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Spectral statistics of driven Bose-Hubbard models 驱动型玻色-哈伯德模型的光谱统计
IF 2.4 3区 物理与天体物理 Q2 MECHANICS Pub Date : 2024-06-11 DOI: 10.1088/1742-5468/ad4e26
Jesús Mateos, Fernando Sols and Charles Creffield
We study the spectral statistics of a one-dimensional Bose–Hubbard model subjected to kinetic driving; a form of Floquet engineering where the kinetic energy is periodically driven in time with a zero time-average. As the amplitude of the driving is increased, the ground state of the resulting flat-band system passes from the Mott insulator regime to an exotic superfluid. We show that this transition is accompanied by a change in the system’s spectral statistics from Poisson to GOE-type. Remarkably, and unlike in the conventional Bose–Hubbard model which we use as a benchmark, the details of the GOE statistics are sensitive to the parity of both the particle number and the lattice sites. We show how this effect arises from a hidden symmetry of the Hamiltonian produced by this form of Floquet driving.
我们研究了受到动能驱动的一维玻色-哈伯德模型的频谱统计;动能驱动是弗洛凯工程的一种形式,其动能在时间上周期性地驱动,时间平均值为零。随着驱动振幅的增加,所产生的平带系统的基态从莫特绝缘体状态转变为奇异的超流体。我们的研究表明,这一转变伴随着系统谱统计量从泊松型到 GOE 型的变化。值得注意的是,与我们用作基准的传统玻色-哈伯德模型不同,GOE统计的细节对粒子数和晶格位点的奇偶性都很敏感。我们展示了这种效应是如何从这种形式的弗洛凯驱动所产生的哈密顿隐含对称性中产生的。
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引用次数: 0
Entanglement Hamiltonian in the non-Hermitian SSH model 非ermitian SSH 模型中的纠缠哈密顿
IF 2.4 3区 物理与天体物理 Q2 MECHANICS Pub Date : 2024-06-10 DOI: 10.1088/1742-5468/ad4860
Federico Rottoli, Michele Fossati, Pasquale Calabrese
Entanglement Hamiltonians provide the most comprehensive characterisation of entanglement in extended quantum systems. A key result in unitary quantum field theories is the Bisognano-Wichmann theorem, which establishes the locality of the entanglement Hamiltonian. In this work, our focus is on the non-Hermitian Su-Schrieffer-Heeger (SSH) chain. We study the entanglement Hamiltonian both in a gapped phase and at criticality. In the gapped phase we find that the lattice entanglement Hamiltonian is compatible with a lattice Bisognano-Wichmann result, with an entanglement temperature linear in the lattice index. At the critical point, we identify a new imaginary chemical potential term absent in unitary models. This operator is responsible for the negative entanglement entropy observed in the non-Hermitian SSH chain at criticality.
纠缠哈密顿量为扩展量子系统中的纠缠提供了最全面的描述。比索纳诺-维赫曼定理是单元量子场论的一个关键结果,它确立了纠缠哈密顿的局域性。在这项工作中,我们的重点是非赫米特 Su-Schrieffer-Heeger (SSH) 链。我们研究了间隙阶段和临界状态下的纠缠哈密顿。在间隙阶段,我们发现晶格纠缠哈密顿与晶格比索纳诺-维奇曼结果相容,纠缠温度与晶格指数成线性关系。在临界点,我们发现了一个新的虚化学势项,它在单元模型中是不存在的。这个算子是非赫米特 SSH 链在临界点观察到的负纠缠熵的原因。
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引用次数: 0
Impact of dephasing probes on incommensurate lattices 去相位探针对不对称晶格的影响
IF 2.4 3区 物理与天体物理 Q2 MECHANICS Pub Date : 2024-06-10 DOI: 10.1088/1742-5468/ad4861
Bishal Ghosh, Sandipan Mohanta, Manas Kulkarni, Bijay Kumar Agarwalla
We investigate open quantum dynamics for a one-dimensional incommensurate Aubry–André–Harper lattice chain, a part of which is initially filled with electrons and is further connected to dephasing probes at the filled lattice sites. This setup is akin to a step-initial configuration where the non-zero part of the step is subjected to dephasing. We investigate the quantum dynamics of local electron density, the scaling of the density front as a function of time both inside and outside of the initial step, and the growth of the total number of electrons outside the step. We analyze these quantities in all three regimes, namely, the de-localized, critical, and localized phases of the underlying lattice. Outside the initial step, we observe that the density front spreads according to the underlying nature of single-particle states of the lattice, for both the de-localized and critical phases. For the localized phase, the spread of the density front hints at a logarithmic behavior in time that has no parallel in the isolated case (i.e. in the absence of probes). Inside the initial step, due to the presence of the probes, the density front spreads in a diffusive manner for all the phases. This combination of rich and different dynamical behavior, outside and inside the initial step, results in the emergence of mixed dynamical phases. While the total occupation of electrons remains conserved, the value outside or inside the initial step turns out to have a rich dynamical behavior. Our work is widely adaptable and has interesting consequences when disordered/quasi-disordered systems are subjected to a thermodynamically large number of probes.
