We study theoretically a large quantum dot in the fractional quantum Hall regime that is strongly coupled to $\mathcal{M}$ leads via single-mode quantum point contacts. In the case $\mathcal{M}=2$, when the system is mapped onto the two-channel charge Kondo problem, we predict a universal expression for the conductance in the vicinity of a strong-coupling fixed point. The power of the leading temperature correction to the maximal conductance is determined by the fractional filling factor $\nu =1/m$. For $\mathcal{M}>2$, we examine the case in which $\mathcal{M}-1$ quantum point contacts are fully open, reproducing a single-channel circuit coupled to a dissipative Ohmic environment. The system is treated as a Luttinger liquid with an impurity, whose effective interaction parameter is defined as $K=\nu (\mathcal{M}-1)/\mathcal{M}$. Conductance scaling in the weak and strong tunnel regimes is used to discuss the low-temperature transport behavior of multichannel single- and double-charge Kondo devices.

Living systems adapt to various environmental conditions by changing their internal states through processes such as gene expression and epigenetic modification. In this paper, we propose a generic mechanism for optimization that combines fast oscillatory dynamics with a slower feedback fixation process. Through extensive model simulations, we demonstrate that the fast chaotic dynamics serve as a global search for optimal states, which are then fixed by the slower dynamics. This mechanism becomes more effective as the number of elements is increased. We also discuss the potential relevance of this optimization mechanism to problems in artificial neural networks.

Witnessing nonclassical behavior is a crucial ingredient in quantum information processing. For that, one has to optimize the quantum features a given physical setup can give rise to, which is a hard computational task currently tackled with semidefinite programming, a method limited to linear objective functions and that becomes prohibitive as the complexity of the system grows. Here, we propose an alternative strategy, which exploits a feedforward artificial neural network to optimize the correlations compatible with arbitrary quantum networks. A remarkable step forward with respect to existing methods is that it deals with nonlinear optimization constraints and objective functions, being applicable to scenarios featuring independent sources and nonlinear entanglement witnesses. Furthermore, it offers a significant speedup in comparison with other approaches, thus allowing to explore previously inaccessible regimes. We also extend the use of the neural network to the experimental realm, a situation in which the statistics are unavoidably affected by imperfections, retrieving device-independent uncertainty estimates on Bell-like violations obtained with independent sources of entangled photon states. In this way, this work paves the way for the certification of quantum resources in networks of growing size and complexity.

We investigate the nonequilibrium dynamics of the $S=1$ quantum spin chain subjected to a time-dependent external drive, where the driving frequency is adiabatically decreased as a function of time (Floquet adiabatic evolution). We show that, when driving the rhombic anisotropy term (known as the two-axis countertwisting in the context of squeezed spin states) of a Néel antiferromagnet, we can induce an overall enhancement in the quadrupole polarization, while at the same time suppressing the staggered magnetization order. The system evolves into a new state with a net quadrupole moment and antiferroquadrupolar correlations. This state remains stable at long times once the driving frequency is kept constant. On the other hand, we find that we cannot achieve a quadrupole polarization for the symmetry-protected Haldane phase, which remains robust against such driving.

We present a systematic study of the dynamical phase diagram of a periodically driven BCS system as a function of drive strength and frequency. Three different driving mechanisms are considered and compared: oscillating density of states, oscillating pairing interaction, and oscillating external paring field. We identify the locus in parameter space of parametric resonances and four dynamical phases: Rabi-Higgs, gapless, synchronized Higgs, and time-crystal phases. We demonstrate that the main features of the phase diagram are quite robust to different driving protocols and discuss the order of the transitions. By mapping the BCS problem to a collection of nonlinear and interacting classical oscillators, we shed light on the origin of time-crystal phases and parametric resonances appearing for subgap excitations.

Hierarchical Bayesian inference is an essential tool for studying the population properties of compact binaries with gravitational waves. The basic premise is to infer the unknown prior distribution of binary black hole and/or neutron star parameters such component masses, spin vectors, and redshift. These distributions shed light on the fate of massive stars, how and where binaries are assembled, and the evolution of the Universe over cosmic time. Hierarchical analyses model the binary black hole population using a prior distribution conditioned on hyperparameters, which are inferred from the data. However, a misspecified model can lead to faulty astrophysical inferences. In this paper we answer the question: given some data, which prior distribution—from the set of all possible prior distributions—produces the largest possible population likelihood? This distribution (which is not a true prior) is $\sout{\pi }$ (pronounced “pi stroke”), and the associated maximum population likelihood is $\sout{\mathcal{L}}$ (pronounced “L stroke”). The structure of $\sout{\pi }$ is a linear superposition of delta functions, a result which follows from Carathéodory's theorem. We show how $\sout{\pi }$ and $\sout{\mathcal{L}}$ can be used for model exploration/criticism. We apply this $\sout{\mathcal{L}}$ formalism to study the population of binary black hole mergers observed in the LIGO-Virgo-KAGRA Collaboration's third gravitational-wave transient catalog. Based on our results, we discuss possible improvements for gravitational-wave population models.

We examine a macroscopic system in a quantum superposition of two spatially separated localized states as a detector for a stream of weakly interacting relativistic particles. We do this using the explicit example of neutrinos with $\mathrm{MeV}$-scale energy scattering from a solid object via neutral-current neutrino-nucleus scattering. Presuming the (anti)neutrino source to be a nuclear fission reactor, we utilize the estimated flux and coherent elastic neutrino-nucleus cross section to constrain the spatial separation $\mathrm{\Delta }x$ and describe the temporal evolution of the sensing system. Particularly, we find that a potentially measurable relative phase between quantum superposed components is obtained for a single gram scale mass placed in a superposition of spatial components separated by ${10}^{-14} \mathrm{m}$ under sufficient cooling and background suppression.

