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Broadband multidimensional variational measurement allows to overcome Standard Quantum Limit (SQL) of a classical mechanical force detection, resulting from quantum back action, which perturbs evolution of a mechanical oscillator. In this…
The interest of compressive sampling in ultrasound imaging has been recently extensively evaluated by several research teams. Following the different application setups, it has been shown that the RF data may be reconstructed from a small…
Conventional renormalization methods in statistical physics and lattice quantum field theory assume a flat metric background. We outline here a generalization of such methods to models on discretized spaces without metric background.…
Starting from noncommutative quantum mechanics algebra, we investigate the variances of the deformed two-mode quadrature operators under the evolution of three types of two-mode squeezed states in noncommutative space. A novel conclusion…
Compositional minimisation can be an effective technique to reduce the state space explosion problem. This technique considers a parallel composition of several processes. In its simplest form, each sequential process is replaced by an…
The methods of mode decomposition and Fourier analysis of classical and quantum fields on curved spacetimes previously available mainly for the scalar field on Friedman- Robertson-Walker (FRW) spacetimes are extended to arbitrary vector…
We consider a generalized Jaynes-Cummings model of a two-level atom interacting with a multimode nondegenerate coherent field. The sum of the mode frequencies is equal to the two-level transition frequency, creating the resonance condition.…
We develop a method for optimization in shape spaces, i.e., sets of surfaces modulo re-parametrization. Unlike previously proposed gradient flows, we achieve superlinear convergence rates through a subtle approximation of the shape Hessian,…
Autoencoders are a prominent model in many empirical branches of machine learning and lossy data compression. However, basic theoretical questions remain unanswered even in a shallow two-layer setting. In particular, to what degree does a…
By optimizing the rate-distortion-realism trade-off, generative compression approaches produce detailed, realistic images, even at low bit rates, instead of the blurry reconstructions produced by rate-distortion optimized models. However,…
The configuration space of $n$ marked points on the complex plane is considered. We investigate a decomposition of this space by so-called Gauss-skizze i.e. a class of graphs being forests, introduced by Gauss. It is proved that this…
The paper aims at investigating two types of decay structure for linear symmetric hyperbolic systems with non-symmetric relaxation. Precisely, the system is of the type $(p,q)$ if the real part of all eigenvalues admits an upper bound…
Quantum mechanical few-body systems in reduced dimensionalities can exhibit many interesting properties such as scale-invariance and universality. Analytical descriptions are often available for integer dimensionality, however, numerical…
In this paper, we present methods for image compression on the basis of eigenvalue decomposition of normal matrices. The proposed methods are convenient and self-explanatory, requiring fewer and easier computations as compared to some…
Grain boundaries (GBs) merge and grains disappear during microstructure evolution. However, the Peach-Koehler model predicts that particular stress states may reverse such a process by exerting differential Peach-Koehler forces on different…
The squeezed photons, as a quantum-correlated light with reduced noise, have emerged as a great resource for sensing the structures of matter. Here we study the transient absorption (TA) scheme using the squeezed photons whose spectral…
Ultrasound imaging is widely used in noninvasive medical diagnostics due to its efficiency, portability, and avoidance of ionizing radiation. However, its utility is limited by the quality of the signal. Signal-dependent speckle noise,…
This paper develops a geometric framework for the stability analysis of differential inclusions governed by maximally monotone operators. A key structural decomposition expresses the operator as the sum of a convexified limit mapping and a…
Spin squeezing of collective atomic spins can be achieved conditionally via probing with light and subsequent homodyne detection, as is done in a Quantum Nondemolition measurement. Recently it has been shown that squeezing can also be…
Harnessing entanglement and quantum coherence plays a central role in advancing quantum technologies. In quantum optical light-atom platforms, these two fundamental resources are often associated with a Jaynes-Cummings model description…