Electron polarizability of crystalline solids in quantizing magnetic fields and topological gap numbers

A theory of the static electron polarizability of crystals whose energy spectrum is modified by quantizing magnetic fields is presented. It is argued that The polarizability is strongly affected by non-dissipative Hall currents induced by the presence of crossed electric and magnetic fields: these can even change its sign. Results are illustrated in detail for a two dimensional square lattice. The polarizability and the Hall conductivity are respectively linked to the two topological quantum numbers entering the so--called Diophantine equation. These numbers could in principle be detected in actual experiments

Entropy estimates for a class of schemes for the euler equations

In this paper, we derive entropy estimates for a class of schemes for the Euler equations which present the following features: they are based on the internal energy equation (eventually with a positive corrective term at the righ-hand-side so as to ensure consistency) and the possible upwinding is performed with respect to the material velocity only. The implicit-in-time first-order upwind scheme satisfies a local entropy inequality. A generalization of the convection term is then introduced, which allows to limit the scheme diffusion while ensuring a weaker property: the entropy inequality is satisfied up to a remainder term which is shown to tend to zero with the space and time steps, if the discrete solution is controlled in L $\infty$ and BV norms. The explicit upwind variant also satisfies such a weaker property, at the price of an estimate for the velocity which could be derived from the introduction of a new stabilization term in the momentum balance. Still for the explicit scheme, with the above-mentioned generalization of the convection operator, the same result only holds if the ratio of the time to the space step tends to zero

Extension of the osp(m|n)~ so(m-n) Correspondence to the Infinite-Dimensional Chiral Spinors and Self Dual Tensors

The spinor representations of the orthosymplectic Lie superalgebras osp(m|n) are considered and constructed. These are infinite-dimensional irreducible representations, of which the superdimension coincides with the dimension of the spinor representation of so(m-n). Next, we consider the self dual tensor representations of osp(m|n) and their generalizations: these are also infinite-dimensional and correspond to the highest irreducible component of the $p^{th}$ power of the spinor representation. We determine the character of these representations, and deduce a superdimension formula. From this, it follows that also for these representations the osp(m|n)~ so(m-n) correspondence holds

Ro-vibrational relaxation of HCN in collisions with He: Rigid bender treatment of the bending-rotation interaction

We present a new theoretical method to treat atom-rigid bender inelastic collisions at the Close Coupling level (RBCC) in the space fixed frame. The coupling between rotation and bending is treated exactly within the rigid bender approximation and we obtain the cross section for the rotational transition between levels belonging to different bending levels. The results of this approach are compared with those obtained when using the rigid bender averaged approximation (RBAA) introduced in our previous work dedicated to this system. We discuss the validity of this approximation and of the previous studies based on rigid linear HCN

Symmetry breaking in (gravitating) scalar field models describing interacting boson stars and Q-balls

We investigate the properties of interacting Q-balls and boson stars that sit on top of each other in great detail. The model that describes these solutions is essentially a (gravitating) two-scalar field model where both scalar fields are complex. We construct interacting Q-balls or boson stars with arbitrarily small charges but finite mass. We observe that in the interacting case - where the interaction can be either due to the potential or due to gravity - two types of solutions exist for equal frequencies: one for which the two scalar fields are equal, but also one for which the two scalar fields differ. This constitutes a symmetry breaking in the model. While for Q-balls asymmetric solutions have always corresponding symmetric solutions and are thus likely unstable to decay to symmetric solutions with lower energy, there exists a parameter regime for interacting boson stars, where only asymmetric solutions exist. We present the domain of existence for two interacting non-rotating solutions as well as for solutions describing the interaction between rotating and non-rotating Q-balls and boson stars, respectively.Comment: 33 pages including 21 figures; v2: version considerably extended: 6 new figures added, equations of motion added, discussion on varying gravitational coupling added, references adde

U-duality in three and four dimensions

Using generalised geometry we study the action of U-duality acting in three and four dimensions on the bosonic fields of eleven dimensional supergravity. We compare the U-duality symmetry with the T-duality symmetry of double field theory and see how the $SL(2)\otimes SL(3)$ and SL(5) U-duality groups reduce to the SO(2,2) and SO(3,3) T-duality symmetry groups of the type IIA theory. As examples we dualise M2-branes, both black and extreme. We find that uncharged black M2-branes become charged under U-duality, generalising the Harrison transformation, while extreme M2-branes will become new extreme M2-branes. The resulting tension and charges are quantised appropriately if we use the discrete U-duality group $E_d(Z)$.Comment: v1: 35 pages; v2: minor corrections in section 4.1.2, many references added; v3: further discussion added on the conformal factor of the generalised metric in section 2 and on the Wick-rotation used to construct examples in section

Quantum Non-Equilibrium Steady States Induced by Repeated Interactions

We study the steady state of a finite XX chain coupled at its boundaries to quantum reservoirs made of free spins that interact one after the other with the chain. The two-point correlations are calculated exactly and it is shown that the steady state is completely characterized by the magnetization profile and the associated current. Except at the boundary sites, the magnetization is given by the average of the reservoirs' magnetizations. The steady state current, proportional to the difference in the reservoirs' magnetizations, shows a non-monotonous behavior with respect to the system-reservoir coupling strength, with an optimal current state for a finite value of the coupling. Moreover, we show that the steady state can be described by a generalized Gibbs state.Comment: to appear in Phys. Rev. Let

Foreword

This work reports on the performances of ohmic contacts fabricated on highly p-type doped 4H-SiC epitaxial layer selectively grown by vapor-liquid-solid transport. Due to the very high doping level obtained, the contacts have an ohmic behavior even without any annealing process. Upon variation of annealing temperatures, it was shown that both 500 and 800 °C annealing temperature lead to a minimum value of the Specific Contact Resistance (SCR) down to 1.3×10−6 Ω⋅cm2. However, a large variation of the minimum SCR values has been observed (up to 4×10−4 Ω⋅cm2). Possible sources of this fluctuation have been also discussed in this paper