Nonintegrable Systems Research Articles

Construction and Local Equivalence of Dual-Unitary Operators: From Dynamical Maps to Quantum Combinatorial Designs

While quantum circuits built from two-particle dual-unitary (maximally entangled) operators serve as minimal models of typically nonintegrable many-body systems, the construction and characterization of dual-unitary operators themselves are only partially understood. A nonlinear map on the space of unitary operators was proposed in PRL.~125, 070501 (2020) that results in operators being arbitrarily close to dual unitaries. Here we study the map analytically for the two-qubit case describing the basins of attraction, fixed points, and rates of approach to dual unitaries. A subset of dual-unitary operators having maximum entangling power are 2-unitary operators or perfect tensors, and are equivalent to four-party absolutely maximally entangled states. It is known that they only exist if the local dimension is larger than $d=2$. We use the nonlinear map, and introduce stochastic variants of it, to construct explicit examples of new dual and 2-unitary operators. A necessary criterion for their local unitary equivalence to distinguish classes is also introduced and used to display various concrete results and a conjecture in $d=3$. It is known that orthogonal Latin squares provide a ``classical combinatorial design" for constructing permutations that are 2-unitary. We extend the underlying design from classical to genuine quantum ones for general dual-unitary operators and give an example of what might be the smallest sized genuinely quantum design of a 2-unitary in $d=4$.

Formation of robust bound states of interacting microwave photons

Systems of correlated particles appear in many fields of modern science and represent some of the most intractable computational problems in nature. The computational challenge in these systems arises when interactions become comparable to other energy scales, which makes the state of each particle depend on all other particles1. The lack of general solutions for the three-body problem and acceptable theory for strongly correlated electrons shows that our understanding of correlated systems fades when the particle number or the interaction strength increases. One of the hallmarks of interacting systems is the formation of multiparticle bound states2–9. Here we develop a high-fidelity parameterizable fSim gate and implement the periodic quantum circuit of the spin-½ XXZ model in a ring of 24 superconducting qubits. We study the propagation of these excitations and observe their bound nature for up to five photons. We devise a phase-sensitive method for constructing the few-body spectrum of the bound states and extract their pseudo-charge by introducing a synthetic flux. By introducing interactions between the ring and additional qubits, we observe an unexpected resilience of the bound states to integrability breaking. This finding goes against the idea that bound states in non-integrable systems are unstable when their energies overlap with the continuum spectrum. Our work provides experimental evidence for bound states of interacting photons and discovers their stability beyond the integrability limit.

Finite-temperature dynamics in gapped one-dimensional models in the sine-Gordon family

The sine-Gordon model appears as the low-energy effective field theory of various one-dimensional gapped quantum systems. Here we investigate the dynamics of generic, nonintegrable systems belonging to the sine-Gordon family at finite temperature within the semiclassical approach. Focusing on timescales where the effect of nontrivial quasiparticle scatterings becomes relevant, we obtain universal results for the long-time behavior of dynamical correlation functions. We find that correlation functions of vertex operators behave neither ballistically nor diffusively but follow a stretched exponential decay in time. We also study the full counting statistics of the topological current and find that distribution of the transferred charge is non-Gaussian with its cumulants scaling nonuniformly in time.

Multiphase nonlinear electron plasma waves.

We present a method for constructing multiphase excitations in the generally nonintegrable system of warm fluid equationsdescribing plasma oscillations. It is based on autoresonant excitation of nonlinear electron plasma waves by phase locking with small amplitude chirped-frequency ponderomotive drives. We demonstrate the excitation of these multiphase waves by performing fully nonlinear numerical simulations of the fluid equations. We develop a simplified model based on a weakly nonlinear analytical theory by applying Whitham's averaged Lagrangian procedure. The simplified model predictions are in good agreement with the results from the warm fluid simulations. Such autoresonantly excited multiphase waves form coherent quasicrystalline structures, which can potentially be used as plasma photonic or accelerating devices. Finally, we discuss the laser parameters required for the autoresonant excitation of nonlinear waves in a plasma.

