Yu. Dabaghian, R. Blümel
Based on earlier work on regular quantum graphs we show that a large class of scaling quantum graphs with arbitrary topology are explicitly analytically solvable. This is surprising since quantum graphs are excellent models of quantum chaos and quantum chaotic systems are not usually explicitly analytically solvable.
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We present an exact analytical solution of the spectral problem of quasi one-dimensional scaling quantum graphs. Strongly stochastic in the classical limit, these systems are frequently employed as models of quantum chaos. We show that despite their classical stochasticity all scaling quantum graphs are explicitly solvable in the form $E_n=f(n)$, where $n$ is the sequence number of the energy level of the quantum graph and $f$ is a known function, which depends only on the physical and geometrical properties of the quantum graph. Our method of solution motivates a new classification scheme for…
The explicit solution to the spectral problem of quantum graphs is used to obtain the exact distributions of several spectral statistics, such as the oscillations of the quantum momentum eigenvalues around the average, $δk_{n}=k_{n}-\bar k_{n}$, and the nearest neighbor separations, $s_{n}=k_{n}-k_{n-1}$.
The explicit solution to the spectral problem of quantum graphs found recently in \cite{Anima}, is used to produce the exact periodic orbit theory description for the probability distributions of spectral statistics, including the distribution for the nearest neighbor separations, $s_{n}=k_{n}-k_{n-1}$, and the distribution of the spectral oscillations around the average, $δk_{n}=k_{n}-\bar k_{n}$.
In this paper, we study coherent exciton transport of continuous-time quantum walks on star graph. Exact analytical results of the transition probabilities are obtained by means of the Gram-Schmidt orthonormalization of the eigenstates. Our results show that the coherent exciton transport displays perfect revivals and strong localization on the initial node. When the initial excitation starts at the central node, the transport on star graph is equivalent to the transport on a complete graph of the same size.
Analytical derivation and extension of the anti-Kibble-Zurek scaling in the transverse field Ising model
本研究解析推导了高斯白噪声下横向场Ising模型的反Kibble-Zurek标度，发现大噪声时可用绝热近似替代微分方程求解，并确定了最小化缺陷密度的参数。
We show that all scaling quantum graphs are explicitly integrable, i.e. any one of their spectral eigenvalues $E_n$ is computable analytically, explicitly, and individually for any given $n$. This is surprising, since quantum graphs are excellent models of quantum chaos [see, e.g., T. Kottos and H. Schanz, Physica E {\bf 9}, 523 (2001)].
We study the Anderson transition in lattices with the connectivity of a random-regular graph. Our results indicate that fractal dimensions are continuous across the transition, but a discontinuity occurs in their derivatives, implying the non-ergodicity of the metal near the Anderson transition. A critical exponent $ν= 1.00 \pm0.02$ and critical disorder $W= 18.2\pm 0.1$ are found via a scaling approach. Our data support that the predictions of the relevant Gaussian Ensemble are only recovered at zero disorder.
Scaling of Computational Order Parameters in Rydberg Atom Graph States
本研究在里德伯原子模拟器上构建图态，利用始终开启的相互作用实现纠缠，并通过Clifford群逻辑运算构造计算序参量，以测量纠缠有效性并参数化有限尺寸标度，为量子设备计算能力测试提供途径。
The superior intrinsic properties of graphene have been a key research focus for the past few years. However, external components, such as metallic contacts, serve not only as essential probing elements, but also give rise to an effective electron cavity, which can form the basis for new quantum devices. In previous studies, quantum interference effects were demonstrated in graphene heterojunctions formed by a top gate. Here phase coherent transport behavior is demonstrated in a simple two terminal graphene structure with clearly-resolved Fabry-Perot oscillations in sub-100 nm devices. By aggr…
Many-body localization in a disordered system of interacting spins coupled by the long-range interaction $1/R^α$ is investigated combining analytical theory considering resonant interactions and a finite size scaling of exact numerical solutions with a number of spins $N$. The numerical results for a one-dimensional system are consistent with the general expectations of analytical theory for $d$-dimensional system including the absence of localization in the infinite system at $α<2d$ and a universal scaling of a critical energy disordering $W_{c} \propto N^{\frac{2d-α}{d}}$. %The finite size e…
We study the Anderson transition on a generic model of random graphs with a tunable branching parameter $1<K\le 2$, through large scale numerical simulations and finite-size scaling analysis. We find that a single transition separates a localized phase from an unusual delocalized phase which is ergodic at large scales but strongly non-ergodic at smaller scales. In the critical regime, multifractal wavefunctions are located on few branches of the graph. Different scaling laws apply on both sides of the transition: a scaling with the linear size of the system on the localized side, and an unusua…
The focusing of a propagating untrapped Bose-Einstein condensate is studied theoretically. We use a scaling solution method comprising a time-dependent scaling function to analytically examine the dynamics of a falling Bose-Einstein condensate in different regimes of propagation including the expansion and compression zones. Our model is based on the Gross-Pitaevskii equation which involves the interparticle interactions between atoms, and consequently their influence on the focused structures. We investigate the focused profile characteristic factors such as the resolution and peak density fo…
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