Long-time Saturation Research Articles

Hilbert Space Delocalization under Random Unitary Circuits.

The unitary dynamics of a quantum system initialized in a selected basis state yield, generically, a state that is a superposition of all the basis states. This process, associated with the quantum information scrambling and intimately tied to the resource theory of coherence, may be viewed as a gradual delocalization of the system's state in the Hilbert space. This work analyzes the Hilbert space delocalization under the dynamics of random quantum circuits, which serve as a minimal model of the chaotic dynamics of quantum many-body systems. We employ analytical methods based on the replica trick and Weingarten calculus to investigate the time evolution of the participation entropies which quantify the Hilbert space delocalization. We demonstrate that the participation entropies approach, up to a fixed accuracy, their long-time saturation value in times that scale logarithmically with the system size. Exact numerical simulations and tensor network techniques corroborate our findings.

Assessing the saturation of Krylov complexity as a measure of chaos.

Krylov complexity is a novel approach to study how an operator spreads over a specific basis. Recently, it has been stated that this quantity has a long-time saturation that depends on the amount of chaos in the system. Since this quantity not only depends on the Hamiltonian but also on the chosen operator, in this work we study the level of generality of this hypothesis by studying how the saturation value varies in the integrability to chaos transition when different operators are expanded. To do this, we work with an Ising chain with a longitudinal-transverse magnetic field and compare the saturation of the Krylov complexity with the standard spectral measure of quantum chaos. Our numerical results show that the usefulness of this quantity as a predictor of the chaoticity is strongly dependent on the chosen operator.

Out-of-time-order correlations and the fine structure of eigenstate thermalization.

Out-of-time-order correlators (OTOCs) have become established as a tool to characterise quantum information dynamics and thermalization in interacting quantum many-body systems. It was recently argued that the expected exponential growth of the OTOC is connected to the existence of correlations beyond those encoded in the standard Eigenstate Thermalization Hypothesis (ETH). We show explicitly, by an extensive numerical analysis of the statistics of operator matrix elements in conjunction with a detailed study of OTOC dynamics, that the OTOC is indeed a precise tool to explore the fine details of the ETH. In particular, while short-time dynamics is dominated by correlations, the long-time saturation behavior gives clear indications of an operator-dependent energy scale ω_{GOE} associated to the emergence of an effective Gaussian random matrix theory. We provide an estimation of the finite-size scaling of ω_{GOE} for the general class of observables composed of sums of local operators in the infinite-temperature regime and found linear behavior for the models considered.

Recovery of Damaged Information and the Out-of-Time-Ordered Correlators

The evolution with a complex Hamiltonian generally leads to information scrambling. A time-reversed dynamics unwinds this scrambling and thus leads to the original information recovery. We show that if the scrambled information is, in addition, partially damaged by a local measurement, then such a damage can still be treated by application of the time-reversed protocol. This information recovery is described by the long-time saturation value of a certain out-of-time-ordered correlator of local variables. We also propose a simple test that distinguishes between quantum and reversible classical chaotic information scrambling.

Towards an analytic solution for pulsed CEST.

Chemical exchange saturation transfer (CEST) is an imaging method based on magnetization exchange between solutes and water. This exchange generates changes in the measured signal after off-resonance radiofrequency irradiation. Although the analytic solution for CEST with continuous wave (CW) irradiation has been determined, most studies are performed using pulsed irradiation. In this work, we derive an analytic solution for the CEST signal after pulsed irradiation that includes both short-time rotation effects and long-time saturation effects in a two-pool system corresponding to water and a low-concentration exchanging solute pool. Several approximations are made to balance the accuracy and simplicity of the resulting analytic form, which is tested against numerical solutions of the coupled Bloch equations and is found to be largely accurate for amides at high fields, but less accurate at the higher exchange rates, lower offsets and typically higher irradiation powers of amines.

Long‐Time Saturation Exposure Changes Gut Microbiota Composition And Intestinal Antimicrobial Defense In Mice

PURPOSELong‐time saturation exposure may induce anxiety, loss of appetite, and digestive disorders, which relate to impairment of intestinal mucosal immune system and gut microbiota homeostasis. Our study examined the effects of 4‐day of saturation exposure on gut microbiota and intestinal antimicrobial peptides (AMPs) in mice.METHOD20 male C57 Mice, 8‐week old, were randomly divided into saturation exposure group (SE, n=10) and control group (CON, n=10). SE exposed to N2/O2 mixed gas at 500kPa for 4 days in pressure chamber. Intestines were excised and stained with HE and AB‐PAS. Feces and Intestines were collected and extract gDNA and RNA respectively. We used qPCR to assay bacterial population (Bacteroides, Clostridia, Lactobacilli, Enterobacteria, and Akkermansia muciniphila) of the feces, and the AMPs (Defα5/β1, Retnlβ, Reg3β/γ) of small intestine and colon.RESULTSWithin 4 days, SE mice did not exhibit nitrogen narcosis behavior. By comparing with the 16S rRNA genes, results revealed a significant increase in the relative abundances of A. muciniphila (9.28±5.67) and Clostridia (3.45±0.63) in SE. The relative abundance of Lactobacilli was lower (0.40±0.24) in SE. Moreover, a distinct increase of Enterobacteria (23.34±8.88) was observed in SE compared with CON. Gene expressions for Defα5/β1 in SE were decreased in small intestine, while Defβ1 and Reg3γ in SE were significantly decreased, and Defα5 and Reg3β increased in colon.CONCLUSIONIn sum, the data showed that a four‐day saturation exposure induced changes in the mRNA level of AMPs, and the gut microbiota composition in mice.Found: NSFC 31471135

Ageing and confinement in non-ergodic heterogeneous diffusion processes

We study the effects of ageing—the time delay between initiation of the physical process at t = 0 and start of observation at some time —and spatial confinement on the properties of heterogeneous diffusion processes (HDPs) with deterministic power-law space-dependent diffusivities, . From analysis of the ensemble and time averaged mean squared displacements and the ergodicity breaking parameter quantifying the inherent degree of irreproducibility of individual realizations of the HDP we obtain striking similarities to ageing subdiffusive continuous time random walks with scale-free waiting time distributions. We also explore how both processes can be distinguished. For confined HDPs we study the long-time saturation of the ensemble and time averaged particle displacements as well as the magnitude of the inherent scatter of time averaged displacements and contrast the outcomes to the results known for other anomalous diffusion processes under confinement.

