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在分數的量子霍爾效應中任意于固態化的模擬

程思誠

Published Jan 1, 1994• 0 citations
OpenAlex

Abstract

[[abstract]]在強磁場的作用下二維空間的電子氣體可 以形成不可壓縮的流體態,這種不可壓縮的流 體態祇能在某些特殊的Fillingfactor V/sub m/,V/sub m/可以是1/3, 1/5, 1/7, 1/9等值,而當Filling factorV .neq.V/sub m/時此二維電子氣體可以形成固體態, 此固體態的形成可由螢光光譜實驗中獲得驗證 ;可是光譜實驗無法明示此固體是由電子群還 是由任意子群所構成?吾人從實驗結果中分析 認為此固體應由任意子群所形成,為了證明吾 人的假設,吾人提出此計畫去計算任意子固體 的基態能,以便與電子固體的基態能比較,能量 低者即為系統在V.neq.V/sub m/時的狀態.

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[[abstract]]在強磁場的作用下二維空間的電子氣體可 以形成不可壓縮的流體態,這種不可壓縮的流 體態祇能在某些特殊的Fillingfactor V/sub m/,V/sub m/可以是1/3, 1/5, 1/7, 1/9等值,而當Filling factorV .neq.V/sub m/時此二維電子氣體可以形成固體態, 此固體態的形成可由螢光光譜實驗中獲得驗證 ;可是光譜實驗無法明示此固體是由電子群還 是由任意子群所構成?吾人從實驗結果中分析 認為此固體應由任意子群所形成,為了證明吾 人的假設,吾人提出此計畫去計算任意子固體 的基態能,以便與電子固體的基態能比較,能量 低者即為系統在V.neq.V/sub m/時的狀態.
A verified Kubo-Martin-Schwinger (KMS) relation, after a drive has ceased, is not sufficient evidence to prove equilibrium. We demonstrate this in a large-NNN large-qqq Sachdev-Ye-Kitaev (SYK) quench protocol. Although all post-quench fermion correlators are exactly thermal, a second quench back to the initial Hamiltonian reveals hidden memory of the initial state. It is encoded in correlators connecting to times before the first quench. This memory is an extensive nonequilibrium (NEQ) witness with its decay rate being the Lyapunov exponent λLλ_LλL​. Thus λLλ_LλL​ sets the rate at which the state becomes effectively indistinguishable from a Gibbs state. Despite being a unitary interacting many-body system, the complete NEQ real-time evolution is obtained exactly in the large-NNN, large-qqq limit, making the setup ideal for analytically studying thermalization.
Non-equilibrium (NEQ) many-body dynamics are ubiquitous, ranging from glassy systems to the emergence of structure in the early universe. Ultracold atomic gases provide an ideal, highly controllable platform for studying these phenomena, and this thesis presents a comprehensive investigation into the NEQ dynamics of coupled bilayer two-dimensional (2D) Bose gases. In this thesis, we numerically investigate Josephson effects in bilayer 2D superfluids using classical-field simulations. We show that the system exhibits damped Josephson oscillations and macroscopic quantum self-trapping, and we discuss the associated excitations that emerge in the system. We then experimentally study the phase-ordering dynamics following a coupling quench that drives the system from a disordered to an ordered phase, realized using a well-controlled multiple-radio-frequency (MRF) dressed double-well potential. The resulting NEQ dynamics are probed using matter-wave interferometry, which provides direct access to correlation functions and vortex excitations of the relative-phase mode. Our results demonstrate that the system undergoes universal dynamics in the form of diffusion-type coarsening, in excellent agreement with classical-field numerical simulations. This work broadens the understanding of NEQ and universal dynamics, and the methods presented here serve as a novel and highly tunable approach for exploring a wide range of NEQ dynamics.
推导了非线性光子晶体线缺陷波导中抽运光群速度与光参量放大增益的理论模 型. 理论结果表明, 慢光抽运可以增强光参量放大效应. 为获得相同的增益, 当波导长度不变时, 慢光波导所需的抽运光功率可以减少为普通波导的(vgn/c)2; 当抽运光功率不变时, 慢光波导所需的长度可以减少为普通波导的(vgn/c)2, 其中n为普通波导的材料折射率, vg为慢光波导的群速度, c为真空中的光速. 数值计算结果验证了我们的理论预测.