Krylov complexity in saddle-dominated scrambling Bhattacharjee, Budhaditya; Cao, Xiangyu; Nandy, Pratik ...
The journal of high energy physics,
05/2022, Letnik:
2022, Številka:
5
Journal Article
Recenzirano
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A
bstract
In semi-classical systems, the exponential growth of the out-of-time-order correlator (OTOC) is believed to be the hallmark of quantum chaos. However, on several occasions, it has been ...argued that, even in integrable systems, OTOC can grow exponentially due to the presence of unstable saddle points in the phase space. In this work, we probe such an integrable system exhibiting saddle-dominated scrambling through Krylov complexity and the associated Lanczos coefficients. In the realm of the universal operator growth hypothesis, we demonstrate that the Lanczos coefficients follow the linear growth, which ensures the exponential behavior of Krylov complexity at early times. The linear growth arises entirely due to the saddle, which dominates other phase-space points even away from itself. Our results reveal that the exponential growth of Krylov complexity can be observed in integrable systems with saddle-dominated scrambling and thus need not be associated with the presence of chaos.
A
bstract
We study the operator growth in open quantum systems with dephasing dissipation terms, extending the Krylov complexity formalism of
1
. Our results are based on the study of the ...dissipative
q
-body Sachdev-Ye-Kitaev (SYK
q
) model, governed by the Markovian dynamics. We introduce a notion of “operator size concentration” which allows a diagrammatic and combinatorial proof of the asymptotic linear behavior of the two sets of Lanczos coefficients (
a
n
and
b
n
) in the large
q
limit. Our results corroborate with the semi-analytics in finite
q
in the large
N
limit, and the numerical Arnoldi iteration in finite
q
and finite
N
limit. As a result, Krylov complexity exhibits exponential growth following a saturation at a time that grows logarithmically with the inverse dissipation strength. The growth of complexity is suppressed compared to the closed system results, yet it upper bounds the growth of the normalized out-of-time-ordered correlator (OTOC). We provide a plausible explanation of the results from the dual gravitational side.
A Universal Operator Growth Hypothesis Parker, Daniel E.; Cao, Xiangyu; Avdoshkin, Alexander ...
Physical review. X,
10/2019, Letnik:
9, Številka:
4
Journal Article
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We present a hypothesis for the universal properties of operators evolving under Hamiltonian dynamics in many-body systems. The hypothesis states that successive Lanczos coefficients in the continued ...fraction expansion of the Green’s functions grow linearly with rateαin generic systems, with an extra logarithmic correction in 1D. The rateα—an experimental observable—governs the exponential growth of operator complexity in a sense we make precise. This exponential growth prevails beyond semiclassical or large-Nlimits. Moreover,αupper bounds a large class of operator complexity measures, including the out-of-time-order correlator. As a result, we obtain a sharp bound on Lyapunov exponentsλL≤2α, which complements and improves the known universal low-temperature boundλL≤2πT. We illustrate our results in paradigmatic examples such as nonintegrable spin chains, the Sachdev-Ye-Kitaev model, and classical models. Finally, we use the hypothesis in conjunction with the recursion method to develop a technique for computing diffusion constants.
Cadmium, a heavy metal pollutant in industrial production, is found in air, water and soil, which is harmful to human health and can lead to diseases, such as asthma, lung cancer, and emphysema. In ...this study, the toxicity of cadmium on human bronchial epithelial cells (BEAS-2B) was investigated. Cell viability, mitochondrial membrane potential, reactive oxygen species (ROS) level, apoptosis and the related signaling pathways were detected with MTT assay, Rhodamine staining, DCFH-DA staining, Hoechst33258 staining and Western blot methods respectively. The results showed that the cell viability decreased, the mitochondrial membrane potential declined, ROS was accumulated and apoptotic rate raised in BEAS-2B cells. Meanwhile, the expression of B-cell lymphoma-2 (Bcl-2) was downregulated, while the expression of Bcl-2-associated X protein (Bax) and the cleaved caspase-3 was upregulated, which indicated mitochondria-mediated intrinsic apoptosis pathway was activated. Furthermore, the phosphorylation of JNK, ERK and p38 was enhanced respectively, which manifested that MAPK signaling pathways were activated. Therefore, it could be concluded that cadmium could increase intracellular ROS, result in cellular oxidative stress, activate JNK, ERK and p38 MAPK pathways and ultimately lead to apoptosis of BEAS-2B cells by activating mitochondria-mediated intrinsic apoptosis pathway. This study provided useful information to elucidate the toxicity of cadmium and revealed the possible mechanism for the occurrence of lung disease induced by cadmium.
