Related papers: A constrained optimization problem in quantum stat…
We consider optimization problems with polynomial inequality constraints in non-commuting variables. These non-commuting variables are viewed as bounded operators on a Hilbert space whose dimension is not fixed and the associated polynomial…
Maximizing the precision in estimating parameters in a quantum system subject to instrumentation constraints is cast as a convex optimization problem. We account for prior knowledge about the parameter range by developing a worst-case and…
We propose an energy-driven stochastic master equation for the density matrix as a dynamical model for quantum state reduction. In contrast, most previous studies of state reduction have considered stochastic extensions of the Schr\"odinger…
We consider $\mathbb{S}^2$-valued maps on a domain $\Omega\subset\mathbb{R}^N$ minimizing a perturbation of the Dirichlet energy with vertical penalization in $\Omega$ and horizontal penalization on $\partial\Omega$. We first show the…
Constrained optimization problems are ubiquitous in science and industry. Quantum algorithms have shown promise in solving optimization problems, yet none of the current algorithms can effectively handle arbitrary constraints. We introduce…
We present an ``orbital'' free density functional theory for computing the quantum ground state of atomic clusters and liquids. Our approach combines the Bohm hydrodynamical description of quantum mechanics with an information theoretical…
We prove the existence of non-trivial global minimizers of a class of free energies related to aggregation equations with degenerate diffusion on $\Real^d$. Such equations arise in mathematical biology as models for organism group dynamics…
We investigate entropy minimization problems for quantum states subject to convex block-separable constraints. Our principal result is a quantitative stability theorem: under a natural confining (fixed-support) hypothesis, if a state has…
Levitated nanoparticles provide a controllable and isolated platform for probing fundamental quantum phenomena at the macroscopic scale. In this work, we introduce an optimization method to determine optimal static potentials for the…
The aim of this paper is to prove the existence of minimizers for a variational problem involving the minimization under volume constraint of the sum of the perimeter and a non-local energy of Wasserstein type. This extends previous partial…
We analyze space-time finite element methods for the numerical solution of distributed parabolic optimal control problems with energy regularization in the Bochner space $L^2(0,T;H^{-1}(\Omega))$. By duality, the related norm can be…
A persistent focus on the concept of emergence as a core element of the scientific method allows a clean separation, insofar as this is possible, of the physical and philosophical aspects of the problem of outcomes in quantum mechanics. The…
In these two related parts we present a set of methods, analytical and numerical, which can illuminate the behaviour of quantum system, especially in the complex systems. The key points demonstrating advantages of this approach are: (i)…
We consider classical and quantum dynamics of a free particle in de Sitter's space-times with different topologies to see what happens to space-time singularities of removable type in quantum theory. We find analytic solution of the…
This paper is concerned with the variational problem for the elastic energy defined on symmetric graphs under the unilateral constraint. Assuming that the obstacle function satisfies the symmetric cone condition, we prove (i) uniqueness of…
In this paper, we examine the optimal quantization of signals for system identification. We deal with memoryless quantization for the output signals and derive the optimal quantization schemes. The objective functions are the errors of…
In the case of quantum systems interacting with multiple environments, the time-evolution of the reduced density matrix is described by the Liouvillian. For a variety of physical observables, the long-time limit or steady state solution is…
We address a broad class of optimization problems of finding quantum measurements, which includes the problems of finding an optimal measurement in the Bayes criterion and a measurement maximizing the average success probability with a…
We consider the notion of equilibration for an isolated quantum system exhibiting Anderson localization. The system is assumed to be in a pure state, i.e., described by a wave-function undergoing unitary dynamics. We focus on the simplest…
This paper is devoted to spherical measures and point configurations optimizing three-point energies. Our main goal is to extend the classic optimization problems based on pairs of distances between points to the context of three-point…