Related papers: Quantization of Measures and Gradient Flows: a Per…
Studies of quantum metrology have shown that the use of many-body entangled states can lead to an enhancement in sensitivity when compared to product states. In this paper, we quantify the metrological advantage of entanglement in a setting…
This paper studies the benefits of pressure-robust discretizations in the scope of optimal control of incompressible flows. Gradient forces that may appear in the data can have a negative impact on the accuracy of state and control and can…
We introduce action-driven flows for causal variational principles, being a class of non-convex variational problems emanating from applications in fundamental physics. In the compact setting, H\"older continuous curves of measures are…
Many tasks in machine learning and signal processing can be solved by minimizing a convex function of a measure. This includes sparse spikes deconvolution or training a neural network with a single hidden layer. For these problems, we study…
We study the dissipation measure arising in the inviscid limit of two-dimensional incompressible fluids. It is proved that the dissipation is Lebesgue in time and, for almost every time, it is absolutely continuous with respect to the…
We consider the Landau-Lifshitz equations of ferromagnetism (including the harmonic map heat-flow and Schroedinger flow as special cases) for degree m equivariant maps from R^2 to S^2. If m \geq 3, we prove that near-minimal energy…
Quantum metrology offers an enhanced performance in experiments such as gravitational wave-detection, magnetometry or atomic clocks frequency calibration. The enhancement, however, requires a delicate tuning of relevant quantum features…
Most quantum metrology protocols harness highly entangled probe states and globally accessible measurements to surpass the standard quantum limit. However, it is challenging to satisfy these requirements in realistic many-body sensors. We…
Quantum technologies exploit entanglement to enhance various tasks beyond their classical limits including computation, communication and measurements. Quantum metrology aims to increase the precision of a measured quantity that is…
We show that the invariant measure of point vortices, when conditioning the Hamiltonian to a finite interval, converges weakly to the enstrophy measure by conditioning the renormalized energy to the same interval. We also prove the…
We study an optimal stretching problem, which is a variant lattice point problem, for convex domains in $\mathbb{R}^d$ ($d\geq 2$) with smooth boundary of finite type that are symmetric with respect to each coordinate hyperplane/axis. We…
We investigate geometric analysis on metric measure spaces equipped with asymmetric distance functions. Extending concepts from the symmetric case, we introduce upper gradients and corresponding $L^q$-energy functionals as well as…
Standard variational methods tend to obtain upper bounds on the ground state energy of quantum many-body systems. Here we study a complementary method that determines lower bounds on the ground state energy in a systematic fashion, scales…
Cavity flow problems in two dimensions, as well as in the axially symmetric three-dimensional case, have been extensively studied in the literature from a qualitative perspective. While numerous results exist concerning minimizers or stable…
Calculations of highly excited and delocalized molecular vibrational states are computationally challenging tasks, which strongly depends on the choice of coordinates for describing vibrational motions. We introduce a new method that…
The number of times that we can access a system to extract information via quantum metrology is always finite, and possibly small, and realistic amounts of prior knowledge tend to be moderate. Thus theoretical consistency demands a…
Current metrological bounds typically assume full control over all particles that are involved in the protocol. Relaxing this assumption we study metrological performance when only limited control is available. As an example, we measure a…
This letter describes a method for estimating regions of attraction and bounds on permissible perturbation amplitudes in nonlinear fluids systems. The proposed approach exploits quadratic constraints between the inputs and outputs of the…
We study Hamiltonian flows in a real separable Hilbert space endowed with a symplectic structure. Measures on the Hilbert space that are invariant with respect to the flows of completely integrable Hamiltonian systems are investigated.…
This paper is devoted to the investigation of gradient flows in asymmetric metric spaces (for example, irreversible Finsler manifolds and Minkowski normed spaces) by means of discrete approximation. We study basic properties of curves and…