Cadmium increased the reactive oxygen species (ROS) generation, induced cell apoptosis and activated MAPK cell signaling pathway. Meanwhile, cadmium accelerated mitochondria damage and activated mitochondria-mediated intrinsic apoptosis pathway in BEAS-2B cells. Display omitted
•Cadmium induced the accumulation of ROS and cell apoptosis in BEAS-2B.•Cadmium activated MAPK pathways, including JNK, ERK and p38 MAPK.•Cadmium decreased mitochondrial membrane potential, activated the apoptosis pathway.
A dual-frequency reconfigurable reflectarray (RRA) is proposed and verified experimentally. The RRA consists of 1600 electronically controllable elements. By integrating only a single PIN diode, the ...proposed element is capable to operate at two working frequencies with 1-bit phase resolution. The dual-frequency mechanism is explained through the mode analysis, and a parametric study is performed to provide guidelines for determining the two working frequencies. As an example, a 1600-element RRA prototype is realized by assembling five identical 8 x 40 subarrays. An field programmable gate array control board is used to achieve real-time phase control of each element individually. The experimental results show that the broadside gains of the RRA are 29.3 and 30.8 dBi at 11.1 and 14.3 GHz, respectively. Excellent beam scanning performance is also obtained at both frequencies.
Superconductor-ferromagnet interfaces in two-dimensional heterostructures present a unique opportunity to study the interplay between superconductivity and ferromagnetism. The realization of such ...nanoscale heterostructures in van der Waals (vdW) crystals remains largely unexplored due to the challenge of making atomically-sharp interfaces from their layered structures. Here, we build a vdW ferromagnetic Josephson junction (JJ) by inserting a few-layer ferromagnetic insulator Cr
Ge
Te
into two layers of superconductor NbSe
. The critical current and corresponding junction resistance exhibit a hysteretic and oscillatory behavior against in-plane magnetic fields, manifesting itself as a strong Josephson coupling state. Also, we observe a central minimum of critical current in some JJ devices as well as a nontrivial phase shift in SQUID structures, evidencing the coexistence of 0 and π phase in the junction region. Our study paves the way to exploring sensitive probes of weak magnetism and multifunctional building-blocks for phase-related superconducting circuits using vdW heterostructures.
A design approach aimed at reducing the radar cross section (RCS) of microstrip antenna in wide frequency band is proposed. First, two different artificial magnetic conductor (AMC) unit cells are ...designed to obtain 180 ° ( ±30 ° ) reflection phase difference over broadband frequency range. Then, chessboard configuration is structured with the two AMC unit cells and is applied to a microstrip antenna for RCS reduction. The simulated results indicate that the proposed antenna possesses remarkable RCS reduction from 8.0 GHz to 20.0 GHz for both polarizations, covering the working band of the original antenna. The maximum reduction is 31.9 dB. Moreover, the radiation performance of the antenna has been well kept. Measured results of the fabricated prototype are in good agreement with the simulations.
Abstract
It was recently conjectured that in generic quantum many-body systems, the spectral density of local operators has the slowest high-frequency decay as permitted by locality. We show that the ...infinite-temperature version of this ‘universal operator growth hypothesis’ holds for the quantum Ising spin model in
d
⩾ 2 dimensions, and for the chaotic Ising chain (with longitudinal and transverse fields) in one dimension. Moreover, the disordered chaotic Ising chain that exhibits many-body localization can have the same high-frequency spectral density asymptotics as thermalizing models. Our argument is statistical in nature, and is based on the observation that the moments of the spectral density can be written as a sign-problem-free sum over paths of Pauli string operators.
In this letter, a coding diffuse metasurface for radar cross section (RCS) reduction is designed, simulated, and measured. First, two kinds of artificial magnetic conductor (AMC) unit cell are ...analyzed, and 5 × 5 AMC unit cells construct metamaterials block. A linear array factor is optimized by the ergodic algorithm, and the sequence is expanded from one-dimension code to two-dimension code. Then, the diffuse metasurface is constructed through the metamaterials blocks arrangement. Simulation results show that the bandwidth of RCS reduction is expanded compared to the classical chessboard arrangement. The diffuse characteristic of the metasurface is achieved under normal and oblique incidence wave. Experiment results verify the validity of the theoretical design and simulation. This letter provides a rapid design method to obtain diffuse metasurface, and this metasurface may achieve potential applications on low-scattering vehicle.
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