arXiv subjects

Weitao Chen

Publications and source records attributed to Weitao Chen.

21 records · Page 2Linked to original sources

arXiv2022

Characterizing the Bulk-Boundary Correspondence of one-dimensional non-Hermitian interacting systems by edge entanglement entropy

Dramatically different from the Hermitian systems, the conventional Bulk-Boundary Correspondence (BBC) is broken in the non-Hermitian systems. In this article, we use edge entanglement entropy to characterize the topological properties of non-Hermitian Su-Schrieffer-Heeger Hubbard model. For free Fermions, we study the scaling behavior of entanglement entropy and demonstrate that the edge entanglement entropy is a good indicator to delimit different phases of non-Hermitian systems. We further generalize the edge entanglement entropy to the non-Hermitian interacting Hubbard chain, and obtain the topological phase diagram in the plane of interaction and non-Hermitian hopping amplitudes. It is found that the Hubbard interaction diminishes and weakens the breakdown of Bulk-Boundary Correspondence, which eventually disappears at some critical value of interaction.

cond-mat.str-el↗

arXiv2021

Recovery of a Time-Dependent Bottom Topography Function from the Shallow Water Equations via an Adjoint Approach

We develop an adjoint approach for recovering the topographical function included in the source term of one-dimensional hyperbolic balance laws. We focus on a specific system, namely the shallow water equations, in an effort to recover the riverbed topography. The novelty of this work is the ability to robustly recover the bottom topography using only noisy boundary data from one measurement event and the inclusion of two regularization terms in the iterative update scheme. The adjoint scheme is determined from a linearization of the forward system and is used to compute the gradient of a cost function. The bottom topography function is recovered through an iterative process given by a three-operator splitting method which allows the feasibility to include two regularization terms. Numerous numerical tests demonstrate the robustness of the method regardless of the choice of initial guess and in the presence of discontinuities in the solution of the forward problem.

math.OC↗

arXiv2020

Equilibrium Equality for Free Energy Difference

Jarzynski Equality (JE) and the thermodynamic integration method are conventional methods to calculate free energy difference (FED) between two equilibrium states with constant temperature of a system. However, a number of ensemble samples should be generated to reach high accuracy for a system with large size, which consumes a lot computational resource. Previous work had tried to replace the non-equilibrium quantities with equilibrium quantities in JE by introducing a virtual integrable system and it had promoted the efficiency in calculating FED between different equilibrium states with constant temperature. To overcome the downside that the FED for two equilibrium states with different temperature can't be calculated efficiently in previous work, this article derives out the Equilibrium Equality for FED between any two different equilibrium states by deriving out the equality for FED between states with different temperatures and then combining the equality for FED between states with different volumes. The equality presented in this article expresses FED between any two equilibrium states as an ensemble average in one equilibrium state, which enable the FED between any two equilibrium states can be determined by generating only one canonical ensemble and thus the samples needed are dramatically less and the efficiency is promoted a lot. Plus, the effectiveness and efficiency of the equality are examined in Toda-Lattice model with different dimensions.

cond-mat.stat-mech↗