Induced Pluripotent Stem Cell (iPSC) Lines from a Family with Resistant Epileptic Encephalopathy Caused by Compound Heterozygous Mutations in SZT2 Gene.

Mutations in the SZT2 gene have been associated with developmental and epileptic encephalopathy-18, a rare severe autosomal recessive neurologic disorder, characterized by psychomotor impairment/intellectual disability, dysmorphic facial features and early onset of refractory seizures. Here we report the generation of the first induced pluripotent stem cell (iPSC) lines from a patient with treatment-resistant epilepsy, carrying compound heterozygous mutations in SZT2 (Mut1: c.498G>T and Mut2: c.6553C>T), and his healthy heterozygous parents. Peripheral blood mononuclear cells were reprogrammed by a non-integrating Sendai virus-based reprogramming system. The generated human iPSC lines exhibited expression of the main pluripotency markers, the potential to differentiate into all three germ layers and presented a normal karyotype. These lines represent a valuable resource to study neurodevelopmental alterations, and to obtain mature, pathology-relevant neuronal populations as an in vitro model to perform functional assays and test the patient's responsiveness to novel antiepileptic treatments.

Disparities in melanoma-specific mortality by race/ethnicity, socioeconomic status, and health care systems

Despite encouraging trends in survival, sociodemographic inequalities persist among patients with melanoma. We sought to quantify the effect of race/ethnicity, socioeconomic status, and health care systems on melanoma-specific mortality within an insured population of patients. Using a retrospective cohort study, we identified insured adults diagnosed with Stage I to IV melanoma from January 1, 2009, to December 31, 2014, followed through 2017, from the California Cancer Registry. We compared melanoma-specific mortality between insured patients diagnosed within the largest vertically integrated health care system in California, Kaiser Permanente Southern California, and insured patients with other private insurance (OPI). Our cohort included 14,614 adults diagnosed with melanoma. Multivariable analyses demonstrated that race/ethnicity was not associated with survival disparities, while socioeconomic status was a strong predictor of melanoma-specific mortality, particularly for those with OPI. For example, hazard ratios demonstrate that the poorest patients with OPI have a 70% increased risk of dying from their melanoma compared to their wealthiest counterparts, while the poorest patients in Kaiser Permanente Southern California have no increased risk. Our main limitation includes inadequate data for certain racial/ethnic groups, such as Native Americans. Our findings underscore the persistence of socioeconomic disparities within an insured population, specifically among those in non-integrated health care systems.

Driving quantum many-body scars in the PXP model

Periodic driving has been established as a powerful technique for engineering novel phases of matter and intrinsically out-of-equilibrium phenomena such as time crystals. Recent work by Bluvstein et al. [Science 371, 1355 (2021)] has demonstrated that periodic driving can also lead to a significant enhancement of quantum many-body scarring, whereby certain non-integrable systems can display persistent quantum revivals from special initial states. Nevertheless, the mechanisms behind driving-induced scar enhancement remain poorly understood. Here we report a detailed study of the effect of periodic driving on the PXP model describing Rydberg atoms in the presence of a strong Rydberg blockade - the canonical static model of quantum many-body scarring. We show that periodic modulation of the chemical potential gives rise to a rich phase diagram, with at least two distinct types of scarring regimes that we distinguish by examining their Floquet spectra. We formulate a toy model, based on a sequence of square pulses, that accurately captures the details of the scarred dynamics and allows for analytical treatment in the large-amplitude and high-frequency driving regimes. Finally, we point out that driving with a spatially inhomogeneous chemical potential allows to stabilize quantum revivals from arbitrary initial states in the PXP model, via a mechanism similar to prethermalization.

