Two-hole ground state wavefunction: Non-BCS pairing in a tt-JJ two-leg ladder system

Superconductivity is usually described in the framework of the Bardeen-Cooper-Schrieffer (BCS) wavefunction, which even includes the resonating-valence-bond (RVB) wavefunction proposed for the high-temperature superconductivity in the cuprate. A natural question is \emph{if} any fundamental physics could be possibly missed by applying such a scheme to strongly correlated systems. Here we study the pairing wavefunction of two holes injected into a Mott insulator/antiferromagnet in a two-leg ladder using variational Monte Carlo (VMC) approach. By comparing with density matrix renormalization group (DMRG) calculation, we show that a conventional BCS or RVB pairing of the doped holes makes qualitatively wrong predictions and is incompatible with the fundamental pairing force in the $t$-$J$ model, which is kinetic-energy-driven by nature. By contrast, a non-BCS-like wavefunction incorporating such novel effect will result in a substantially enhanced pairing strength and improved ground state energy as compared to the DMRG results. We argue that the non-BCS form of such a new ground state wavefunction is essential to describe a doped Mott antiferromagnet at finite doping.Comment: 11 pages, 5 figure

A De Giorgi Iteration-based Approach for the Establishment of ISS Properties for Burgers' Equation with Boundary and In-domain Disturbances

This note addresses input-to-state stability (ISS) properties with respect to (w.r.t.) boundary and in-domain disturbances for Burgers' equation. The developed approach is a combination of the method of De~Giorgi iteration and the technique of Lyapunov functionals by adequately splitting the original problem into two subsystems. The ISS properties in $L^2$-norm for Burgers' equation have been established using this method. Moreover, as an application of De~Giorgi iteration, ISS in $L^\infty$-norm w.r.t. in-domain disturbances and actuation errors in boundary feedback control for a 1-$D$ {linear} {unstable reaction-diffusion equation} have also been established. It is the first time that the method of De~Giorgi iteration is introduced in the ISS theory for infinite dimensional systems, and the developed method can be generalized for tackling some problems on multidimensional spatial domains and to a wider class of nonlinear {partial differential equations (PDEs)Comment: This paper has been accepted for publication by IEEE Trans. on Automatic Control, and is available at http://dx.doi.org/10.1109/TAC.2018.2880160. arXiv admin note: substantial text overlap with arXiv:1710.0991

In-domain control of a heat equation: an approach combining zero-dynamics inverse and differential flatness

This paper addresses the set-point control problem of a heat equation with in-domain actuation. The proposed scheme is based on the framework of zero dynamics inverse combined with flat system control. Moreover, the set-point control is cast into a motion planing problem of a multiple-input, multiple-out system, which is solved by a Green's function-based reference trajectory decomposition. The validity of the proposed method is assessed through convergence and solvability analysis of the control algorithm. The performance of the developed control scheme and the viability of the proposed approach are confirmed by numerical simulation of a representative system.Comment: Preprint of an original research pape

Comparing the Tsallis distribution with and without thermodynamical description in p+p collisions

We compare two types of Tsallis distribution, i.e., with and without thermodynamical description, using the experimental data from the STAR, PHENIX, ALICE and CMS Collaborations on the rapidity and energy dependence of the transverse momentum spectra in p+p collisions. Both of them can give us the similar fitting power to the particle spectra. We show that the Tsallis distribution with thermodynamical description gives lower temperatures than the ones without it. The extra factor $m_T$ (transverse mass) in the Tsallis distribution with thermodynamical description plays an important role in the discrepancies between the two types of Tsallis distribution. But for the heavy particles, the choice to use the $m_T$ or $E_T$ (transverse energy) in the Tsallis distribution becomes more crucial.Comment: 9 pages, 5 figure

Input-to-State Stability with Respect to Boundary Disturbances for a Class of Semi-linear Parabolic Equations

This paper studies the input-to-state stability (ISS) properties based on the method of Lyapunov functionals for a class of semi-linear parabolic partial differential equations (PDEs) with respect to boundary disturbances. In order to avoid the appearance of time derivatives of the disturbances in ISS estimates, some technical inequalities are first developed, which allow directly dealing with the boundary conditions and establishing the ISS based on the method of Lyapunov functionals. The well-posedness analysis of the considered problem is carried out and the conditions for ISS are derived. Two examples are used to illustrate the application of the developed result.Comment: Manuscript submitted to Automatic