Search

We investigate the spin-squeezing behavior under thermal effects in a one-dimensional transverse field XY model with spin-1/2. The exact solution of the model helps us to compute the spin-squeezing parameter as a function of temperature and also in all excited states with higher energy than the ground state. We find that below the thermal factorized field, h_f(T_{co}), there is no transition temperature. At the thermal factorized field, a transition from a thermal squeezed state to an unsqueezed state occurs at a specific temperature called the coherent temperature. Interestingly, we show that the finite temperature can create squeezed states from a state which at zero temperature is a coherent state. To complete our study, we also analyze the variation of the spin-squeezing parameter in the excited states and provide a behavioral analysis of the thermal spin-squeezing parameter.

We study the problem of robot navigation in dense and interactive crowds with environmental constraints such as corridors and furniture. Previous methods fail to consider all types of interactions among agents and obstacles, leading to unsafe and inefficient robot paths. In this article, we leverage a graph-based representation of crowded and constrained scenarios and propose a structured framework to learn robot navigation policies with deep reinforcement learning. We first split the representations of different components in the environment and propose a heterogeneous spatio-temporal (st) graph to model distinct interactions among humans, robots, and obstacles. Based on the heterogeneous st-graph, we propose HEIGHT, a novel navigation policy network architecture with different components to capture heterogeneous interactions among entities through space and time. HEIGHT utilizes attention mechanisms to prioritize important interactions and a recurrent network to track changes in the dynamic scene over time, encouraging the robot to avoid collisions adaptively. Through extensive simulation and real-world experiments, we demonstrate that HEIGHT outperforms state-of-the-art baselines in terms of success and efficiency in challenging navigation scenarios. Furthermore, we demonstrate that our pipeline achieves better zero-shot generalization capability than previous works when the densities of humans and obstacles change. More videos are available at https://sites.google.com/view/crowdnav-height/home.

We prove that cubic polynomial maps with a fixed Siegel disk and a critical orbit eventually landing inside that Siegel disk lie in the support of the bifurcation measure. This answers a question of Dujardin in positive. Our result implies the existence of holomorphic disks in the support of the bifurcation measure, and also implies that the set of rigid parameters is not closed in the moduli space of cubic polynomials.

Dynamical quantum phase transitions are non-analyticities in a dynamical free energy (or return rate) which occur at critical times. Although extensively studied in one dimension, the exact nature of the non-analyticity in two and three dimensions has not yet been fully investigated. In two dimensions, results so far are known only for relatively simple two-band models. Here we study the general two- and three-dimensional cases. We establish the relation between the non-analyticities in different dimensions, and the functional form of the densities of Fisher zeroes. We show, in particular, that entering a critical region where the density of Fisher zeroes is non-zero at the boundary always leads to a cusp in the derivative of the return rate while the return rate itself is smooth. We illustrate our results by obtaining analytical results for exemplary two- and three-dimensional models.

Purpose: Artificial intelligence (AI) techniques have been extensively utilized for diagnosing and prognosis of several diseases in recent years. This study identifies, appraises and synthesizes published studies on the use of AI for the prognosis of COVID-19. Method: Electronic search was performed using Medline, Google Scholar, Scopus, Embase, Cochrane and ProQuest. Studies that examined machine learning or deep learning methods to determine the prognosis of COVID-19 using CT or chest X-ray images were included. Polled sensitivity, specificity area under the curve and diagnostic odds ratio were calculated. Result: A total of 36 articles were included; various prognosis-related issues, including disease severity, mechanical ventilation or admission to the intensive care unit and mortality, were investigated. Several AI models and architectures were employed, such as the Siamense model, support vector machine, Random Forest , eXtreme Gradient Boosting, and convolutional neural networks. The models achieved 71%, 88% and 67% sensitivity for mortality, severity assessment and need for ventilation, respectively. The specificity of 69%, 89% and 89% were reported for the aforementioned variables. Conclusion: Based on the included articles, machine learning and deep learning methods used for the prognosis of COVID-19 patients using radiomic features from CT or CXR images can help clinicians manage patients and allocate resources more effectively. These studies also demonstrate that combining patient demographic, clinical data, laboratory tests and radiomic features improves model performances.