我们研究了一维不相容奥布里-安德烈-哈珀晶格链的开放量子动力学,该晶格链的一部分最初由电子填充,并进一步与填充晶格位点的去相探针相连。这种设置类似于阶跃初始构型,其中阶跃的非零部分受到去相作用。我们研究了局部电子密度的量子动力学、初始阶梯内外密度前沿随时间变化的缩放以及阶梯外电子总数的增长。我们在底层晶格的去局域、临界和局域三种状态下分析了这些量。我们观察到,在初始阶跃外,密度前沿会根据晶格单粒子态的基本性质进行扩散,包括去局域阶段和临界阶段。在局部阶段,密度前沿的扩散暗示了时间上的对数行为,而这种行为在孤立情况下(即在没有探测器的情况下)是不存在的。在初始阶段,由于探针的存在,密度前沿在所有阶段都以扩散的方式扩散。初始阶梯内外丰富而不同的动力学行为相结合,导致了混合动力学阶段的出现。虽然电子的总占有率保持不变,但初始阶梯内外的值却具有丰富的动力学行为。我们的工作具有广泛的适应性,当无序/准无序系统受到大量热力学探针的作用时,会产生有趣的结果。
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引用次数: 0
Entangled multiplets, asymmetry, and quantum Mpemba effect in dissipative systems 耗散系统中的纠缠多子、不对称和量子姆彭巴效应
IF 2.4 3区 物理与天体物理 Q2 MECHANICS Pub Date : 2024-06-10 DOI: 10.1088/1742-5468/ad4537
Fabio Caceffo, Sara Murciano, Vincenzo Alba
Recently, the entanglement asymmetry emerged as an informative tool to understand dynamical symmetry restoration in out-of-equilibrium quantum many-body systems after a quantum quench. For integrable systems the asymmetry can be understood in the space-time scaling limit via the quasiparticle picture, as it was pointed out in Ares et al (2023 Nat. Commun.14 2036) . However, a quasiparticle picture for quantum quenches from generic initial states was still lacking. Here we conjecture a full-fledged quasiparticle picture for the charged moments of the reduced density matrix, which are the main ingredients to construct the asymmetry. Our formula works for quenches producing entangled multiplets of an arbitrary number of excitations. We benchmark our results in the XX spin chain. First, by using an elementary approach based on the multidimensional stationary phase approximation we provide an ab initio rigorous derivation of the dynamics of the charged moments for the quench treated in Ares et al (2023 SciPost Phys.15 089). Then, we show that the same results can be straightforwardly obtained within our quasiparticle picture. As a byproduct of our analysis, we obtain a general criterion ensuring a vanishing entanglement asymmetry at long times. Next, by using the Lindblad master equation, we study the effect of gain and loss dissipation on the entanglement asymmetry. Specifically, we investigate the fate of the so-called quantum Mpemba effect (QME) in the presence of dissipation. We show that dissipation can induce QME even if unitary dynamics does not show it, and we provide a quasiparticle-based interpretation of the condition for the QME.
