Related papers: Rigorous upper bound for the persistent current in…
We explore the behavior of persistent current and low-field magnetic response in mesoscopic one-channel rings and multi-channel cylinders within the tight-binding framework. We show that the characteristic properties of persistent current…
The persistent current is here studied in one-dimensional disordered rings that contain interacting electrons. We used the density matrix renormalization group algorithms in order to compute the stiffness, a measure that gives the magnitude…
Entanglement entropies of two-dimensional gapped ground states are expected to satisfy an area law, with a constant correction term known as the topological entanglement entropy (TEE). In many models, the TEE takes a universal value that…
In this paper, we investigate the maximum and minimum of the dynamic pressure in a regular wave train with underlying currents and infinite depth respectively. The result is obtained using maximum principles in combination with exploiting…
We analyze fluctuations of persistent current (PC) produced by a charged quantum particle moving in a ring and interacting with a dissipative environment formed by diffusive electron gas. We demonstrate that in the presence of interactions…
We generalize to some PDEs a theorem by Nekhoroshev on the persistence of invariant tori in Hamiltonian systems with $r$ integrals of motion and $n$ degrees of freedom, $r\leq n$. The result we get ensures the persistence of an…
We study the energy spectrum and the persistent current in an ideal one-dimensional mesoscopic ring coupled to a fermionic reservoir. We find that the tunnel coupling in general leads to the suppression of the persistent current. However,…
We introduce a geometry on the cone of positive closed currents of bidegree (p,p) and apply it to define the intersection of such currents. We also construct and study the Green currents and the equilibrium measure for horizontal-like…
The Bloch theorem is a general theorem restricting the persistent current associated with a conserved U(1) charge in a ground state or in a thermal equilibrium. It gives an upper bound of the magnitude of the current density, which is…
We consider chiral fluids within the standard framework of a chiral-invariant underlying field theory, anomalous in presence of electromagnetic fields. Apart from the Noether axial current of the underlying theory, in the limit of ideal…
The nonaxisymmetric Tayler instability of toroidal magnetic fields due to axial electric currents is studied for conducting incompressible fluids between two coaxial cylinders without endplates. The inner cylinder is considered as so thin…
Geometric phase shift associated with an electron propagating through a dimerized-disordered continuum is shown to be 0, or $\pm \pi$ (modulo 2$\pi$), according as the associated circuit traversed in the two-dimensional parameter space…
Although the critical Reynolds number for linear instability of the laminar flow in a straight pipe is infinite, we show that it is finite for a divergent pipe, and approaches infinity as the inverse of the divergence angle. The velocity…
The relative entropy of entanglement $E_R$ is defined as the distance of a multi-partite quantum state from the set of separable states as measured by the quantum relative entropy. We show that this optimisation is always achieved, i.e. any…
We study a parametric family of piecewise rotations of the torus, in the limit in which the rotation number approaches the rational value 1/4. There is a region of positive measure where the discontinuity set becomes dense in the limit; we…
In this paper, we establish the global well-posedness of the incompressible magnetohydrodynamics (MHD) system on $n-$dimensional $(n\geq 2)$ periodic boxes with either no magnetic diffusivity (non-resistive case) or no fluid viscosity…
We present a first-principles study of the energy and elastic properties of solid helium at pressures below the range in which is energetically stable. We find that the limit of mechanical stability in hcp 4He is $P_{s}$ = -33.82 bar, which…
This paper presents numerical linear stability analysis of a cylindrical Taylor-Couette flow of liquid metal carrying axial electric current in a generally helical external magnetic field. Axially symmetric disturbances are considered in…
New condition Re>Re_th_min=124 of linear (exponential) instability of the Hagen-Poisseuille (HP) with respect to extremely small by magnitude axially-symmetric disturbances of the tangential component of the velocity field is obtained. For…
The Tayler instability of an azimuthal magnetic field with one or two ``rings'' along the radius is studied for an axially unbounded Taylor-Couette flow. The rotation law of the conducting fluid is a quasi-Keplerian one. Without rotation…