Results 51 to 60 of about 230,209 (162)
Low‐Energy Atomic Scattering: S‐Wave Relation Between the Interaction Potential and the Phase Shift
Annalen der Physik, EarlyView.The validity of the on‐shell approximation for s‐wave scattering is examined across one, two, and three dimensions using exactly solvable model interaction potentials. By comparing exact and approximate s‐wave components of the interaction potential, the analysis reveals that the approximation improves with increasing momentum and decreasing ...
Francesco Lorenzi, Luca Salasnich
wiley +1 more source
Quasi‐invariance of Gaussian measures for the 3d$3d$ energy critical nonlinear Schrödinger equation
Communications on Pure and Applied Mathematics, EarlyView.Abstract We consider the 3d$3d$ energy critical nonlinear Schrödinger equation with data distributed according to the Gaussian measure with covariance operator (1−Δ)−s$(1-\Delta)^{-s}$, where Δ$\Delta$ is the Laplace operator and s$s$ is sufficiently large. We prove that the flow sends full measure sets to full measure sets. We also discuss some simple
Chenmin Sun, Nikolay Tzvetkov
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Communications on Pure and Applied Mathematics, EarlyView.Abstract We consider a planar Coulomb gas ensemble of size N$N$ with the inverse temperature β=2$\beta =2$ and external potential Q(z)=|z|2−2clog|z−a|$Q(z)=|z|^2-2c \log |z-a|$, where c>0$c>0$ and a∈C$a \in \mathbb {C}$. Equivalently, this model can be realised as N$N$ eigenvalues of the complex Ginibre matrix of size (c+1)N×(c+1)N$(c+1) N \times (c+1)
Sung‐Soo Byun +2 more
wiley +1 more source
Non-commutative fermion mass matrix and gravity
, 2013 The first part is an introductory description of a small cross-section of the literature on algebraic methods in non-perturbative quantum gravity with a specific focus on viewing algebra as a laboratory in which to deepen understanding of the nature of ...
Baez J. C. +12 more
core +1 more source
On the Density–Density Correlations of the Non‐Interacting Finite Temperature Electron Gas
Contributions to Plasma Physics, EarlyView.ABSTRACT The density–density correlations of the non‐interacting finite temperature electron gas are discussed in detail. Starting from the ideal linear density response function and utilizing general relations from linear response theory, known and novel expressions are derived for the pair correlation function, static structure factor, dynamic ...
Panagiotis Tolias +2 more
wiley +1 more source
, 2017 Geometric Algebra (GA) is a mathematical language that aids a unified approach and understanding in topics across mathematics, physics and engineering. In this contribution, we introduce the Spacetime Algebra (STA), and discuss some of its applications ...
A. Lasenby
semanticscholar +1 more source
Global and microlocal aspects of Dirac operators: Propagators and Hadamard states
Mathematische Nachrichten, EarlyView.Abstract We propose a geometric approach to construct the Cauchy evolution operator for the Lorentzian Dirac operator on Cauchy‐compact globally hyperbolic 4‐manifolds. We realize the Cauchy evolution operator as the sum of two invariantly defined oscillatory integrals—the positive and negative Dirac propagators—global in space and in time, with ...
Matteo Capoferri, Simone Murro
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Heisenberg‐smooth operators from the phase‐space perspective
Mathematische Nachrichten, EarlyView.Abstract Cordes' characterization of Heisenberg‐smooth operators bridges a gap between the theory of pseudo‐differential operators and quantum harmonic analysis (QHA). We give a new proof of the result by using the phase‐space formalism of QHA. Our argument is flexible enough to generalize Cordes' result in several directions: (1) we can admit general ...
Robert Fulsche, Lauritz van Luijk
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Process, Distinction, Groupoids and Clifford Algebras: an Alternative View of the Quantum Formalism [PDF]
, 2012 In this paper we start from a basic notion of process, which we structure into two groupoids, one orthogonal and one symplectic. By introducing additional structure, we convert these groupoids into orthogonal and symplectic Clifford algebras respectively.
B. Hiley
semanticscholar +1 more source
Unveiling New Perspectives on the Hirota–Maccari System With Multiplicative White Noise
Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT In this study, we delve into the stochastic Hirota–Maccari system, which is subjected to multiplicative noise according to the Itô sense. The stochastic Hirota–Maccari system is significant for its ability to accurately model how stochastic affects nonlinear wave propagation, providing valuable insights into complex systems like fluid dynamics
Mohamed E. M. Alngar +3 more
wiley +1 more source