Nicolas Cherroret, Andreas Buchleitner
We show that the entanglement of an initially frequency-entangled photon pair propagating through a disordered scattering medium can be read off in transmission from the coincidence counting rate. The very same quantity also encodes the Thouless time of the medium.
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We investigate disordered graphene with strong long-range impurities. Contrary to the common belief that delocalization should persist in such a system against any disorder, as the system is ex-pected to be equivalent to a disordered two-dimensional Dirac Fermionic system, we find that states near the Dirac points are localized for sufficiently strong disorder and the transition between the localized and delocalized states is of Kosterlitz-Thouless type. Our results show that the transition originates from bounding and unbounding of local current vortices.
The Berezinski-Kosterlitz-Thouless transition is a unique two dimensional phase transition, separating two phases with exponentially and power-law decaying correlations, respectively. In disordered systems, these correlations propagate along favorable paths, with the transition marking the point where global coherence is lost. Here we propose an experimental method to probe locally these particular paths in superconducting thin films, which exhibit this transition, and demonstrate theoretically that close to the transition the coherence propagate along a ramified network, reminiscent of a perc…
Absence of disordered Thouless pumps at finite frequency
该研究探究无序与有限频率的共同作用对Thouless泵的影响，揭示非绝热跃迁导致泵浦速率指数级慢衰减，预测了绝热极限下临界无序强度处的泵浦速率标度，结果可在超冷原子与光子平台实验验证。
We study the phase transition between conducting and insulating states taking place in disordered multi-channel Luttinger liquids with inter-channel interactions. We derive renormalisation group equations which are perturbative in disorder but nonperturbative in interaction. In the vicinity of the simultaneous phase transition in all channels, these equations become a set of coupled Berezinskii--Kosterlitz--Thouless equations, which we analyze within two models: an array of identical wires and a two-channel model with distinct channels. We show that a competition between disorder and interacti…
Berezinskii-Kosterlitz-Thouless localization-localization transitions in disordered two-dimensional quantized quadrupole insulators
本文研究了二维量子化四极绝缘体中从拓扑角态到正常Anderson局域态的局域-局域转变，通过有限尺寸标度分析揭示了其Hermitian与非Hermitian系统均具有Berezinskii-Kosterlitz-Thouless类型的临界特征。
We demonstrate a three-dimensional Kosterlitz-Thouless (KT) transition in the random field XY model driven out of thermal equilibrium. By employing the spin-wave approximation and functional renormalization group approach, in the weak disorder regime, the three-dimensional driven random field XY model is found to exhibit a quasi-long-range order phase, wherein the correlation function shows power-law decay with a non-universal exponent that depends on the disorder strength. This result is consistent with that reported in a previous numerical study. We further develop a phenomenological theory …
Spectral statistics of disordered systems encode Thouless and Heisenberg time scales whose ratio determines whether the system is chaotic or localized. Identifying similarities between system size and disorder strength scaling of Thouless time for disordered quantum many-body systems with results for 3D and 5D Anderson models, we argue that the two-parameter scaling breaks down in the vicinity of the transition to the localized phase signalling subdiffusive dynamics.
