The quantum to classical transition has been shown to depend on a number of parameters. Key among these are a scale length for the action, $\hbar$, a measure of the coupling between a system and its environment, $D$, and, for chaotic systems, the classical Lyapunov exponent, $λ$. We propose computing a measure, reflecting the proximity of quantum and classical evolutions, as a multivariate function of $(\hbar,λ,D)$ and searching for transformations that collapse this hyper-surface into a function of a composite parameter $ζ= \hbar^αλ^βD^γ$. We report results for the quantum Cat Map, showing extremely accurate scaling behavior over a wide range of parameters and suggest that, in general, the technique may be effective in constructing universality classes in this transition.
We numerically investigated the quantum-classical transition in rf-SQUID systems coupled to a dissipative environment. It is found that chaos emerges and the degree of chaos, the maximal Lyapunov exponent $λ_{m}$, exhibits non-monotonic behavior as a function of the coupling strength $D$. By measuring the proximity of quantum and classical evolution with the uncertainty of dynamics, we show that the uncertainty is a monotonic function of $λ_{m}/D$. In addition, the scaling holds in SQUID systems to a relatively smaller $\hbar_{eff}$, suggesting the universality for this scaling.
We present a formulation for investigating quench dynamics across quantum phase transitions in the presence of decoherence. We formulate decoherent dynamics induced by continuous quantum non-demolition measurements of the instantaneous Hamiltonian. We generalize the well-studied universal Kibble-Zurek behavior for linear temporal drive across the critical point. We identify a strong decoherence regime wherein the decoherence time is shorter than the standard correlation time, which varies as the inverse gap above the groundstate. In this regime, we find that the freeze-out time $\bar{t}\simτ^{…
Quantum critical dynamics and emergent universality in decoherent digital quantum processors
Leibniz Universität Hannover（汉诺威莱布尼茨大学）；University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；IBM Quantum, IBM T.J. Watson Research Center（IBM量子，IBM T.J.沃森研究中心）；MIT-IBM Watson AI Lab（MIT-IBM沃森人工智能实验室）
Classical predictability and coarse-grained evolution of the quantum baker's map
我们研究如何经典预测的粗粒度演化的量子面包师映射依赖于粗粒度的字符。我们的分析将Brun和Hartle [Phys. Rev. D 60，123503（1999）]的早期工作扩展到混沌映射的情况。为了量化的可预测性，我们比较了一个家庭的粗粒度的退相干历史形式主义的熵增加率。我们发现，熵增加的速率是由表征粗粒化的尺度的数量占主导地位。
In this paper we introduce a diagnostic for measuring the quantum-classical difference for open quantum systems, which is the normalized size of the quantum terms in the Master equation for Wigner function evolution. For a driven Duffing oscillator, this measure shows remarkably precise scaling over long time-scales with the parameter $ζ_0=\hbar^2/D$. We also see that, independent of $ζ_0$ the dynamics follows a similar pattern. For small $ζ_0$ all of our curves collapses to essentially a single curve when scaled by the maximum value of the quantum-classical difference. In both limits of large…
The spectral properties of interacting strongly chaotic systems are investigated for growing interaction strength. A very sensitive transition from Poisson statistics to that of random matrix theory is found. We introduce a new random matrix ensemble modeling this dynamical symmetry breaking transition which turns out to be universal and depends on a single scaling parameter only. Coupled kicked rotors, a dynamical systems paradigm for such transitions, are compared with this ensemble and excellent agreement is found for the nearest-neighbor-spacing distribution. It turns out that this transit…
Semiclassical scaling of eigenstate thermalization in single-particle chaotic systems
University of Science and Technology of China（中国科学技术大学）；Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Wilczek Quantum Center, Shanghai Institute for Advanced Studies（复旦张肇韦量子中心，上海高等研究院）；CAS Key Laboratory of Microscale Magnetic Resonance（中国科学院微观磁学共振重点实验室）
We study quantum kicked rotator in the classically fully chaotic regime, in the domain of the semiclassical behaviour. We use Izrailev's N-dimensional model for various N<=4000, which in the limit N-> infinity tends to the quantized kicked rotator, not only for K=5 as studied previously, but for many different values of the classical kick parameter 5<=K<=35, and also of the quantum parameter k. We describe the dynamical localization of chaotic eigenstates as a paradigm for other both time-periodic and time-independent fully chaotic or/and mixed type Hamilton systems. We generalize the localiza…
The out-of-time-ordered correlator (OTOC) is central to the understanding of information scrambling in quantum many-body systems. In this work, we show that the OTOC in a quantum many-body system close to its critical point obeys dynamical scaling laws which are specified by a few universal critical exponents of the quantum critical point. Such scaling laws of the OTOC imply a universal form for the butterfly velocity of a chaotic system in the quantum critical region and allow one to locate the quantum critical point and extract all universal critical exponents of the quantum phase transition…
The entanglement of eigenstates in two coupled, classically chaotic kicked tops is studied in dependence of their interaction strength. The transition from the non-interacting and unentangled system towards full random matrix behavior is governed by a universal scaling parameter. Using suitable random matrix transition ensembles we express this transition parameter as a function of the subsystem sizes and the coupling strength for both unitary and orthogonal symmetry classes. The universality is confirmed for the level spacing statistics of the coupled kicked tops and a perturbative descriptio…
