Related papers: Minimal Pole Representation and Controlled Analyti…
We present a method able to recover location and residue of poles of functions meromorphic in a half--plane from samples of the function on the real positive semi-axis. The function is assumed to satisfy appropriate asymptotic conditions…
We prove that every nonnegative continuous real-valued function on a given compact metric space is the uniform limit of some increasing sequence of nonnegative simple functions being linear combinations of indicators of open sets; here the…
We introduce a closure model for coarse-grained kinetic theories of polar active fluids. Based on a quasi-equilibrium approximation of the particle distribution function, the model closely captures important analytical properties of the…
New model-independent compact representations of imaginary-time data are presented in terms of the intermediate representation (IR) of analytical continuation. This is motivated by a recent numerical finding by the authors [J. Otsuki et…
In this work we study qualitative properties of real analytic bounded maps. The main tool is approximation of real valued functions analytic in rectangular domains of the complex plane by continued g-fractions of Wall. As an application,…
This article proposes a new way to construct computationally efficient `wrappers' around fine scale, microscopic, detailed descriptions of dynamical systems, such as molecular dynamics, to make predictions at the macroscale `continuum'…
In this paper we provide a rigorous mathematical foundation for continuous approximations of a class of systems with piece-wise continuous functions. By using techniques from the theory of differential inclusions, the underlying piece-wise…
For a given diagrammatic approximation in many-body perturbation theory it is not guaranteed that positive observables, such as the density or the spectral function, retain their positivity. For zero-temperature systems we developed a…
This article investigates the exact controllability of three-dimensional stochastic Maxwell equations, a coupled system comprising two stochastic partial differential equations. The research establishes the observability inequality for the…
There is today a growing need to accurately model the angular scattering response of metasurfaces for optical analog processing applications. However, the current metasurface modeling techniques are not well suited for such a task since…
We cannot use directly the results of zero-temperature at finite temperature, for at finite temperature the average is to be carried over all highly degenerate excited states unlike zero-temperature average is only on unique ground state.…
The process of dynamic state estimation (filtering) based on point process observations is in general intractable. Numerical sampling techniques are often practically useful, but lead to limited conceptual insight about optimal…
We introduce a definition of pressure for almost-additive sequences of continuous functions defined over (non-compact) countable Markov shifts. The variational principle is proved. Under certain assumptions we prove the existence of Gibbs…
The Lipkin-Meshkov-Glick model is used to examine the validity of some approximate methods in a many-body theory at finite temperatures. Namely, the thermal random phase approximation (TRPA) and the thermal renormalized random phase…
Functions with discontinuities appear in many applications such as image reconstruction, signal processing, optimal control problems, interface problems, engineering applications and so on. Accurate approximation and interpolation of these…
This thesis investigates optimal trajectory tracking of nonlinear dynamical systems with affine controls. The control task is to enforce the system state to follow a prescribed desired trajectory as closely as possible. The concept of…
We present a generalization of the discrete Lehmann representation (DLR) to three-point correlation and vertex functions in imaginary time and Matsubara frequency. The representation takes the form of a linear combination of judiciously…
We give a survey on the theory of representation-finite and certain minimal representation-infinite algebras.The main goals are the existence of multiplicative bases and of coverings with good properties. Both are attained via…
This paper presents a novel method for transient stability analysis (TSA) that circumvents the limitations of sequential numerical integration and energy functions. The proposed method begins by constructing a trajectory-dependent stability…
We theoretically examine the finite-temperature spectral function of Fermi polarons in three dimensions, by using a self-consistent many-body $T$-matrix theory in real frequency. In comparison with the previous results from a…