Unusual bound or localized states

Two-Photon Scattering in One Dimension by Localized Two-Level System

We study two-photon scattering in a one-dimensional coupled resonator arrays (CRA) by a two-level system (TLS), which is localized as a quantum controller. The $S$-matrix is analytically calculated for various two-photon scattering processes by TLS, e.g., one photon is confined by TLS to form a bound state while the other is in the scattering state. It is discovered from the poles of the $S$-matrix that there exist two kinds of three-body bound states for describing two bound photons localized around TLS.

Effect of magnetic fields on bound localized electron states

An approximate analytic solution for the ground electron state are found to the Schroedinger equation for a combination of a uniform magnetic field and single attractive delta-potential. Effect of the magnetic field on this bound localized electron state is discussed. We show that above effect leads to appearing the probability current density in some region centered in the point of the delta-potential as well as to enlarging (for a number of physical models) the localization region of the electron in the plane perpendicular to the magnetic field. We are expected that these properties can be o…

可解的吸收量子行走

Boundary-localized non-Hermitian modes in an absorbing quantum walk

本文研究了一种连续时间量子行走的吸收机制，通过引入任意强度的Lindblad边界漏斗，从基本原理出发求解了该问题，并推导了精确的传播子和首次通过统计特性，揭示了弱耦合和强耗散下吸收概率的对称性。

块纠缠界定了区域局部纠缠的分布

Block entanglement bounds distribution of regionally localized entanglement

本文提出区域局部纠缠概念，证明其总量受枢纽与其余部分块纠缠的上下界约束，并验证了典型量子态及噪声下的有效性，揭示了不同态类的纠缠结构差异。

Bounding the resources for thermalizing many-body localized systems

Understanding under which conditions physical systems thermalize is a long-standing question in many-body physics. While generic quantum systems thermalize, there are known instances where thermalization is hindered, for example in many-body localized (MBL) systems. Here we introduce a class of stochastic collision models coupling a many-body system out of thermal equilibrium to an external heat bath. We derive upper and lower bounds on the size of the bath required to thermalize the system via such models, under certain assumptions on the Hamiltonian. We use these bounds, expressed in terms o…

Controlling the dynamics of open quantum systems with periodic driving field

In this paper, we study the exact dynamics of open quantum systems to the case with periodic driving field. It is shown that different from the static adjustment of the system on-site energy that can either generate or destroy the dissipationless localized bound states, the periodic driving can either preserve the existed localized bound states or destroy some of them but cannot generate new localized bound states. With the picture of energy transfer involved with the driving field, we find the condition for the survival of the localized bound states when the driving amplitude is weak. For the…

Runge-Lenz Vector, Accidental SU(2) Symmetry, and Unusual Multiplets for Motion on a Cone

We consider a particle moving on a cone and bound to its tip by $1/r$ or harmonic oscillator potentials. When the deficit angle of the cone divided by $2 π$ is a rational number, all bound classical orbits are closed. Correspondingly, the quantum system has accidental degeneracies in the discrete energy spectrum. An accidental SU(2) symmetry is generated by the rotations around the tip of the cone as well as by a Runge-Lenz vector. Remarkably, some of the corresponding multiplets have fractional ``spin'' and unusual degeneracies.

准一维电子金刚石项链链中的紧凑局域边界态

Compact localized boundary states in a quasi-1D electronic diamond-necklace chain

该研究在准一维金刚石项链链中发现并实现了不衰减进入体态的紧凑局域零能边界态，为可编织的鲁棒量子比特提供了新途径。

Coherent shift of localized bound pair in Bose Hubbard model

Based on the exact results obtained by Bethe ansatz, we demonstrate the existence of stable bound pair (BP) wave packet in Bose Hubbard model with arbitrary on-site interaction U. In large-U regime, it is found that an incoming single-particle (SP) can coherently pass through a BP wave packet and leave a coherent shift in the position of it. This suggests a simple scheme for constructing a BP charge qubit to realize a quantum switch, which is capable of controlling the coherent transport of one and only one photon in a one-dimensional waveguide.

连续介质中的Lieb-Robinson界：基于局域化框架

Lieb-Robinson bounds in the continuum via localized frames

本文通过引入格点局域化框架，证明了连续介质中相互作用费米子的一般Lieb-Robinson界，并应用于准自由朗道哈密顿量，为分数量子霍尔效应提供动力学基础。

Nonlinear Dirac Equation On Graphs With Localized Nonlinearities: Bound States And Nonrelativistic Limit

In this paper we study the nonlinear Dirac (NLD) equation on noncompact metric graphs with localized Kerr nonlinearities, in the case of Kirchhoff-type conditions at the vertices. Precisely, we discuss existence and multiplicity of the bound states (arising as critical points of the NLD action functional) and we prove that, in the $L^2$-subcritical case, they converge to the bound states of the NLS equation in the nonrelativistic limit.