Search results for "Mathematical physics"

DIFFERENTIAL RENORMALIZATION AND EPSTEIN–GLASER RENORMALIZATION

2001

Scaling violation in the infinite-momentum frame

1978

The theory of scaling violation is studied in asymptotically free gauge theories formulated in the infinite-momentum frame. The transition probabilities occurring in the equation governing the q/sup 2/ dependence of the parton distributions are calculated directly. The equivalence of this formalism for the longitudinal parton distributions with the usual one based on the operator-product expansion is demonstrated. The assets of our method are calculational simplicity and reference to physical intuition.

The classical statistical mechanics of Frenkel-Kontorova models

1995

The scaling properties of the free energy, specific heat, and mean spacing are calculated for classical Frenkel-Kontorova models at low temperature, in three regimes: near the integrable limit, the anti-integrable limit, and the sliding-pinned transition (“transition by breaking of analyticity”). In particular, the renormalization scheme given in previous work for ground states of Frenkel-Kontorova models is extended to nonzero-temperature Gibbs states, and the hierarchical melting phenomenon of Vallet, Schilling, and Aubry is put on a rigorous footing.

An intrinsic characterization of spherically symmetric spacetimes

2010

We give the necessary and sufficient (local) conditions for a metric tensor to be a non conformally flat spherically symmetric solution. These conditions exclusively involve explicit concomitants of the Riemann tensor. As a direct application we obtain the {\em ideal} labeling of the Schwarzschild, Reissner-Nordstr\"om and Lema\^itre-Tolman-Bondi solutions.

An intrinsic characterization of the Kerr metric

2009

We give the necessary and sufficient (local) conditions for a metric tensor to be the Kerr solution. These conditions exclusively involve explicit concomitants of the Riemann tensor.

Scattering on Riemannian Symmetric Spaces and Huygens Principle

2018

International audience; The famous paper by L. D. Faddeev and B. S. Pavlov (1972) on automorphic wave equation explored a highly romantic link between Scattering Theory (in the sense of Lax and Phillips) and Riemann hypothesis. An attempt to generalize this approach to general semisimple Lie groups leads to an interesting evolution system with multidimensional time explored by the author in 1976. In the present paper, we compare this system with a simpler one defined for zero curvature symmetric spaces and show that the Huygens principle for this system in the curved space holds if and only if it holds in the zero curvature limit.

Definition of an appropriate free dynamics and the physical S-matrix in multichannel hyperradial adiabatic scattering

2010

In the hyperradial adiabatic (HA) treatment of the three-body problem the total wave function is i expanded as ΨHA(R, ξ, η) = R−5/2 ∑iχi(R)φi(R|ξ, η),where R denotes the hyperradius and (ξ , η) are internal hyperangles. Integration over ξ and η converts the Schrödinger equation into a system of coupled hyperradial equations. It is a well-known fact that, within the HA approach, the non-adiabatic corrections that couple channels converging to the same asymptotic configuration can show an unphysical long-range behavior ∼ 1/R. Though the latter is of purely kinematic origin and arises from the use of the hyperradius instead of the pertinent Jacobi variables, it is nevertheless the source of the…

Expected performance of an ideal liquid argon neutrino detector with enhanced sensitivity to scintillation light

2014

Scintillation light is used in liquid argon (LAr) neutrino detectors to provide a trigger signal, veto information against cosmic rays, and absolute event timing. In this work, we discuss additional opportunities offered by detectors with enhanced sensitivity to scintillation light, that is with light collection efficiencies of about $10^{-3}$. We focus on two key detector performance indicators for neutrino oscillation physics: calorimetric neutrino energy reconstruction and neutrino/antineutrino separation in a non-magnetized detector. Our results are based on detailed simulations, with neutrino interactions modelled according to the GENIE event generator, while the charge and light respo…

Existence and orbital stability of standing waves to nonlinear Schr��dinger system with partial confinement

2018

We are concerned with the existence of solutions to the following nonlinear Schr\"odinger system in $\mathbb{R}^3$: \begin{equation*} \left\{ \begin{aligned} -\Delta u_1 + (x_1^2+x_2^2)u_1&= \lambda_1 u_1 + \mu_1 |u_1|^{p_1 -2}u_1 + \beta r_1|u_1|^{r_1-2}u_1|u_2|^{r_2}, \\ -\Delta u_2 + (x_1^2+x_2^2)u_2&= \lambda_2 u_2 + \mu_2 |u_2|^{p_2 -2}u_2 +\beta r_2 |u_1|^{r_1}|u_2|^{r_2 -2}u_2, \end{aligned} \right. \end{equation*} under the constraint \begin{align*} \int_{\mathbb{R}^3}|u_1|^2 \, dx = a_1>0,\quad \int_{\mathbb{R}^3}|u_2|^2 \, dx = a_2>0, \end{align*} where $\mu_1, \mu_2, \beta >0, 2 1, r_1 + r_2 < \frac{10}{3}$. In the system, the parameters $\lambda_1, \lambda_2 \in \R$ are unknown …

Minimum main sequence mass in quadratic Palatini f(R) gravity

2019

General relativity yields an analytical prediction of a minimum required mass of roughly $\ensuremath{\sim}0.08--0.09\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$ for a star to stably burn sufficient hydrogen to fully compensate photospheric losses and, therefore, to belong to the main sequence. Those objects below this threshold (brown dwarfs) eventually cool down without any chance to stabilize their internal temperature. In this work we consider quadratic Palatini $f(\mathcal{R})$ gravity and show that the corresponding Newtonian hydrostatic equilibrium equation contains a new term whose effect is to introduce a weakening/strengthening of the gravitational interaction inside astrophysical…