Critical life cycle assessment of the innovative passive nZEB building concept ‘be 2226’ in view of net-zero carbon targets

Buildings constructed today need to be nearly-zero energy/emission buildings (nZEB) during operation. Amongst strategies to meet today's nZEB performance requirements are passive building concepts. However, it is unclear to which degree such concepts aid buildings to achieve net-zero carbon targets. To address this research gap, we conduct a life cycle assessment (LCA) of the passive nZEB concept '2226' based on its original prototype office building in Austria. We deploy a quantity takeoff and the measured end-energy demand to calculate the embodied and operational GHG emissions. In line with the recent draft of the building LCA standard EN15978, we split energy usage into building-integrated and non-integrated systems. Embodied GHG emissions make up about a third of the total life cycle GHG emissions (33%), and operational energy use accounts for two-thirds (67%) of the life cycle GHG emissions, considering the current Austrian energy grid mix. The contextualisation with the literature shows better performance in comparison to existing building standards, yet no reduction is achieved compared to buildings with similar nZEB ambitions. The measured end-energy analysis shows that two-thirds (68%) of the operational GHG emissions are allocated to building-integrated systems, i.e., those regulated by today's EU Energy Performance of Buildings Directive. Almost a third (30%) of the operational GHG emissions can be allocated to non-integrated systems, currently being reported as optional in the latest draft of the standard EN15978. We recommend extending the system boundary of building LCA including these end-energy uses by non-integrated systems in future building regulation and building LCA practice. • LCA of an innovative passive nZEB office building in Austria. • Embodied GHG emissions from BIM-based quantity take off; operational GHG emissions from measured data. • Allocation of operational GHG emissionsin distinct sub-modules B6.1, B6.2 and B6.3 • 30% of operational GHG emissions allocated to non-building integrated systems. • Reflections on other studies and critical discussion in relation to net-zero carbon targets.

Numerically probing the universal operator growth hypothesis.

Recently, a hypothesis on the complexity growth of unitarily evolving operators was presented. This hypothesis states that in generic, nonintegrable many-body systems, the so-called Lanczos coefficients associated with an autocorrelation function grow asymptotically linear, with a logarithmic correction in one-dimensional systems. In contrast, the growth is expected to be slower in integrable or free models. In this paper, we numerically test this hypothesis for a variety of exemplary systems, including one-dimensional and two-dimensional Ising models as well as one-dimensional Heisenberg models. While we find the hypothesis to be practically fulfilled for all considered Ising models, the onset of the hypothesized universal behavior could not be observed in the attainable numerical data for the Heisenberg model. The proposed linear bound on operator growth associated with the hypothesis eventually stems from geometric arguments involving the locality of the Hamiltonian as well as the lattice configuration. We derive and investigate a related geometric bound, and we find that while the bound itself is not sharply achieved for any considered model, the hypothesis is nonetheless fulfilled in most cases.

Long-lived phantom helix states in Heisenberg quantum magnets

Exact solutions for quantum many-body systems are rare but provide valuable insights for the description of universal phenomena such as the non-equilibrium dynamics of strongly interacting systems and the characterization of new forms of quantum matter. Recently, specific solutions of the Bethe ansatz equations for integrable spin models were found. They are dubbed phantom Bethe states and can carry macroscopic momentum yet no energy. Here, we show experimentally that there exist special helical spin patterns in anisotropic Heisenberg chains which are long-lived, relaxing only very slowly in dynamics, as a consequence of such states. We use these phantom spin-helix states to directly measure the interaction anisotropy, which has a major contribution from short-range off-site interactions. We also generalize the theoretical description to higher dimensions and other non-integrable systems and find analogous stable spin helices, which should show non-thermalizing dynamics associated with so-called quantum many-body scars. These results have implications for the quantum simulation of spin physics, as well as many-body dynamics.

Generation of two iPSC cell lines (SIAISi020-A and SIAISi019-A) from an 82-year-old mild cognitive impairment (MCI) and her unaffected child from Chinese Han population

IPSCs have great potential value in cell replacement therapy, pathogenesis research, screening for new drugs, and treatment of clinical disease. An 82-year-old woman with mild cognitive impairment (MCI) and her unaffected child donated their peripheral blood mononuclear cells (PBMC). Their PBMCs were reprogrammed using human OKSM transcription factors (SOX2, OCT3/4, KLF4 and C-MYC) via a non-integrated complementary vector system. In the newly developed hiPSC series SIAISi019-A and SIAISi020-A, immunocytochemistry and the ability to spontaneously differentiate into 3 germ layers in vitro confirmed the pluripotency of transgene-free iPSCs. And their karyotypes were normal.

