Related papers: Geometrically induced spectrum in curved leaky wir…
The nonlinear conductance of a one-dimensional quantum wire adiabatically coupled to Fermi Liquid electron reservoirs is determined in presence of an impurity. We show that electron-electron interaction in connection with the finite length…
We consider the Dirichlet Laplacian in a domain two three-dimensional parallel layers having common boundary and coupled by a window. The window produces the bound states below the essential spectrum; we obtain two-sided estimates for them.…
We discuss Laplacian spectrum on a finite metric graph with vertex couplings violating the time-reversal invariance. For the class of star graphs we determine, under the condition of a fixed total edge length, the configurations for which…
In this paper we investigate the existence of $L^{2}(\pi)$-spectral gaps for $\pi$-irreducible, positive recurrent Markov chains on general state space. We obtain necessary and sufficient conditions for the existence of…
In this paper we present and discuss our results for the conductance and conductance fluctuations of narrow quantum wires with two types of disorder: boundary roughness (hard wall confining potential) and islands of strongly scattering…
We study generalised quantum waveguides in the presence of moderate and strong external magnetic fields. Applying recent results on the adiabatic limit of the connection Laplacian we show how to construct and compute effective Hamiltonians…
We use the time real analyticity of Ricci flow proved by Kotschwar to extend a result in ~\cite{B}, namely, we prove that the Laplace spectra of negatively curved compact surfaces having same genus $\gamma \geq 2$, same area and same…
We are proving $L^2(\R)\times L^2(\R)\,\rightarrow\,L^1(\R)$ bounds for the bilinear Hilbert transform $H_{\Gamma}$ along curves $\Gamma=(t,-\gamma(t))$ with $\gamma$ being a smooth "non-flat" curve near zero and infinity.
A classical particle under spatial constraints is strictly confined to live on a specific space manifold or path, but this assumption is incompatible with the zero-point fluctuations of a quantum particle. One way to describe quantum…
We demonstrate that an undoped two-dimensional carbon plane (graphene) whose bulk is in the integer quantum Hall regime supports a non-chiral Luttinger liquid at an armchair edge. This behavior arises due to the unusual dispersion of the…
Recently, we introduced a non-perturbative quantization of impulsive gravitational null initial data. In this note, we investigate an immediate physical implication of the model. One of the quantum numbers is the total luminosity carried to…
We investigate the discrete spectrum of the Hamiltonian describing a quantum particle living in the two-dimensional straight strip. We impose the combined Dirichlet and Neumann boundary conditions on different parts of the boundary. Several…
We discuss the effect of certain types of static disorder, like that induced by curvature or topological defects, on the quantum correction to the conductivity in graphene. We find that when the intervalley scattering time is long or…
Different approaches to quantum gravity generally predict that the dimension of spacetime at the fundamental level is not 4. The principal tool to measure how the dimension changes between the IR and UV scales of the theory is the spectral…
The scalar perturbation induced gravitational waves are a probe of the primordial density perturbation spectrum on small scales. In this paper, we show that they can also probe the thermal history of the universe. We assume the universe…
Charges associated with gauge symmetries are defined on boundaries of spacetimes. But these constructions typically involve divergent quantities when considering asymptotic boundaries. Different prescriptions exist to address this problem,…
In this paper we consider a family of Riemannian manifolds, not necessarily complete, with curvature conditions in a neighborhood of a ray. Under these conditions we obtain that the essential spectrum of the Laplacian contains an interval.…
We will study the spectral problem related to the Laplace operator in a singularly perturbed periodic waveguide. The waveguide is a quasi-cylinder with contains periodic arrangement of inclusions. On the boundary of the waveguide we…
Quantum waveguide with the shape of planar infinite straight strip and combined Dirichlet and Neumann boundary conditions on the opposite half-lines of the boundary is considered. The absence of the point as well as of the singular…
We consider the Dirichlet Laplacian in a two-dimensional strip composed of segments translated along a straight line with respect to a rotation angle with velocity diverging at infinity. We show that this model exhibits a "raise of…