最近,纠缠不对称性成为理解量子淬火后失衡量子多体系统动态对称性恢复的一种信息工具。对于可积分系统,正如阿瑞斯等人(2023 Nat.然而,从一般初始态出发的量子淬灭仍然缺乏准粒子图景。在这里,我们为还原密度矩阵的带电矩猜想了一个完整的类粒子图景,它们是构建不对称的主要成分。我们的公式适用于产生任意数量激元纠缠多子的淬火。我们在 XX 自旋链中对我们的结果进行了基准测试。首先,通过使用基于多维静止相近似的基本方法,我们对阿瑞斯等人(2023 SciPost Phys.15.089)所处理的淬火的带电矩动力学进行了严格的ab initio推导。然后,我们证明在我们的准粒子图中可以直接得到相同的结果。作为我们分析的副产品,我们得到了一个通用标准,确保纠缠不对称在长时间内消失。接下来,我们利用林德布拉德主方程,研究增益和损耗耗散对纠缠不对称性的影响。具体来说,我们研究了存在耗散时所谓量子姆彭巴效应(QME)的命运。我们证明,即使单元动力学没有显示出耗散,耗散也能诱发 QME,并对 QME 的条件提供了基于准粒子的解释。
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引用次数: 0
Minimum connected dominating set and backbone of a random graph 随机图的最小连接支配集和骨干图
IF 2.4 3区 物理与天体物理 Q2 MECHANICS Pub Date : 2024-06-07 DOI: 10.1088/1742-5468/ad4026
Yusupjan Habibulla, Hai-Jun Zhou
We study the minimum dominating set problem as a representative combinatorial optimization challenge with a global topological constraint. The requirement that the backbone induced by the vertices of a dominating set should be a connected subgraph makes the problem rather nontrivial to investigate by statistical physics methods. Here, we convert this global connectivity constraint into a set of local vertex constraints and build a spin glass model with only five coarse-grained vertex states. We derive a set of coarse-grained belief-propagation equations and obtain theoretical predictions of the relative sizes of the minimum dominating sets for regular random and Erdös–Rényi random graph ensembles. We also implement an efficient message-passing algorithm to construct close-to-minimum connected dominating sets and backbone subgraphs for single random graph instances. Our theoretical strategy may also be applicable to some other global topological constraints.
我们研究的最小支配集问题是一个具有代表性的组合优化难题,它具有全局拓扑约束。支配集的顶点所引起的主干应该是一个连通的子图,这一要求使得用统计物理方法研究这个问题变得相当不容易。在这里,我们将这种全局连通性约束转换成一组局部顶点约束,并建立了一个只有五个粗粒度顶点状态的自旋玻璃模型。我们推导出一组粗粒度信念传播方程,并获得了常规随机图集和埃尔德斯-雷尼随机图集最小支配集相对大小的理论预测。我们还实现了一种高效的信息传递算法,为单个随机图实例构建接近最小连接的支配集和骨干子图。我们的理论策略也可能适用于其他一些全局拓扑约束。
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引用次数: 0
Effect of global shrinkage parameter of horseshoe prior in compressed sensing 压缩传感中马蹄形先验全局收缩参数的影响
IF 2.4 3区 物理与天体物理 Q2 MECHANICS Pub Date : 2024-05-28 DOI: 10.1088/1742-5468/ad3195
Yasushi Nagano and Koji Hukushima
This study investigates the effect of the global shrinkage parameter τ of a horseshoe prior, one of the global–local shrinkage priors, on linear regression in sparse signal processing. Statistical mechanics methods are employed to examine the accuracy of signal estimation. The phase diagram of the success and failure of signal recovery in noiseless compressed sensing with varying τ is discussed from the viewpoint of dynamic characterization of approximate message passing (AMP) as a solving algorithm and static characterization of the free-energy landscape. It is found that there exists a parameter region where the AMP algorithm can hardly recover the true signal, even though the true signal is locally stable. The analysis of the free-energy landscape also provides important insight into the optimal choice of τ.