Spatial, temporal, and thermal contributions to focusing contrast by time reversal in a cavity

The accuracy of wave focusing by time reversal depends on a quantity termed ‘contrast ratio’ that measures the amplitude of a localized peak of velocity relatively to background noise. A comprehensive expression for the contrast ratio in a lossy cavity is derived by modal decomposition of the wave field. This expression accounts for the effects of the mechanical and the dimensional properties of the cavity, the bandwidth of the excitation signal, the number of sources, and the duration of time reversal window. The expression can predict the characteristics of a given process such as the long-time saturation and the single-channel time reversal limit. The expression also models the effect of temperature variations on focusing accuracy and shows that thermal drift exhibits two regimes. In the first regime, small temperature variations have little effect on contrast. The second regime is characterized by a rapid deterioration of contrast. Experimental measurements show close agreement with the theory.

Long-time coherence in echo spectroscopy withπ/2-π-π/2pulse sequence

Motivated by atom optics experiments, we investigate a new class of fidelity functions describing the reconstruction of quantum states by time-reversal operations as $M_{\mathrm{Da}}(t) = | <\psi | e^{i H_2 t / 2} e^{i H_1 t / 2} e^{-i H_2 t / 2} e^{-i H_1 t / 2} | \psi >|^2$. We show that the decay of $M_{\mathrm{Da}}$ is quartic in time at short times, and that it freezes well above the ergodic value at long times, when $H_2-H_1$ is not too large. The long-time saturation value of $M_{\mathrm{Da}}$ contains easily extractable information on the strength of decoherence in these systems.

Long-time saturation of the Loschmidt echo in quantum chaotic billiards

The Loschmidt echo (LE) (or fidelity) quantifies the sensitivity of the time evolution of a quantum system with respect to a perturbation of the Hamiltonian. In a typical chaotic system the LE has been previously argued to exhibit a long-time saturation at a value inversely proportional to the effective size of the Hilbert space of the system. However, until now no quantitative results have been known and, in particular, no explicit expression for the proportionality constant has been proposed. In this paper we perform a quantitative analysis of the phenomenon of the LE saturation and provide the analytical expression for its long-time saturation value for a semiclassical particle in a two-dimensional chaotic billiard. We further perform extensive (fully quantum mechanical) numerical calculations of the LE saturation value and find the numerical results to support the semiclassical theory.

Singlet-triplet decoherence due to nuclear spins in a double quantum dot

We have evaluated hyperfine-induced electron spin dynamics for two electrons confined to a double quantum dot. Our quantum solution accounts for decay of a singlet-triplet correlator even in the presence of a fully static nuclear spin system, with no ensemble averaging over initial conditions. In contrast to an earlier semiclassical calculation, which neglects the exchange interaction, we find that the singlet-triplet correlator shows a long-time saturation value that differs from $\frac{1}{2}$, even in the presence of a strong magnetic field. Furthermore, we find that the form of the long-time decay undergoes a transition from a rapid Gaussian to a slow power law $(\ensuremath{\sim}1∕{t}^{3∕2})$ when the exchange interaction becomes nonzero and the singlet-triplet correlator acquires a phase shift given by a universal (parameter independent) value of $3\ensuremath{\pi}∕4$ at long times. The oscillation frequency and time-dependent phase shift of the singlet-triplet correlator can be used to perform a precision measurement of the exchange interaction and Overhauser field fluctuations in an experimentally accessible system. We also address the effect of orbital dephasing on singlet-triplet decoherence and find that there is an optimal operating point where orbital dephasing becomes negligible.

Quantum diffusion and scaling of localized interacting electrons

A new numerical method is introduced that enables a reliable study of disorder-induced localization of interacting particles. It is based on a quantum mechanical time evolution calculation combined with a finite size scaling analysis. The time evolution of up to four particles in one dimension is studied and localization lengths are defined via the long-time saturation values of the mean radius, the inverse participation ratio and the center of mass extension. A systematic study of finite size effects using the finite size scaling method is performed in order to extract the localization lengths in the limit of an infinite system size. For a single particle, the well-known scaling of the localization length λ1 with disorder strength W is observed, λ1 ∝ W—2. For two particles, an interaction-induced delocalization is found, confirming previous results obtained by numerically calculating matrix elements of the two-particle Green's function: in the limit of small disorder, the localization length increases with decreasing disorder as λ2 ∝ W—4 and can be much larger than <$>\mitlambda λ1. For three and four particles, delocalization is even stronger. Based on analytical arguments, an upper bound for the n-particle localization length λn is derived and shown to be in agreement with the numerical data, λn ∝ λ1. Although the localization length increases superexponentially with particle number and can become arbitrarily large for small disorder, it does not diverge for finite λ1 and n. Hence, no extendedstates exist in one dimension, at least for spinless fermions.