Chaotic dynamics in quantum many-body systems scrambles local information so that at late times it can no longer be accessed locally. This is reflected quantitatively in the out-of-time-ordered correlator of local operators, which is expected to decay to zero with time. However, for systems of finite size, out-of-time-ordered correlators do not decay exactly to zero and in this paper we show that the residual value can provide useful insights into the chaotic dynamics. When energy is conserved, the late-time saturation value of the out-of-time-ordered correlator of generic traceless local oper…
Asymptotic Metrological Scaling and Concentration in Chaotic Floquet Dynamics
KTH Royal Institute of Technology（皇家理工学院）；Zhejiang University（浙江大学）；Nordita, KTH Royal Institute of Technology and Stockholm University（诺迪塔，皇家理工学院和斯德哥尔摩大学）
Nonequilibrium steady state (NESS) is a quasistationary state, in which exist currents that continuously produce entropy, but the local observables are stationary everywhere. We propose a theory of NESS under the framework of quantum chaos. In an isolated quantum system, there exist some initial states for which the thermodynamic limit and the long-time limit are noncommutative. The density matrix $\hat ρ$ of these states displays a universal structure. Suppose that $α$ and $β$ are different eigenstates of the Hamiltonian with energies $E_α$ and $E_β$, respectively. $<α|\hat ρ|β>$ behaves as a…
Kardar-Parisi-Zhang superdiffusion in chaotic quantum circuits
University of Ljubljana（卢布尔雅那大学）；King’s College London（伦敦国王学院）；Laboratoire de Physique de l’École Normale Superieure, CNRS, ENS & Université PSL, Sorbonne Université, Université Paris Cité（法国国家科学研究中心、巴黎高等师范学院、巴黎文理研究大学、索邦大学、巴黎西岱大学联合物理实验室）
Multifractal dimensions allow for characterizing the localization properties of states in complex quantum systems. For ergodic states the finite-size versions of fractal dimensions converge to unity in the limit of large system size. However, the approach to the limiting behavior is remarkably slow. Thus, an understanding of the scaling and finite-size properties of fractal dimensions is essential. We present such a study for random matrix ensembles, and compare with two chaotic quantum systems --- the kicked rotor and a spin chain. For random matrix ensembles we analytically obtain the finite…
We conjecture that in chaotic quantum systems with escape the intensity statistics for resonance states universally follows an exponential distribution. This requires a scaling by the multifractal mean intensity which depends on the system and the decay rate of the resonance state. We numerically support the conjecture by studying the phase-space Husimi function and the position representation of resonance states of the chaotic standard map, the baker map, and a random matrix model, each with partial escape.
The Fisher-Kolmogorov-Petrovsky-Piskunov (FKPP) equation provides a mean-field theory of out-of-time-ordered commutators in locally interacting quantum chaotic systems at high energy density; in the systems with power-law interactions, the corresponding fractional-derivative FKPP equation provides an analogous mean-field theory. However, the fractional FKPP description is potentially subject to strong quantum fluctuation effects, so it is not clear a priori if it provides a suitable effective description for generic chaotic systems with power-law interactions. Here we study this problem using …
Quantum metrology with partially accessible chaotic sensors
Birla Institute of Technology and Science Pilani（比拉理工学院皮拉尼分校）；Harish-Chandra Research Institute, a CI of Homi Bhabha National Institute（哈里什-昌德拉研究所，霍米·巴巴国家大学的附属机构）
The entanglement production in bipartite quantum systems is studied for initially unentangled product eigenstates of the subsystems, which are assumed to be quantum chaotic. Based on a perturbative computation of the Schmidt eigenvalues of the reduced density matrix, explicit expressions for the time-dependence of entanglement entropies, including the von Neumann entropy, are given. An appropriate re-scaling of time and the entropies by their saturation values leads a universal curve, independent of the interaction. The extension to the non-perturbative regime is performed using a recursively …
We study the consequences of having translational invariance in space and in time in many-body quantum chaotic systems. We consider an ensemble of random quantum circuits, composed of single-site random unitaries and nearest neighbour couplings, as a minimal model of translational invariant many-body quantum chaotic systems. We evaluate the spectral form factor (SFF) as a sum over many-body Feynman diagrams, which simplifies in the limit of large local Hilbert space dimension $q$. At sufficiently large $t$, diagrams corresponding to rigid translations dominate, reproducing the chaotic behavior…
Temporal entanglement transition in chaotic quantum many-body dynamics
Princeton University（普林斯顿大学）；University of Geneva（日内瓦大学）；Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；University of California, Berkeley（加州大学伯克利分校）；National University of Singapore（新加坡国立大学）；Rudolf Peierls Centre for Theoretical Physics, University of Oxford（牛津大学鲁道夫·皮尔斯理论物理中心）；KU Leuven（荷语鲁汶大学）；Google Research（谷歌研究）
Quantum walks subject to decoherence generically suffer the loss of their genuine quantum feature, a quadratically faster spreading compared to classical random walks. This intuitive statement has been verified analytically for certain models and is also supported by numerical studies of a variety of examples. In this paper we analyze the long-time behavior of a particular class of decoherent quantum walks, which, to the best of our knowledge, was only studied at the level of numerical simulations before. We consider a local coin operation which is randomly and independently chosen for each ti…
