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Related papers: Multidimensional decay in van der Corput lemma

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The stochastic spectral expansion method offers a simple framework for calculations in de Sitter spacetimes. We show how to extend its reach to metastable vacuum states, both in the case when the potential is bounded from below, and when it…

General Relativity and Quantum Cosmology · Physics 2022-04-07 José Eliel Camargo-Molina , Arttu Rajantie

Multi-dimensional spectroscopy represents a particularly insightful tool for investigating the interplay of nuclear and electronic dynamics, which plays an important role in a number of photophysical processes and photochemical reactions.…

Quantum Physics · Physics 2022-07-26 Frank Ernesto Quintela Rodriguez , Filippo Troiani

In this work we show a class of oscillating configurations for the evolution of the domain walls in Euclidean space. The solutions are obtained analytically. Phase transitions are achieved from the associated fluctuation determinant, by the…

High Energy Physics - Theory · Physics 2015-09-03 R. A. C. Correa , P. H. R. S. Moraes , Roldao da Rocha

The kinetics of the multicomponent condensation after the instantaneous creation of the metastable state is described analytically. Manydimensional problem is reduced to the one-dimensional case. All the main characteristics of the process…

Condensed Matter · Physics 2007-05-23 V. Kurasov

We establish global-in-time decay estimates for the multi-phase Muskat problem in the case where the density takes exactly n+1 distinct constant values. We first linearize the system around a flat stable configuration, followed by the study…

Analysis of PDEs · Mathematics 2026-04-15 Zirui Wang

This paper establishes the optimal decay rate for scalar oscillatory integrals in $n$ variables which satisfy a nondegeneracy condition on the third derivatives. The estimates proved are stable under small linear perturbations, as…

Classical Analysis and ODEs · Mathematics 2007-07-19 Philip T. Gressman

We consider second-order phase transitions in which the order parameter is a replicated overlap matrix. We focus on a tricritical point that occurs in a variety of mean-field models and that, more generically, describes higher order…

Disordered Systems and Neural Networks · Physics 2024-05-27 Luca Leuzzi , Tommaso Rizzo

By expanding the Dirac delta function in terms of the eigenfunctions of the corresponding Sturm-Liouville problem, we construct some new (oscillating) integral transforms. These transforms are then used to solve various finance, physics,…

Pricing of Securities · Quantitative Finance 2022-06-22 Andrey Itkin , Alexander Lipton , Dmitry Muravey

In this partly expository paper we study van der Corput sets in $\Z^d$, with a focus on connections with harmonic analysis and recurrence properties of measure preserving dynamical systems. We prove multidimensional versions of some…

Dynamical Systems · Mathematics 2007-10-26 Vitaly Bergelson , Emmanuel Lesigne

With the help of Van der Corput lemmas, decay estimates are proven for Fourier transforms of mixed homogeneous hypersurface measures with densities that can be quite irregular. The primary results are local in nature, but can be extended to…

Classical Analysis and ODEs · Mathematics 2017-11-15 Michael Greenblatt

We present a new proof of Cramer's rule by interpreting a system of linear equations as a transformation of $n$-dimensional Cartesian-coordinate vectors. To find the solution, we carry out the inverse transformation by convolving the…

General Mathematics · Mathematics 2020-12-16 June-Haak Ee , Jungil Lee , Chaehyun Yu

In this note, by using the result in one variable, we obtain asymptotic expansions of oscillatory integrals for certain multivariable phase functions with {\bf degenerate} singular points. Moreover by using this result, we have asymptotic…

Classical Analysis and ODEs · Mathematics 2020-09-22 Toshio Nagano , Naoya Miyazaki

In this paper we establish sharp estimates (up to logarithmic losses) for the multilinear oscillatory integral operator studied by Phong, Stein, and Sturm and Carbery and Wright on any product $\prod_{j=1}^d L^{p_j}(\mathbb R)$ with each…

Classical Analysis and ODEs · Mathematics 2016-12-02 Maxim Gilula , Philip T. Gressman , Lechao Xiao

We show that an arbitrary spatial distribution of complex refractive index inside an object can be exactly represented as a sum of two "monomorphous" complex distributions, i.e. the distributions with the ratios of the real part to the…

Medical Physics · Physics 2015-12-09 T. E. Gureyev , Ya. I. Nesterets

We apply the Lewis-Riesenfeld invariant method for the harmonic oscillator with time dependent mass and frequency to the modes of a charged scalar field that propagates in a curved, homogeneous and isotropic spacetime. We recover the…

High Energy Physics - Theory · Physics 2017-11-22 Salvador Robles-Perez

We derive a general expression for the expectation value of the phase acquired by a time dependent wave function in a multi component system, as excursions are made in its coordinate space. We then obtain the mean phase for the (linear…

Quantum Physics · Physics 2007-05-23 Robert Englman Asher Yahalom

We present an adaptive delaminating Levin method for evaluating bivariate oscillatory integrals over rectangular domains. Whereas previous analyses of Levin methods impose non-resonance conditions that exclude stationary and resonance…

Numerical Analysis · Mathematics 2025-06-04 Shukui Chen , Kirill Serkh , James Bremer , Murdock Aubry

Damped mechanical systems with various forms of damping are quantized using the path integral formalism. In particular, we obtain the path integral kernel for the linearly damped harmonic oscillator and a particle in a uniform gravitational…

Quantum Physics · Physics 2012-09-20 Dharmesh Jain , A. Das , Sayan Kar

Motivated by the image denoising problem and the undesirable stair-casing effect of the total variation method, we introduce bounded variation spaces with generalized Orlicz growth. Our setup covers earlier variable exponent and double…

Functional Analysis · Mathematics 2025-04-22 Michela Eleuteri , Petteri Harjulehto , Peter Hästö

In this paper, Van der pol equation has been analyzed for stability and bifurcation phenomena with and without forcing component. Analytical solution of the Van der pol equation using Method of Multiple Scales (MMS) is compared with…

Adaptation and Self-Organizing Systems · Physics 2023-09-14 F. A. Chughtai