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Active soft bodies can affect their shape through an internal actuation mechanism that induces a deformation. Similar to recent work, this paper utilizes a differentiable, quasi-static, and physics-based simulation layer to optimize for…
The method of analytic continuation is used to find exact integral equations for a selection of finite-volume energy levels for the non-unitary minimal models $M_{2,2N+3}$ perturbed by their $\varphi_{13}$ operators. The N=2 case is studied…
Motivated by numerical methods for solving parametric partial differential equations, this paper studies the approximation of multivariate analytic functions by algebraic polynomials. We introduce various anisotropic model classes based on…
We calculate the real time non-equilibrium dynamics of quantum spin systems at finite temperatures. The mathematical framework originates from the $C^*$-approach to quantum statistical mechanics and is applied to samples investigated by…
We discuss the formal relationship between the real-time Keldysh and imaginary-time theory for nonequilibrium in quantum dot systems. The latter can be reformulated using the recently proposed Matsubara voltage approach. We establish…
Holomorphic functions are amazing because their values in an ever so small disk in the complex plane completely determine the function values at arbitrary points in their maximum possible domain. The process of extending such a function…
The method of analytical continuation from imaginary to real chemical potential is tested in 2-color QCD. In comparison to previous studies in the same theory, an exact updating algorithm is used and simulations are performed closer to the…
There are many significant applied contexts that require the solution of discontinuous optimization problems in finite dimensions. Yet these problems are very difficult, both computationally and analytically. With the functions being…
We propose a formalism to take account of the correction of the spatial fluctuations to the local self-energy obtained by the dynamical mean-field approximation. For this purpose, the approximate dynamical susceptibility in the framework of…
Uncertainty quantification for neural operators remains an open problem in the infinite-dimensional setting due to the lack of finite-sample coverage guarantees over functional outputs. While conformal prediction offers finite-sample…
In this work we apply the Matsubara-Fradkin formalism and the Nakanishi's auxiliary field method to the quantization of the Podolsky electrodynamics in thermodynamic equilibrium. This approach allows us to write consistently the path…
We use the asymptotic expansion of the heat trace to express all residues of spectral zeta functions as regularized sums over the spectrum. The method extends to those spectral zeta functions that are localized by a bounded operator.
We prove in full generality the thermal operator representation for Matsubara sums in a relativistic field theory of scalar and fermionic particles. It states that the full result of performing the Matsubara sum associated to any given…
Some time ago, Cuniberti et al have proposed a novel method for analytically continuing thermal imaginary-time correlators to real time, which requires no model input and should be applicable with finite-precision data as well. Given that…
We discuss the determination of the $f_0(500)$ (or $\sigma$) resonance by analytic continuation through Pad\'e approximants of the $\pi\pi$-scattering amplitude from the physical region to the pole in the complex energy plane. The aim is to…
An analytical method is advanced for constructing interpolation formulae for complicated problems of statistical mechanics, in which just a few terms of asymptotic expansions are available. The method is based on the self-similar…
Despite the simplicity of one-particle dynamics, explicit expressions for the one-dimensional propagator on a circle suitable to numerical evaluation are surprisingly lacking -- not only in the presence of potentials but even in the free…
The decay rate for a particle in a metastable cubic potential is investigated in the quantum regime by the Euclidean path integral method in semiclassical approximation. The imaginary time formalism allows one to monitor the system as a…
The popular, stable, robust and computationally inexpensive cubic spline interpolation algorithm is adopted and used for finite temperature Green's function calculations of realistic systems. We demonstrate that with appropriate…
Optimal control theory deals with finding protocols to steer a system between assigned initial and final states, such that a trajectory-dependent cost function is minimized. The application of optimal control to stochastic systems is an…