We present Topology-Guided ORCA as an alternative simulator to replace ORCA for planning smooth multi-agent motions in environments with static obstacles. Despite the impressive performance in simulating multi-agent crowd motion in free space, ORCA encounters a significant challenge in navigating the agents with the presence of static obstacles. ORCA ignores static obstacles until an agent gets too close to an obstacle, and the agent will get stuck if the obstacle intercepts an agent's path toward the goal. To address this challenge, Topology-Guided ORCA constructs a graph to represent the topology of the traversable region of the environment. We use a path planner to plan a path of waypoints that connects each agent's start and goal positions. The waypoints are used as a sequence of goals to guide ORCA. The experiments of crowd simulation in constrained environments show that our method outperforms ORCA in terms of generating smooth and natural motions of multiple agents in constrained environments, which indicates great potential of Topology-Guided ORCA for serving as an effective simulator for training constrained social navigation policies., Comment: Accepted by Unsolved Problems in Social Robot Navigation workshop in conjunction with RSS 2024

The bond-dependent Kitaev model offers a playground in which one can search for quantum spin liquids. In these Kitaev materials, a symmetric off-diagonal $\Gamma$ term emerges, hosting a number of remarkable features, which has been particularly challenging to fully understand. One primary question that arises after recognizing a new phase is how information will spread in it. Out-of-time-ordered commutators and entanglement entropy describe processes whereby information about the initial condition of a unitarily evolving system propagates over the system. A possible way to investigate dynamics in such systems is by considering one-dimensional models. We investigate here the one-dimensional spin-1/2 XY model in a transverse field with a $\Gamma$ interaction with periodic boundary conditions imposed. We will show that the $\Gamma$ interaction constructs an asymmetric "light-cone" with different butterfly velocities. In addition, it leads to faster information propagation in the spiral phase and slower propagation in the ferromagnetic and paramagnetic phases. Interestingly, we observe a pronounced effect in the entanglement entropy, explicitly showing up as a two-stage linear growth in time as fast/slow then slow/fast for quenches originating from the spiral phase. We hope our work paves the way for studying more about the spreading of information in one-dimensional Kitaev materials, which can in turn help to discover unknown aspects of higher-dimensional models., Comment: 13 pages, 12 figures

The transformative enhancements of fifth-generation (5G) mobile devices bring about new challenges to achieve better uplink (UL) performance. Particularly, in codebook-based transmission, the wide-band (WB) precoding and the legacy UL codebook may become main bottlenecks for higher efficient data transmission. In this paper, we investigate the codebook-based UL single-layer transmission performance using fully coherent antenna ports in the context of sub-band (SB) precoding. We analyze the SB precoder selection criteria and design an UL codebook used for SB precoding by increasing the number of relative phase shifts of each port. Via link-level simulations, we verify that the UL SB precoding can improve up to 2 dB performance gain in terms of the block error rate (BLER) compared with the UL WB precoding which is the current UL precoding scheme. We also show that UL performance gain is sensitive to the SB size selection as well as the relative phase shift diversity., Comment: This work has been accepted by IEEE VCC 2023. 5 pages, 7 figures

Quantum phase transitions have long been studied in their relation to quantum fluctuations. These fluctuations can be quantified as the degree of spin squeezing in spin models, where one of the two non-commutative observables breaks the standard quantum limit of measurement by minimizing its uncertainty. However, the understanding of their role in dynamical quantum phase transitions (DQPTs) is still incomplete. In this work, we combine the Loschmidt amplitude, which detects DQPTs, and the spin-squeezing parameter (SSP), the quantification of spin squeezing, to study the spin dynamics in a quenched interacting spin model around DQPT. We show that the extremal, mostly maximal, of SSP occurs near DQPTs when the system is quenched between different phases. These phenomena further unveil the spin correlations during DQPTs, for which the highest contribution aligns with the preferred direction of spin interactions in the post-quenched phase. We also demonstrate the time evolution of SSP differs for various quench scenarios. These findings provide us with physical insights into the dynamics of quantum fluctuations around DQPTs and their relation to the equilibrium phase diagrams., Comment: 12 pages, 15 figures

Topological insulators and superconductors have attracted considerable attention, and many different theoretical tools have been used to gain insight into their properties. Here we investigate how perturbations can spread through exemplary one-dimensional topological insulators and superconductors using out-of-time ordered correlators. Out-of-time ordered correlators are often used to consider how information becomes scrambled during quantum dynamics. The wavefront of the out-of-time ordered correlator can be ballistic regardless of the underlying system dynamics, and here we confirm that for topological free fermion systems the wavefront spreads linearly at a characteristic butterfly velocity. We pay special attention to the topologically protected edge states, finding that "information" can become trapped in the edge states and essentially decoupled from the bulk, surviving for relatively long times. We consider different models with multiple possible edge states coexisting on a single edge.