We generalize the dynamical phase diagram of a Bardeen-Cooper-Schrieffer condensate, considering attractive to repulsive, i.e., critical quenches (CQs) and a nonconstant density of states (DOS). We show that different synchronized Higgs dynamical phases can be stabilized, associated with singularities in the DOS and different quench protocols. In particular, the CQ can stabilize an overlooked high-frequency Higgs dynamical phase related to the upper edge of the fermionic band. For a compensated Dirac system we find a Dirac-Higgs mode associated with the cusp singularity at the Fermi level, and we show that synchronized phases become more pervasive across the phase diagram. The relevance of these remarkable phenomena and their realization in ensembles of fermionic cold atoms confined in optical lattices is also discussed.

The ongoing quest for understanding nonequilibrium dynamics of complex quantum systems underpins the foundation of statistical physics as well as the development of quantum technology. Quantum many-body scarring has recently opened a window into novel mechanisms for delaying the onset of thermalization by preparing the system in special initial states, such as the ${\mathbb{Z}}_2$ state in a Rydberg atom system. Here we realize many-body scarring in a Bose-Hubbard quantum simulator from previously unknown initial conditions such as the unit-filling state. We develop a quantum-interference protocol for measuring the entanglement entropy and demonstrate that scarring traps the many-body system in a low-entropy subspace. Our work makes the resource of scarring accessible to a broad class of ultracold-atom experiments, and it allows one to explore the relation of scarring to constrained dynamics in lattice gauge theories, Hilbert space fragmentation, and disorder-free localization.

We study the interplay of disorder and Heisenberg interactions in the Kitaev model on a honeycomb lattice. The effect of disorder on the transition between Kitaev spin liquid and magnetic ordered states as well as the stability of magnetic ordering is investigated. Using Lanczos exact diagonalization we discuss the consequences of two types of disorder: (i) random-coupling disorder and (ii) singular-coupling disorder. They exhibit qualitatively similar effects in the pure Kitaev-Heisenberg model without long-range interactions. The range of spin-liquid phases is reduced and the transition to magnetic ordered phases becomes more crossoverlike. Furthermore, the long-range zigzag and stripy orderings in the clean system are replaced by their three domains with different ordering direction. Especially in the crossover range the coexistence of magnetically ordered and Kitaev spin-liquid domains is possible. With increasing the disorder strength the area of domains becomes smaller and the system goes into a spin-glass state. However, the disorder effect is different in magnetically ordered phases caused by long-range interactions. The stability of such magnetic ordering is diminished by singular-coupling disorder and, accordingly, the range of the spin-liquid regime is extended. This mechanism may be relevant to materials like $\alpha \text{−}{\mathrm{RuCl}}_3$ and ${\mathrm{H}}_3{\mathrm{LiIr}}_2{\mathrm{O}}_6$ where the zigzag ground state is stabilized by weak long-range interactions. We also find that the flux gap closes at a critical disorder strength and vortices appears in the flux arrangement. Interestingly, the vortices tend to form kinds of commensurate ordering.

Collective transport properties of a one-dimensional (1D) asymmetric periodic substrate modulated two-dimensional (2D) dusty plasma driven by an unbiased sinusoidal excitation force are investigated using Langevin dynamical simulations. It is discovered that by changing the amplitude and frequency of the unbiased sinusoidal external excitations, as well as the depth of the 1D asymmetric periodic substrate, both the direction and speed of the persistent particle flow can be adjusted, i.e., both the flow rectification and its reversal of the ratchet effect of the steady drift motion for particles are achieved using various excitations. For the studied 2D dusty plasma under the 1D asymmetric periodic substrate, when the amplitude of the excitation increases from zero, the magnitude of the overall drift velocity increases from zero to its first maximum in the easy direction of the 1D asymmetric periodic substrate, next decreases gradually back to zero, and then increases from zero to its second maximum in the hard direction of the 1D asymmetric periodic substrate before finally gradually decaying. It is found that, as the frequency of the excitation and the depth of the 1D asymmetric periodic substrate change, the maximum overall drift velocity also varies, exhibiting a similar variation trend as that for the change of the excitation amplitude. The observed ratchet effect in both the easy and hard directions of 1D asymmetric periodic substrate for 2D dusty plasma is attributed to the combination of the spatial symmetry breaking of the 1D asymmetric periodic substrate and the inertial effects of particles, which is further confirmed by the three different presented diagnostics.

The adjacency matrix is the most fundamental and intuitive object in graph analysis that is useful not only mathematically but also for visualizing the structures of graphs. Because the appearance of an adjacency matrix is critically affected by the ordering of rows and columns, or vertex ordering, statistical assessment of graphs together with their vertex sequences is important in identifying the characteristic structures of graphs. In this paper, we propose a hypothesis-testing framework that assesses how locally vertices are connected to each other along a specified vertex sequence, which provides a statistical foundation for an optimization problem called envelope reduction or minimum linear arrangement. The proposed tests are particularly suitable for moderately small data sets and formulated based on a combinatorial approach and a block model with intrinsic vertex ordering.

A relational dataset is often analyzed by optimally assigning a label to each element through clustering or ordering. While similar characterizations of a dataset would be achieved by both clustering and ordering methods, the former has been studied much more actively than the latter, particularly for the data represented as graphs. This study fills this gap by investigating methodological relationships between several clustering and ordering methods, focusing on spectral techniques. Furthermore, we evaluate the resulting performance of the clustering and ordering methods. To this end, we propose a measure called the label continuity error, which generically quantifies the degree of consistency between a sequence and partition for a set of elements. Based on synthetic and real-world datasets, we evaluate the extents to which an ordering method identifies a module structure and a clustering method identifies a banded structure.