Search results for "Theorem"
showing 10 items of 1250 documents
High-momentum tails as magnetic-structure probes for strongly correlatedSU(κ)fermionic mixtures in one-dimensional traps
2016
A universal ${k}^{\ensuremath{-}4}$ decay of the large-momentum tails of the momentum distribution, fixed by Tan's contact coefficients, constitutes a direct signature of strong correlations in a short-range interacting quantum gas. Here we consider a repulsive multicomponent Fermi gas under harmonic confinement, as in the experiment of G. Pagano et al. [Nat. Phys. 10, 198 (2014)], realizing a gas with tunable $\text{SU}(\ensuremath{\kappa})$ symmetry. We exploit an exact solution at infinite repulsion to show a direct correspondence between the value of the Tan's contact for each of the $\ensuremath{\kappa}$ components of the gas and the Young tableaux for the ${S}_{N}$ permutation symmetr…
Maxwell Theory as a Classical FieldTheory
2012
Hamilton’s variational principle and the Lagrangian mechanics that rests on it are exceedingly successful in their application to mechanical systems with a finite number of degrees of freedom. Hamilton’s principle characterizes the physically realizable orbits, among the set of all possible orbits, as being the critical elements of the action integral. The Lagrangian function, although not an observable on its own, is not only useful in deriving the equations of motion but is also an important tool for identifying symmetries of the theory and constructing the corresponding conserved quantities, via Noether’s theorem.
Fermion Fields and Their Properties
2011
The fundamental building blocks of matter, i.e. quarks and leptons, carry spin 1/2. There are two formally different but in essence equivalent methods of describing particles with spin: The representation theory of the Poincare group, in the framework of Wigner’s classification hypothesis of particles (see e.g. [QP07], Chap. 6), and the Van der Waerden spinor calculus based on SL(2, \(\mathbb{C}\)).
Beyond the Runge–Gross Theorem
2012
The Runge–Gross theorem (Runge and Gross, Phys Rev Lett, 52:997–1000, 1984) states that for a given initial state the time-dependent density is a unique functional of the external potential. Let us elaborate a bit further on this point. Suppose we could solve the time-dependent Schrodinger equation for a given many-body system, i.e. we specify an initial state \(| \Uppsi_0 \rangle\) at \(t=t_0\) and evolve the wavefunction in time using the Hamiltonian \({\hat{H}} (t).\) Then, from the wave function, we can calculate the time-dependent density \(n (\user2{r},t).\) We can then ask the question whether exactly the same density \(n(\user2{r},t)\) can be reproduced by an external potential \(v^…
Time-dependent density-functional theory for strongly interacting electrons
2017
We consider an analytically solvable model of two interacting electrons that allows for the calculation of the exact exchange-correlation kernel of time-dependent density functional theory. This kernel, as well as the corresponding density response function, is studied in the limit of large repulsive interactions between the electrons and we give analytical results for these quantities as an asymptotic expansion in powers of the square root of the interaction strength. We find that in the strong interaction limit the three leading terms in the expansion of the kernel act instantaneously while memory terms only appear in the next orders. We further derive an alternative expansion for the ker…
Emotional stress & decision-making: an emotional stressor significantly reduces loss aversion
2021
Stress influences loss aversion, the principle that losses loom larger than gains, although the nature of this relationship is unclear. Studies show that stress reduces loss aversion; however, stress response has been only studied by means of physiological measures, but the stressor emotional impact remained unclear. Since emotions can modify stress response and increase the activity of the loss aversion neural substrates, it could be expected that an emotional stressor may produce the opposite effect, i.e. loss aversion increase. 69 participants were divided into experimental and control group. The first one was exposed to emotional stress through a 5-minutes video, and control group viewe…
Analytic solutions of the Navier-Stokes equations
2001
We consider the time dependent incompressible Navier-Stokes equations on an half plane. For analytic initial data, existence and uniqueness of the solution are proved using the Abstract Cauchy-Kovalevskaya Theorem in Banach spaces. The time interval of existence is proved to be independent of the viscosity.
Poincar é-Birkhoff fixed point theorem and periodic solutions of asymptotically linear planar Hamiltonian systems. (Turin Fortnight Lectures on Nonli…
2002
Do pollinator distributions underlie the evolution of pollination ecotypes in the Cape shrub Erica plukenetii?
2013
Background and aims According to the Grant-Stebbins model of pollinator-driven divergence, plants that disperse beyond the range of their specialized pollinator may adapt to a new pollination system. Although this model provides a compelling explanation for pollination ecotype formation, few studies have directly tested its validity in nature. Here we investigate the distribution and pollination biology of several subspecies of the shrub Erica plukenetii from the Cape Floristic Region in South Africa. We analyse these data in a phylogenetic context and combine these results with information on pollinator ranges to test whether the evolution of pollination ecotypes is consistent with the Gra…
Weak mixing implies weak mixing of higher orders along tempered functions
2009
AbstractWe extend the weakly mixing PET (polynomial ergodic theorem) obtained in Bergelson [Weakly mixing PET. Ergod. Th. & Dynam. Sys.7 (1987), 337–349] to much wider families of functions. Besides throwing new light on the question of ‘how much higher-degree mixing is hidden in weak mixing’, the obtained results also show the way to possible new extensions of the polynomial Szemerédi theorem obtained in Bergelson and Leibman [Polynomial extensions of van der Waerden’s and Szemerédi’s theorems. J. Amer. Math. Soc.9 (1996), 725–753].