Related papers: Quasiperiodic Elliptic Operators: Projection Metho…
Quasi-periodic oscillation (QPOs) analysis is important for understanding the dynamical behavior of many astrophysical objects during transient events such as gamma-ray bursts, solar flares, magnetar flares, and fast radio bursts. In this…
The relativistic precession model for quasi periodic oscillations, QPOs, in low mass X-ray binaries is reviewed. The behaviour of three simultaneous types of QPOs is well matched in terms of the fundamental frequencies for geodesic motion…
We consider one-dimensional inhomogeneous parabolic equations with higher-order elliptic differential operators subject to periodic boundary conditions. In our main result we show that the property of continuous maximal regularity is…
Quasi-periodic trajectories with two or more incommensurate frequencies are ubiquitous in nonlinear dynamics, yet the classical Fourier-based time-spectral method is tied to strictly periodic responses. We introduce a torus time-spectral…
We zoom in on the internal structure of the low-frequency quasi-periodic oscillation (LF QPO) often observed in black hole binary systems to investigate the physical nature of the lack of coherence in this feature. We show the limitations…
High error rates and limited fidelity of quantum gates in near-term quantum devices are the central obstacles to successful execution of the Quantum Approximate Optimization Algorithm (QAOA). In this paper we introduce an…
We present numerical upscaling techniques for a class of linear second-order self-adjoint elliptic partial differential operators (or their high-resolution finite element discretization). As prototypes for the application of our theory we…
We study finitely cyclic self-adjoint operators in a Hilbert space, i.e. self-adjoint operators that posses such a finite subset in the domain that the orbits of all its elements with respect to the operator are linearly dense in the space.…
For certain situations we give a geometrical background for quasiclassical KP calculations based on an explicit connection to quantum mechanics and the collapse of coherent states to coadjoint orbits for classical operators.
Quantum oscillation (QOs) measurements constitute one of the most powerful methods for determining the Fermi surface (FS) of metals, exploiting the famous Onsager relation between the FS area and the QO frequency. The recent observation of…
We study the relationship between the Quantum Approximate Optimization Algorithm (QAOA) and the underlying symmetries of the objective function to be optimized. Our approach formalizes the connection between quantum symmetry properties of…
The notion of quasi-unit has been introduced by Yosida in unital Riesz spaces. Later on, a fruitful potential theoretic generalization was obtained by Arsove and Leutwiler. Due to the work of Eriksson and Leutwiler, this notion also turned…
Quantum Optical Coherence Tomography (Q-OCT) is the non-classical counterpart of Optical Coherence Tomography (OCT) - a high-resolution 3D imaging technique based on white-light interferometry. Because Q-OCT uses a source of…
Approximation properties of periodic quasi-projection operators with matrix dilations are studied. Such operators are generated by a sequence of functions $\varphi_j$ and a sequence of distributions/functions $\widetilde{\varphi}_j$. Error…
Quasi-parametric amplification (QPA) is a nonlinear interaction in which the idler wave is depleted through some loss mechanism. QPA plays an important role in signal amplification in ultrafast photonics and quantum light generation. The…
QPOs are a common feature in the X-ray power density spectrum of black hole binaries and a potentially powerful tool to probe the spacetime geometry around these objects. Here we discuss their constraining power to test the Kerr black hole…
We study non-elliptic quadratic differential operators. Quadratic differential operators are non-selfadjoint operators defined in the Weyl quantization by complex-valued quadratic symbols. When the real part of their Weyl symbols is a…
We apply the Operator Product Expansion (OPE) algorithm to the renormalization of scalar-QED theory, with a specific focus on the fixed-charge operator $\phi^Q$. Within the OPE framework, the anomalous dimension of the $\phi^Q$ operator is…
In the lecture notes we start off with an introduction to the $q$-hypergeometric series, or basic hypergeometric series, and we derive some elementary summation and transformation results. Then the $q$-hypergeometric difference equation is…
The low frequency quasi periodic oscillations (QPOs) are commonly observed during hard states of black hole binaries. Several studies have established various observational/empirical correlations between spectral parameters and QPO…