Related papers: On the Discrete Spectrum of Generalized Quantum Tu…
We study the modular pair of $TQ$ equations for the quantum $\sin$-Gordon model in the framework of non-compact $\mathcal{U}_{q,q^*}(\widehat{sl}_2)$. We assume some conjectures for the thermodynamic limit allowing one to obtain its ground…
We develop a general framework to study quantum trajectories resulting from repeated random measurements subject to stationary noise, and generalize results of K\"ummerer and Maassen to this setting. The resulting trajectory of quantum…
We discuss discuss spectral and scattering properties of a particle confined to a straight Dirichlet tube in $\mathbb{R}^3$ with a family of point interactions.
We extend calculus from smooth manifolds to topological manifolds making use of a theory of generalized functions developed for this aim. Actually such extension fits into a boarder context: the universal construction of a site containing…
We study the formulation of the uncertainty principle in quantum mechanics in terms of entropic inequalities, extending results recently derived by Bialynicki-Birula [1] and Zozor et al. [2]. Those inequalities can be considered as…
We consider a quantum particle constrained to a curved layer of a constant width built over an infinite smooth surface. We suppose that the latter is a locally deformed plane and that the layer has the hard-wall boundary. Under this…
A well-known result asserts that any isometric immersion with flat normal bundle of a Riemannian manifold with constant sectional curvature into a space form is (at least locally) holonomic. In this note, we show that this conclusion…
This paper studies the foundations of the geometric fixed point functor in multiplicative equivariant stable homotopy theory. We introduce a new class of equivariant orthogonal spectra called generalized orbit desuspension spectra and…
We study a generalized quantum hard-core dimer model on the square and honeycomb lattices, allowing for first and second neighbor dimers. At generalized RK points, the exact ground states can be constructed, and ground-state correlation…
The energy spectrum and corresponding wave functions of a flat quantum dot with elliptic symmetry are obtained exactly. A detailed study is made of the effect of ellipticity on the energy levels and the corresponding wave functions. The…
We discuss the description of eigenspace of a quantum walk model $U$ with an associating linear operator $T$ in abstract settings of quantum walk including the Szegedy walk on graphs. In particular, we provide the spectral mapping theorem…
In this paper, we study the Fu\v{c}\'{\i}k spectrum of a square matrix $A$ and provide necessary and sufficient conditions for the existence of Fu\v{c}\'{\i}k curves emanating from the point $(\lambda,\lambda)$ with $\lambda$ being a real…
We develop a theoretical formalism to model the linear spectrum of a quantum dot embedded in a high quality cavity, in presence of an arbitrary mechanism modifying the homogeneous spectrum of the quantum dot. Within the simple assumption of…
Quantum spin liquids may be considered "quantum disordered" ground states of spin systems, in which zero point fluctuations are so strong that they prevent conventional magnetic long range order. More interestingly, quantum spin liquids are…
In this article, we explore Higgs bundles on a projective manifold $X$, focusing on their spectral bases, a concept introduced by T.Chen and B.Ng\^{o}. The spectral base is a specific closed subscheme within the space of symmetric…
Mathematical settings in which heterogeneous structures affect electron transport through a tube-shaped quantum waveguide are studied, highlighting the interaction between heterogeneities and geometric parameters like curvature and torsion.…
An operator generalisation of the notion of geometric phase has been recently proposed purely based on physical grounds. Here we provide a mathematical foundation for its existence, while uncovering new geometrical structures in quantum…
We investigate a periodic quantum graph in form of a square lattice with a general self-adjoint coupling at the vertices. We analyze the spectrum, in particular, its high-energy behaviour. Depending on the coupling type, bands and gaps have…
Generalizing Cusick's theorem on the closedness of the classical Lagrange spectrum for the approximation of real numbers by rational ones, we prove that various approximation spectra are closed, using penetration properties of the geodesic…
Entanglement properties are routinely used to characterize phases of quantum matter in theoretical computations. For example the spectrum of the reduced density matrix, or so-called "entanglement spectrum", has become a widely used…