本研究探讨了马蹄先验(全局-局部收缩先验之一)的全局收缩参数 τ 对稀疏信号处理中线性回归的影响。研究采用了统计力学方法来检验信号估计的准确性。从近似信息传递(AMP)作为一种求解算法的动态特征和自由能谱的静态特征的角度,讨论了在τ变化的无噪声压缩传感中信号恢复成功与失败的相图。研究发现,存在一个 AMP 算法难以恢复真实信号的参数区域,即使真实信号是局部稳定的。对自由能谱的分析还为 τ 的最佳选择提供了重要启示。
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引用次数: 0
Pinning-depinning transitions in two classes of discrete elastic-string models in (2+1)-dimensions (2+1)维两类离散弹性弦模型中的针化-去针化转变
IF 2.4 3区 物理与天体物理 Q2 MECHANICS Pub Date : 2024-05-28 DOI: 10.1088/1742-5468/ad4af9
Yongxin Wu and Hui Xia
The pinning-depinning phase transitions of interfaces for two classes of discrete elastic-string models are investigated numerically. In the (1+1)-dimensions, we revisit these two elastic-string models with slight modification to the growth rule, and compare the estimated values with the previous numerical and experimental results. For the (2+1)-dimensional case, we perform extensive simulations on pinning-depinning transitions in these discrete models with quenched disorder. For full comparisons in the physically relevant spatial dimensions, we also perform numerically two distinct universality classes, including the quenched Edwards–Wilkinson, and the quenched Kardar–Parisi–Zhang equations with and without external driving forces. The critical exponents of these systems in the presence of quenched disorder are numerically estimated. Our results show that the critical exponents satisfy scaling relations well, and these two discrete elastic-string models do not fall into the existing universality classes. In order to visually comparisons of these discrete systems with quenched disorder in the (2+1)-dimensional cases, we present surface morphologies with various external driving forces during the saturated time regimes. The relationships between surface morphologies, scaling exponents and correlation length are also revealed.
我们用数值方法研究了两类离散弹性弦模型的界面针化-去针化相变。在(1+1)维情况下,我们对这两种弹性弦模型的生长规则稍作修改后重新进行了研究,并将估计值与之前的数值和实验结果进行了比较。对于(2+1)维情况,我们对这些具有淬火无序性的离散模型中的针销-脱销转变进行了大量模拟。为了在物理相关的空间维度上进行全面比较,我们还对两个不同的普遍性类别进行了数值模拟,包括淬火爱德华-威尔金森方程和淬火卡达尔-帕里西-张方程(有无外部驱动力)。我们对这些系统在淬火无序情况下的临界指数进行了数值估算。我们的结果表明,临界指数很好地满足了比例关系,而且这两个离散弹性弦模型不属于现有的普遍性类别。为了直观地比较这些离散系统在(2+1)维情况下的淬火无序性,我们展示了饱和时间内各种外部驱动力作用下的表面形态。我们还揭示了表面形态、缩放指数和相关长度之间的关系。
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引用次数: 0
Weak (non)conservation and stochastic dynamics of angular momentum 角动量的弱(非)守恒和随机动力学
IF 2.4 3区 物理与天体物理 Q2 MECHANICS Pub Date : 2024-05-27 DOI: 10.1088/1742-5468/ad3cce
Ashot Matevosyan
Angular momentum conservation influences equilibrium statistical mechanics, leading to a generalized microcanonical density for an isolated system and a generalized Gibbs density for a weakly coupled system. We study the stochastic decay of angular momentum due to the weakly imperfect rotational symmetry of the external potential that confines the isolated many-particle system. We present a mesoscopic description of the system, deriving Langevin and Fokker–Planck equations, which are consistent with equilibrium statistical mechanics when rotational symmetry is maintained. When the symmetry is weakly violated, we formulate a coarse-grained stochastic differential equation governing the decay of total angular momentum over time. To validate our analytical predictions, we conduct numerical simulations of the microcanonical ensemble, an isolated system undergoing thermalization due to weak two-body interactions. Our coarse-grained Langevin equation accurately characterizes both the decay of the angular momentum and its fluctuations in a steady state. Furthermore, we estimate the parameters of our mesoscopic model directly from simulations, providing insights into the dissipative phenomenological coefficients, such as friction. More generally, this study contributes to a deeper understanding of the behavior of the integrals of motion when the corresponding symmetry is weakly violated.