Flat input based canonical form observers for non-integrable nonlinear systems

In this contribution, the design of canonical form observers for nonlinear non-integrable systems is investigated. These systems cannot be transformed into observer canonical form, therefore an exact observer error linearization cannot be achieved. However, using flat inputs and dynamic compensators, the original dynamics can be rendered into an integrable flat system. For this modified flat input system a canonical form observer can be designed. By utilizing a state transformation, it is then possible to obtain an estimate of the original state, where the observer error is approximately linearized. This procedure is exemplified by the Rössler system. Furthermore, we illustrate the relationship of this approach with high-gain observers.

Experimental verification of generalized eigenstate thermalization hypothesis in an integrable system

Identifying the general mechanics behind the equilibration of a complex isolated quantum system towards a state described by only a few parameters has been the focus of attention in non-equilibrium thermodynamics. And several experimentally unproven conjectures are proposed for the statistical description of quantum (non-)integrable models. The plausible eigenstate thermalization hypothesis (ETH), which suggests that each energy eigenstate itself is thermal, plays a crucial role in understanding the quantum thermalization in non-integrable systems; it is commonly believed that it does not exist in integrable systems. Nevertheless, integrable systems can still relax to the generalized Gibbs ensemble. From a microscopic perspective, understanding the origin of this generalized thermalization that occurs in an isolated integrable system is a fundamental open question lacking experimental investigations. Herein, we experimentally investigated the spin subsystem relaxation in an isolated spin–orbit coupling quantum system. By applying the quantum state engineering technique, we initialized the system with various distribution widths in the mutual eigenbasis of the conserved quantities. Then, we compared the steady state of the spin subsystem reached in a long-time coherent dynamics to the prediction of a generalized version of ETH and the underlying mechanism of the generalized thermalization is experimentally verified for the first time. Our results facilitate understanding the origin of quantum statistical mechanics.

Hypergrid subgraphs and the origin of scarred quantum walks in many-body Hilbert space

Following the recent observation of wave function revivals in large Rydberg atom quantum simulators, much effort has focused on understanding the emergence of many-body scars in non-integrable quantum systems. Here we explore the origin of scarred wavefunction revivals in a family of models obtained by deforming the graph adjacency matrix of the PXP model - the effective model of Rydberg atoms in the strong Rydberg blockade regime. We consider deformations that either enhance the Rydberg constraint, ultimately resulting in an effective tight-binding model of two hypercubes joined at a single vertex, or relax the constraint until reaching the free spin-1/2 model. In the former case, we argue that the model of two joined hypercubes captures the essential features of many-body scarring present in the PXP model. On the other hand, relaxing the constraint leads to a sequence of new scarred models, some with more robust scarring signatures than the PXP model, as can be understood from the graph-theoretic viewpoint. Our results shed light on the nature of scarring in the PXP model by identifying its simple parent model, while also highlighting its distinction from the free-spin precession.

Performance assessment of energy-preserving, adaptive time-step variational integrators

A fixed time-step variational integrator cannot preserve momentum, energy, and symplectic form simultaneously for nonintegrable systems. This barrier can be overcome by treating time as a discrete dynamic variable and deriving adaptive time-step variational integrators that conserve the energy in addition to being symplectic and momentum-preserving. Their utility, however, is still an open question due to the numerical difficulties associated with solving the discrete governing equations. In this work, we investigate the numerical performance of energy-preserving, adaptive time-step variational integrators. First, we compare the time adaptation and energy performance of the energy-preserving adaptive algorithm with the adaptive variational integrator for Kepler’s two-body problem. Second, we apply tools from Lagrangian backward error analysis to investigate numerical stability of the energy-preserving adaptive algorithm. Finally, we consider a simple mechanical system example to illustrate the backward stability of this energy-preserving, adaptive time-step variational integrator.

