for the graphene step and Zener barrier. A comparison between the theoretical model and experimental results shows the similarities of graphene nanoribbons and infinite sheet graphene.

New quantum oscillations in the magnetization of graphene flakes induced by magnetic fields, which depend on the shape of the flake, are described. At small values of the field they are due to the Aharonov-Bohm effect and with increasing field they are transformed into dHvA oscillations. The specific form of the dHvA oscillations is analyzed in terms of their energy spectrum, which has a form of Hofstadter's butterfly. Numerical results using a lattice tight-binding model and a continuum Dirac equation are presented and compared. Possible experiments to investigate the quantum oscillations in Moire and graphene anti-dot superlattices are discussed.

With nanomagnets increasingly being used and proposed as functional units for in vivo applications, it is vital to understand how to optimize their structure, geometry, and size, and their responses to electromagnetic stimulation. Herein, we predicate how to do so for synthetic antiferromagnetic structures that are subjected to external magnetic control. Because the structures are on the scale of biological entities, interactions with cells and molecular constituents can be extreme and careful design must be undertaken to avoid detrimental effects. Thus, the magnetic responses of multilayers, as demonstrated in experiments by Koh et al. [e.g., Hu et al., Adv. Mater. 20, 1479 (2008) and Koh et al., J. Appl. Phys. 107, 09B522 (2010)], are understood using a fully dynamical investigation based on Landau–Lifshitz–Gilbert equations. We find that during the fabrication of the structures the axial positions of the nanomagnets become offset from each other, leading to the characteristic magnetic hysteresis shapes witnessed. We then find the magnetic nano-mechanical forces generated by such structures. The conical synthetic antiferromagnetic nanoparticles with two magnetic layers – Left: the magnetic flux density is shown on the surface of the structure in a magnetic flux density of B = 0.08 T. Middle and right: orientations of the magnetic moments of the two magnetic layers.

Charge transfer and spin conversion compounds are most spectacular examples of systems exhibiting photo-induced phase transitions. In that class of systems, thermal phase transition might also be light (or pressure) induced. Though the driving mechanism of a photo-induced phase transition appears to be electron-phonon coupling, an approach incorporating that coupling within a unified model has not yet been formulated. Two types of treatments, regarding electrons as localised and delocalised are generally considered. We briefly present existing approaches and discuss the main result. The problem of searching common features in thermodynamic properties of such a class of compounds is introduced and the methods in case of charge transfer systems are outlined.

The ground state of an electronic system of compounds revealing photo-induced phase transitions might be regarded as a multiple-well, on-site potential. Different types of asymmetric, multi-stable potentials correspond to compounds of different types: to spin conversion systems and to charge transfer systems. Thermodynamic properties of one-dimensional lattice systems with an asymmetric on-site double well and triple well potential are then considered in quantum and classical approaches. Studying a variety of regimes, one finds that the key feature is a level of asymmetry distinguished as a shift type and shape type in limiting cases. Nearly singular behaviour of heat capacity in shape type systems indicates an entropy driven phase transformation.

An analytical theory of the Urbach-Martienssen tail for the Wannier-Mott excitons in polar crystals and alloys is developed on the basis of the expansion of all quantities in the small parameter δ ≪ Ei(μ/M), where M and μ are the translation and the reduced masses of the exciton; Ei is the exciton Rydberg, and δ is the photon deficit. The exciton absorption coefficient and the length of the absorption tail are calculated. The latter characterizes the width of the exciton absorption band. The results obtained are compared with experiments on the exciton absorption in layered polar crystals. [Russian Text Ignored].