Related papers: Exact integrability conditions for cotangent vecto…
Is it possible to trap a quantum particle in an open geometry? In this work we deal with the boundary value problem of the stationary Schroedinger (or Helmholtz) equation within a waveguide with straight segments and a rectangular bending.…
We propose an integrable Kondo problem in a one-dimensional (1D) $t-J$ model. With the open boundary condition of the wave functions at the impurity sites, the model can be exactly solved via Bethe ansatz for a class of $J_{R,L}$ (Kondo…
We prove a completely new integral criterion for the existence and completeness of the wave operators $W_{\pm}(-\Delta_h,-\Delta_g, I_{g,h})$ corresponding to the (unique self-adjoint realizations of) the Laplace-Beltrami operators…
Fluid dynamics is one of the cornerstones of modern physics and has recently found applications in the transport of electrons in solids. In most solids electron transport is dominated by extrinsic factors, such as sample geometry and…
The applicability of relativistic magnetohydrodynamics (RMHD) and its generalization to two-fluid models (including the Hall and inertial effects) is systematically investigated by using the method of dominant balance in the two-fluid…
We study the classical and quantum models of a Friedmann-Robertson-Walker (FRW) cosmology, coupled to a perfect fluid, in the context of the $f(R)$ gravity. Using the Schutz' representation for the perfect fluid, we show that, under a…
We show that it is possible to describe the ground state of the Luttinger model in terms of a Jastrow-Slater wave function. Moreover, our findings reveal that one-particle excitations and their corresponding dynamics can be faithfully…
We study the existence of solutions for the following fractional Hamiltonian systems $$ \left\{ \begin{array}{ll} - _tD^{\alpha}_{\infty}(_{-\infty}D^{\alpha}_{t}u(t))-\lambda L(t)u(t)+\nabla W(t,u(t))=0,\\[0.1cm] u\in…
he contact angle of a liquid droplet on a surface under partial wetting conditions differs for a nanoscopically rough or periodically corrugated surface from its value for a perfectly flat surface. Wenzel's relation attributes this…
In this paper we study the steepest descent $L^2$-gradient flow of the functional $\SW_{\lambda_1,\lambda_2}$, which is the the sum of the Willmore energy, $\lambda_1$-weighted surface area, and $\lambda_2$-weighted enclosed volume, for…
The wave operators $W_\pm(H_1,H_0)$ of two selfadjoint operators $H_0$ and $H_1$ are analyzed at asymptotic spectral values. Sufficient conditions for $\|(W_\pm(H_1,H_0)-P_{1}^\mathrm{ac}P_{0}^\mathrm{ac})f(H_0)\| <\infty$ are given, where…
Hydrodynamic transport coefficients may be evaluated from first principles in a weakly coupled scalar field theory at arbitrary temperature. In a theory with cubic and quartic interactions, the infinite class of diagrams which contribute to…
We establish necessary and sufficient conditions for the boundedness of the relativistic Schr\"odinger operator $\mathcal{H} = \sqrt{-\Delta} + Q$ from the Sobolev space $W^{1/2}_2 (\R^n)$ to its dual $W^{-1/2}_2 (\R^n)$, for an arbitrary…
The inflow problem of full compressible Navier-Stokes equations is considered on the half line $(0,+\infty)$. Firstly, we give the existence (or non-existence) of the boundary layer solution to the inflow problem when the right end state…
In this paper we consider the steady water wave problem for waves that possess a merely $L_r-$integrable vorticity, with $r\in(1,\infty)$ being arbitrary. We first establish the equivalence of the three formulations--the velocity…
We explore a combined effect of hexagonal warping and of finite effective mass on both the tunneling density of electronic states (TDOS) and structure of Landau levels (LLs) of 3D topological insulators. We find the increasing warping to…
We show the existence and orthogonality of wave operators naturally associated to a compatible Laplacian on a complete manifold with a corner of codimension 2. In fact, we prove asymptotic completeness i.e. that the image of these wave…
This work interprets the quantum terms in a Lagrangian, and consequently of the wave equation and momentum tensor, in terms of a modified spacetime metric. Part I interprets the quantum terms in the Lagrangian of a Klein Gordon field as…
If we study the quantum effects in plasmas in terms of traditional hydrodynamics via the continuity and Euler equations we find the quantum Bohm potential and the force of spin-spin interaction. However, if we extend the set hydrodynamic…
Coherent structures, such as solitary waves, appear in many physical problems, including fluid mechanics, optics, quantum physics, and plasma physics. A less studied setting is found in geophysics, where highly viscous fluids couple to…