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Related papers: A variational method for $\Phi^4_3$

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Perturbation theory, as well as most thermal field resummation methods widely used to study finite-temperature quantum field theories, presents a non-negligible renormalization scale dependence. To address this limitation, we propose an…

High Energy Physics - Phenomenology · Physics 2026-05-11 Lucas G. Câmara , Marcus Benghi Pinto , Rudnei O. Ramos

In lattice Hamiltonian systems with a quartic coupling $\gamma$, a critical value $\gamma^*$ may exist such that, when $\gamma=\gamma^*$, the leading irrelevant operator decouples from the Hamiltonian and the leading nonscaling contribution…

Statistical Mechanics · Physics 2009-11-07 Massimo Campostrini , Pietro Parruccini , Paolo Rossi

The divergent series for a function defined through Lapalce integral and the ground state energy of the quartic anharmonic oscillator to large orders are studied to test the generalized binomial transform which is the renamed version of…

Quantum Physics · Physics 2017-03-08 Hirofumi Yamada

We consider the inverse problem of recovering a continuous-domain function from a finite number of noisy linear measurements. The unknown signal is modeled as the sum of a slowly varying trend and a periodic or quasi-periodic seasonal…

Functional Analysis · Mathematics 2025-05-16 Julien Fageot

We study the Sine-Gordon model for $\beta^{2}< 4 \pi$ in infinite volume. We give a variatonal characterization of it's laplace transform, and deduce from this large deviations. Along the way we obtain estimates which are strong enough to…

Probability · Mathematics 2022-10-05 Nikolay Barashkov

We start the investigation of free boundary variational models featuring varying singularities. The theory depends strongly on the nature of the singular power $\gamma(x)$ and how it changes. Under a mild continuity assumption on…

Analysis of PDEs · Mathematics 2025-11-12 Damião Araújo , Aelson Sobral , Eduardo V. Teixeira , José Miguel Urbano

We investigate the Dirichlet boundary control of the Laplace equation, considering the control in $H^{1/2}(\partial \Omega)$, which is the natural space for Dirichlet data when the state belongs to $H^1(\Omega)$. The cost of the control is…

Numerical Analysis · Mathematics 2025-07-17 Ulrich Langer , Richard Löscher , Olaf Steinbach , Huidong Yang

For massless $\phi^4$ theory, we explicitly compute the lowest order non-local contributions to the one-loop effective action required for the determination of the trace anomaly. Imposing exact conformal invariance of the local part of the…

High Energy Physics - Theory · Physics 2008-11-26 Krzysztof A. Meissner , Hermann Nicolai

In this work, our aim is to reconstruct the unknown initial value from terminal data. We develop a numerical framework on nonuniform time grids for fractional wave equations under the lower regularity assumptions. Then, we introduce a…

Numerical Analysis · Mathematics 2025-06-25 Dakang Cen , Zhiyuan Li , Wenlong Zhang

Scalar field theory at finite temperature is investigated via an improved renormalization group prescription which provides an effective resummation over all possible non-overlapping higher loop graphs. Explicit analyses for the lambda…

High Energy Physics - Theory · Physics 2009-10-28 Sen-Ben Liao , Michael Strickland

Borel summable divergent series usually appear when studying solutions of analytic ODE near a multiple singular point. Their sum, uniquely defined in certain sectors of the complex plane, is obtained via the Borel--Laplace transformation.…

Classical Analysis and ODEs · Mathematics 2015-11-04 Martin Klimes

In this article, we deal with the fine boundary regularity, a weighted H\"{o}lder regularity of weak solutions to the problem involving the fractional $(p,q)$ Laplacian denoted by $(-\Delta)_{p}^{s} u + (-\Delta)_{q}^{s} u = f(x)$ in…

Analysis of PDEs · Mathematics 2025-05-22 R. Dhanya , Ritabrata Jana , Uttam Kumar , Sweta Tiwari

We investigate the infinite volume limit of the variational description of Euclidean quantum fields introduced in a previous work. Focussing on two dimensional theories for simplicity, we prove in details how to use the variational approach…

Probability · Mathematics 2023-12-06 Nikolay Barashkov , Massimiliano Gubinelli

Motivated by the problem of the small-scale sign distribution of Laplace eigenfunctions, we introduce a strong notion of sign-balance for (eigen)functions, and prove that random eigenfunctions are sign-balanced above a precisely determined…

Probability · Mathematics 2026-05-22 Stephen Muirhead , Igor Wigman

Consider the Laplacian in a bounded domain in R^d with general (mixed) homogeneous boundary conditions. We prove that its eigenfunctions are `quasi-orthogonal' on the boundary with respect to a certain norm. Boundary orthogonality is proved…

Mathematical Physics · Physics 2007-05-23 Alex H. Barnett

We prove necessary optimality conditions of Euler-Lagrange type for generalized problems of the calculus of variations on time scales with a Lagrangian depending not only on the independent variable, an unknown function and its delta…

Optimization and Control · Mathematics 2011-05-02 Natalia Martins , Delfim F. M. Torres

We consider the problem of approximating the solution of variational problems subject to the constraint that the admissible functions must be convex. This problem is at the interface between convex analysis, convex optimization, variational…

Numerical Analysis · Mathematics 2015-03-19 Adam M. Oberman

The probabilistic interpretation of Laplace transforms is used to help to describe the Laplace Transform $L(s)$ of improper random variables. In particular, busy periods in queueing models are examined. The value of $L(0)$ is explained in…

Probability · Mathematics 2021-08-10 Janhavi Prabhu , Myron Hlynka

Optical phase measurement is a simple example of a quantum--limited measurement problem with important applications in metrology such as gravitational wave detection. The formulation of optimal strategies for such measurements is an…

Quantum Physics · Physics 2012-12-18 K. R. W. Jones

We use the technique developed in [32]-[33] to construct the upper and the lower bounds for classes of problems containing non-local terms, including problems in micromagnetics and problems arising in the variational study of the Method of…

Analysis of PDEs · Mathematics 2015-02-10 Arkady Poliakovsky
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