We present a numerical study of the quasi-particle density of states (DoS) of two-dimensional d-wave superconductors in the presence of disorder, focusing on the influence of the range of the disorder. We find qualitatively different behavior for smooth and short-ranged disorder. In the former case, we find power law scaling of the DoS with an exponent depending on the strength of the disorder and the superconducting order parameter in quantitative agreement with the theory of Nersesyan {\em et al.}. For strong disorder, a qualitative change to an energy independent DoS occurs. In contrast, fo…
We experimentally investigate spectral statistics in Anderson localization in two-dimensional amorphous disordered media. Intensity distributions captured over an ultrabroad wavelength range of $\sim 600$~nm and averaged over numerous configurations provided the Ioffe-Regel parameter to be $\sim2.5$ over the investigated wavelength range. The spectra of the disordered structures provided access to several quasimodes, whose widths and separations allowed to directly estimate the optical Thouless conductance $g_{Th}$, consistently observed to be below unity. The probability distribution of $g_{T…
We model the QCD Dirac operator as a power-law random banded matrix (RBM) with the appropriate chiral symmetry. Our motivation is the form of the Dirac operator in a basis of instantonic zero modes with a corresponding gauge background of instantons. We compare the spectral correlations of this model to those of an instanton liquid model (ILM) and find agreement well beyond the Thouless energy. In the bulk of the spectrum the (dimensionless) Thouless energy of the RBM scales with the square root of system size in agreement with the ILM and chiral perturbation theory. Near the origin the scalin…
Machine learning analysis of dimensional reduction conjecture for nonequilibrium Berezinskii-Kosterlitz-Thouless transition in three dimensions
利用机器学习技术，通过训练神经网络区分三维驱动随机场XY模型快照与二维纯XY模型时空轨迹，证实了非平衡Berezinskii-Kosterlitz-Thouless相变的降维猜想。
Disordered quantum systems feature an energy scale know as the Thouless energy. For energy ranges below this scale, the properties of the energy spectrum can be described by random matrix theory. Above this scale a different behavior sets in. For a metallic system it has been long ago shown by Altshuler and Shklovskii that the number variance should increase as a power law with a power dependent only on the dimensionality of the system. Although tantalizing hints for this behavior have been seen in previous numerical studies, it is quite difficult to verify this prediction using the standard l…
Hierarchy of timescales in a disordered spin-$1/2$ XX ladder
研究无序自旋-1/2 XX链中松弛时标层次，揭示自旋扩散快于能量扩散的特性。
Thermal and many-body localized phases are separated by a dynamical phase transition of a new kind. We analyze the distribution of off-diagonal matrix elements of local operators across the many-body localization transition (MBLT) in a disordered spin chain, and use it to characterize the breakdown of the eigenstate thermalization hypothesis and to extract the many-body Thouless energy. We find a wide critical region around the MBLT, where Thouless energy becomes smaller than the level spacing, while matrix elements show critical dependence on the energy difference. In the same region, matrix …
Possible Topological Decoherence Transition in Relativistic Electron Beams Propagating through Coulomb-Disordered Media
研究探讨了相对论电子束在库仑无序介质中传播时的拓扑退相干相变，通过有效二维紧凑相位场和格格斯自由场作用分析，发现临界样本厚度可能引发Berezinskii-Kosterlitz-Thouless相变，区分代数退相干与自由涡流增殖导致的指数退相干。
We present angular-resolved correlation measurements between photons after propagation through a three-dimensional disordered medium. The multiple scattering process induces photon correlations that are directly measured for light sources with different photon statistics. We find that multiple scattered photons between different angular directions with angles much larger than the average speckle width are strongly correlated. The time dependence of the angular photon correlation function is investigated and the coherence time of the light source is determined. Our results are found to be in ex…
We study dephasing by electron interactions in a small disordered quasi-one dimensional (1D) ring weakly coupled to leads. We use an influence functional for quantum Nyquist noise to describe the crossover for the dephasing time $\Tph (T)$ from diffusive or ergodic 1D ($ \Tph^{-1} \propto T^{2/3}, T^{1}$) to 0D behavior ($\Tph^{-1} \propto T^{2}$) as $T$ drops below the Thouless energy. The crossover to 0D, predicted earlier for 2D and 3D systems, has so far eluded experimental observation. The ring geometry holds promise of meeting this longstanding challenge, since the crossover manifests it…
Disordered monitored free fermions
本文研究了连续监控下随机势场中的自由费米子，发现临界相在有限无序度下保持稳定且符合BKT普适类，同时监控会破坏局域化，为在电子系统中探测相变和量子控制开辟了新途径。
We present a detailed theory for finite-frequency conductivities Re$[σ_{αβ}(ω)]$ of quantum Hall stripes, which form at Landau level $N\geq 2$ close to half filling, in the presence of weak Gaussian disorder. We use an effective elastic theory to describe the low-energy dynamics of the stripes with the dynamical matrix being determined through matching the density-density correlation function obtained in the microscopic time-dependent Hartree-Fock approximation. We then apply replicas and the Gaussian variational method to deal with the disorder. Within this method, a set of saddle point equat…
Trimers, pairs and localisation on disordered random graphs
本文研究图上成对动力学如何涌现群体交互（三体束缚态），发现无序图上三体比单粒子和二体更易局域化，且其玻璃转变阈值远低于单粒子体系，表明群体交互对异质性更敏感。
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