Antisymmetric relation

About: Antisymmetric relation is a research topic. Over the lifetime, 3322 publications have been published within this topic receiving 64365 citations. The topic is also known as: antisymmetric property & anti-symmetric property.

A wavelet based sparse grid method for the electronic Schrödinger equation

Abstract: We present a direct discretization of the electronic Schrodinger equation. It is based on one-dimensional Meyer wavelets from which we build an anisotropic multiresolution analysis for general particle spaces by a tensor product construction. We restrict these spaces to the case of antisymmetric functions. To obtain finite-dimensional subspaces we first discuss semidiscretization with respect to the scale parameter by means of sparse grids which relies on mixed regularity and decay properties of the electronic wave functions. We then propose different techniques for a discretization with respect to the position parameter. Furthermore we present the results of our numerical experiments using this new generalized sparse grid methods for Schrodinger�s equation.

Graph contractions and a generalized möbius inversion

Abstract: Summary This work presents a generalization of Mobius inversion by constructing, on partially ordered sets, pairs of “contracted” matrices which are inverses of each other. We commence by defining some nonstandard matrix operations, for which a number of results are derived, culminating in a theorem that furnishes conditions under which matrix contraction will commute with matrix multiplication. One consequence of mapping these results into graph theoretical operations on partial ordering graphs (transitive, antisymmetric digraphs) is to suggest a novel class of functions defined thereon which generalize the Riemann and Mobius functions in a way that may lead to new algorithms for matrix inversion. The usefulness of these functions in physical science is illustrated with two examples which in recent publications made implicit use of graph contraction. The work suggests a number of tantalizing (as yet unsolved) problems; our paper concludes with a summary of these.

Thermalization, prethermalization and impact of the temperature in the quench dynamics of two $unequal$ Luttinger liquids

Abstract: We study the effect of a quantum quench between two tunnel coupled Tomonaga-Luttinger liquids (TLLs) with different speed of sound and interaction parameter The quench dynamics is induced by switching off the tunnelling and letting the two systems evolve independently We fully diagonalize the problem within a quadratic approximation for the initial tunnelling Both the case of zero and finite temperature in the initial state are considered We focus on correlation functions associated with the antisymmetric and symmetric combinations of the two TLLs (relevant for interference measurements), which turn out to be coupled due to the asymmetry in the two systems' Hamiltonians The presence of different speeds of sound leads to multiple lightcones separating different decaying regimes In particular, in the large time limit, we are able to identify a prethermal regime where the two-point correlation functions of symmetric and antisymmetric sector can be characterized by two emerging effective temperatures, eventually drifting towards a thermal regime, where these two correlators become time independent and are characterized by a unique effective temperature If the initial state is at equilibrium at non-zero temperature $T_0$, all the effective temperatures acquire a linear correction in $T_0$, leading to faster decay of the correlation functions Such effects can play a crucial role for the correct description of currently running cold atoms experiments