角动量守恒影响着平衡统计力学,导致孤立系统的广义微观调控密度和弱耦合系统的广义吉布斯密度。我们研究了由于限制孤立多粒子系统的外部势的弱不完全旋转对称性而导致的角动量随机衰减。我们对该系统进行了介观描述,推导出朗格文方程和福克-普朗克方程,当旋转对称性保持不变时,这些方程与平衡统计力学一致。当对称性受到微弱破坏时,我们提出了一个粗粒度随机微分方程来控制总角动量随时间的衰减。为了验证我们的分析预测,我们对微经典集合进行了数值模拟,微经典集合是一个孤立的系统,由于弱的双体相互作用而正在经历热化。我们的粗粒度朗格文方程准确地描述了角动量的衰减及其在稳定状态下的波动。此外,我们直接从模拟中估算了介观模型的参数,为摩擦等耗散现象学系数提供了见解。更广泛地说,这项研究有助于加深对相应对称性被弱违反时运动积分行为的理解。
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引用次数: 0
Thermal conductivity in one-dimensional nonlinear disordered lattices: two kinds of scattering effects of hard-type and soft-type anharmonicities 一维非线性无序晶格中的导热性:硬型和软型非谐波的两种散射效应
IF 2.4 3区 物理与天体物理 Q2 MECHANICS Pub Date : 2024-05-27 DOI: 10.1088/1742-5468/ad4025
Jianjin Wang, Chi Xiong and Daxing Xiong
Amorphous solids can be theoretically modeled by anharmonic disordered lattices, but most of the theoretical studies on thermal conductivity in such lattices only consider hard-type (HT) anharmonicity. In this study, we investigate the thermal conductivity κ of one-dimensional disordered lattices with both HT and soft-type (ST) anharmonic on-site potentials. Our results from molecular dynamics simulations and the quasi-harmonic Green–Kubo (QHGK) method show that while the HT model exhibits non-monotonic dependence of κ on anharmonicity, the ST model shows a monotonically increasing trend. This trend provides a novel approach to enhancing thermal conductivity in disordered systems. Additionally, the QHGK predictions for κ in the HT model are consistent with simulation results over a wide range of anharmonicity values; however, for the ST model, deviations appear as the anharmonicity becomes softer. This peculiar feature may be attributed to delocalization effects being dominant in contrast to the competing roles played by both delocalization and localization effects observed in the HT model.
无定形固体可以通过非谐波无序晶格进行理论建模,但有关此类晶格导热性的理论研究大多只考虑了硬型(HT)非谐波性。在本研究中,我们研究了同时具有 HT 和软型(ST)非谐现场势的一维无序晶格的热导率 κ。我们通过分子动力学模拟和准谐波格林-库勃(QHGK)方法得出的结果表明,HT 模型的κ与非谐波性呈现非单调依赖关系,而 ST 模型则呈现单调上升趋势。这种趋势为提高无序系统的热导率提供了一种新方法。此外,HT 模型中 QHGK 对 κ 的预测在很大的非谐波值范围内与模拟结果一致;然而,对于 ST 模型,当非谐波变得更柔和时就会出现偏差。这一奇特的特征可能是由于脱局域效应占主导地位,而在 HT 模型中则观察到脱局域效应和局域效应同时发挥作用。
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引用次数: 0
Constant speed random particles spontaneously confined on the surface of an expanding sphere 自发限制在膨胀球体表面的恒速随机粒子
IF 2.4 3区 物理与天体物理 Q2 MECHANICS Pub Date : 2024-05-27 DOI: 10.1088/1742-5468/ad4023
Maurizio Serva
The particles that we describe here can only move at the speed of light c in three-dimensional space. The velocity, which randomly but continuously changes direction, can be represented as a point on the surface of a sphere of constant radius c, and its trajectories may only connect points of this variety. The Wiener process that we use to describe the velocity dynamics on the surface of the sphere is anisotropic since the infinitesimal variation of the velocity is not only always orthogonal to the velocity itself (which guarantees a constant speed), but also to the position. This choice for the infinitesimal variation of the velocity is the one that best slows down the diffusion of particles in space by random motion at the speed of light. As a result of these dynamics, the position of the particles spontaneously remain confined on the surface of an expanding sphere whose radius increases, for large times, as the square root of time.
我们在这里描述的粒子只能以光速 c 在三维空间中运动。速度随机但持续地改变方向,可以表示为半径为 c 的恒定球体表面上的一个点,其轨迹只能连接这个种类的点。我们用来描述球面上速度动态的维纳过程是各向异性的,因为速度的无穷小变化不仅总是与速度本身正交(这保证了速度恒定),而且也与位置正交。对速度无穷小变化的这种选择最能减缓粒子在空间中以光速随机运动的扩散。由于这些动力学原理,粒子的位置自发地限制在一个不断扩大的球体表面上,这个球体的半径在较大的时间内随着时间的平方根而增加。
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引用次数: 0
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Journal of Statistical Mechanics: Theory and Experiment
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