Out-of-time-order correlators of nonlocal block-spin and random observables in integrable and nonintegrable spin chains

Out-of-time-order correlators (OTOC) in the Ising Floquet system, that can be both integrable and nonintegrable is studied. Instead of localized spin observables, we study contiguous symmetric blocks of spins or random operators localized on these blocks as observables. We find only power-law growth of OTOC in both integrable and nonintegrable regimes. In the non-integrable regime, beyond the scrambling time, there is an exponential saturation of the OTOC to values consistent with random matrix theory. This motivates the use of "pre-scrambled" random block operators as observables. A pure exponential saturation of OTOC in both integrable and nonintegrable system is observed, without a scrambling phase. Averaging over random observables from the Gaussian unitary ensemble, the OTOC is found to be exactly same as the operator entanglement entropy, whose exponential saturation has been observed in previous studies of such spin-chains.

Transient expression of an adenine base editor corrects the Hutchinson-Gilford progeria syndrome mutation and improves the skin phenotype in mice

Hutchinson-Gilford progeria syndrome (HGPS) is a rare premature ageing disorder caused by a point mutation in the LMNA gene (LMNA c.1824 C > T), resulting in the production of a detrimental protein called progerin. Adenine base editors recently emerged with a promising potential for HGPS gene therapy. However adeno-associated viral vector systems currently used in gene editing raise concerns, and the long-term effects of heterogeneous mutation correction in highly proliferative tissues like the skin are unknown. Here we use a non-integrative transient lentiviral vector system, expressing an adenine base editor to correct the HGPS mutation in the skin of HGPS mice. Transient adenine base editor expression corrected the mutation in 20.8-24.1% of the skin cells. Four weeks post delivery, the HGPS skin phenotype was improved and clusters of progerin-negative keratinocytes were detected, indicating that the mutation was corrected in both progenitor and differentiated skin cells. These results demonstrate that transient non-integrative viral vector mediated adenine base editor expression is a plausible approach for future gene-editing therapies.

Parametric resonance in a conservative system of coupled nonlinear oscillators.

We study a dimer in a periodic potential well, which is a conservative but nonintegrable system. This seemingly simple system exhibits a surprisingly rich dynamics. Using a systematic asymptotic analysis, we demonstrate that the translation mode of the dimer (center of mass motion) may induce a parametric resonance of the oscillatory mode. No external forcing occurs, thus this system belongs to the class of autoparametric systems. When the dimer energy is such that both particles are trapped in neighboring potential wells, we derive the relevant amplitude equationsfor the eigenmodes (center of mass motion and relative motion) and show that they are integrable. In the opposite limit, when the dimer slides along the external potential so that the center of mass motion is basically a translation, we also exhibit autoparametric amplification of the relative motion. In both cases our calculations provide reliable estimates of the relevant parameters for the autoparametric resonance to appear. Moreover, the comparison between the numerical integration of the actual system and the asymptotic analysis evidences an excellent quantitative agreement.

Generation of a human induced pluripotent stem cell line (JSPHi002-A) from a patient with long-QT syndrome type 1 caused by KCNQ1 c.773A > T mutation

We generated an iPSCs line from the peripheral blood mononuclear cells (PBMCs) collected from a patient with long QT syndrome type 1 (LQT1) via a non-integrating system. We identified and verified a missense mutation in the KCNQ1 gene (c.773A > T) by whole-exome sequencing and Sanger sequencing. The established iPSC line was tested for pluripotency, differentiation potential, and karyotype. This cell-based model can help study the molecular mechanism and develop personalized drug therapies for LQT1.

Typicality of nonequilibrium quasi-steady currents

The understanding of the emergence of equilibrium statistical mechanics has progressed significantly thanks to developments from typicality, canonical and dynamical, and from the eigenstate thermalization hypothesis. Here we focus on a nonequilibrium scenario in which two nonintegrable systems prepared in different states are locally and nonextensively coupled to each other. Using both perturbative analysis and numerical exact simulations of up to 28 spin systems, we demonstrate the typical emergence of nonequilibrium quasi-steady current for weak coupling between the subsystems. We also identify that these currents originate from a prethermalization mechanism, which is the weak and local breaking of the conservation of the energy for each subsystem.