Dynamical quantum phase transitions can occur following quenches in quantum systems when the rate function, a dynamical analogue of the free energy, becomes non-analytic at critical times. Here we exhaustively investigate in an exemplary model how the dynamically evolving state responds to a second quench. We demonstrate that for quenches where the initial and final Hamiltonian belong to different phases always result in dynamical quantum phase transitions, irrespective of the intermediate quench and dynamics or the time of the second quench. However, if the initial and final Hamiltonian belong to the same equilibrium phase then the intermediate Hamiltonian must belong to a different phase. In this case, the second quench time in relation to the critical times of the first quench becomes crucial to the existence of dynamical quantum phase transitions.

In this paper, we prove the relation between special cycles on a Rapoport-Smithling-Zhang Shimura variety and special values of the derivative of a Hilbert Eisenstein series.

We analyze the behavior of steady-state quantum correlations (QCs) in the spin-1/2 transverse field XY chains analytically, in terms of quench dynamics at zero-temperature. We show that steady-state QCs are strikingly greater than the equilibrium ones in its ground-state, where a single quench is performed from ferro- into para-magnetic phases. Another framework to amplify the QCs here is a feasible protocol called double quench dynamics. To fulfill this purpose, we probe a middle quench point and spending time T (defined as the time passing from the middle quench point before reaching a second quench). By doing so, both single and double quenches act as practical tools to control the enhancement of the steady-state QCs in the final quenched point. In particular, and in parallel to expectations for some other quantities, we indicate that the nonequilibrium quantum phase transitions also can be identified by nonanalyticities in the steady-state QCs. Our work may be testable with the current class of trapped-ion or ultracold-atom experiments, and encourage the possible potential in the quantum information field., Comment: 13 pages, 8 figures

In this paper we build a geometric model for the renormalisation of irrationally indifferent fixed points. The geometric model incorporates the fine arithmetic properties of the rotation number at the fixed point. Using this model for the renormalisation, we build a topological model for the dynamics of a holomorphic map near an irrationally indifferent fixed point. Then, we explain the topology of the maximal invariant set for the model, and also explain the dynamics of the map on the maximal invariant set., Comment: 73 pages, this article is the first part of the article arXiv:1706.02678, which has been extended to a complete model for the renormalisation. The second part of arXiv:1706.02678 will appear under that title with an updated version. Latest version: Minor modifications following referee comments

We study the time evolution of spin squeezing in the one-dimensional spin-1/2 XY model subject to a sudden quantum quench of a transverse magnetic field. The initial state is selected from the ground state phase diagram of the model, consisting of ferro- and paramagnetic phases separated by a critical value of the transverse field. Our analysis, based on exact results for the model, reveals that by a proper choice of protocol, a quantum quench from an unsqueezed state can create spin squeezed nonequilibrium states. We also identify a nonanalyticity in the long-time average of the spin-squeezing parameter when quenching to the equilibrium quantum critical point. This suggests that the ferro- and paramagnetic phases also define distinct phases for how the transverse field redistributes quantum fluctuations among the spin components away from equilibrium., Comment: 14 pages, 10 figures, Revised version, Added references, corrected calculation of off-diagonal spin correlations

Let $\mathcal{CM}_{\Phi}$ be the (integral model of the) stack of principally polarized CM Abelian varieties with a CM-type $\Phi$. Considering a pair of nearby CM-types (i.e. such that they are different in exactly one embedding) $\Phi_1, \Phi_2$, we let $X = \mathcal{CM}_{\Phi_1} \times \mathcal{CM}_{\Phi_2}$ and define arithmetic divisors $\mathcal{Z}(\alpha)$ on $X$ such that the Arakelov degree of $\mathcal{Z}(\alpha)$ is (up to multiplication by an explicit constant) equal to the central value of the $\alpha^{\text{th}}$ coefficient of the Fourier expansion of the derivative of a Hilbert Eisenstein series., Comment: 19 pages - Some typos were fixed

We consider the ground-state phase diagram of a one-dimensional spin-1/2 XXZ chain with spatially modulated Dzyaloshinskii-Moriya interaction in the presence of applied along with the $\hat{z}$ axis alternating magnetic field. The model is studied using the continuum-limit bosonization approach and the finite system exact numerical technique. In the absence of the magnetic field, the ground-state phase diagram of the model includes besides the ferromagnetic and gapless Luttiger-Liquid (LL) phases two gapped phases, the composite (C1) phase characterized by the coexistence of the long-range-ordered (LRO) alternating dimerization and the spin chirality patterns, and the composite (C2) phase characterized in addition to the coexisting spin dimerization and alternating chirality patterns, by the presence of LRO antiferromagnetic order. In the case of two-letter gapped phases, in the case of a uniform magnetic field, the commensurate-incommensurate type quantum phase transitions (QPT) from a gapful phase into the gapless phase have been identified and described using the bosonization treatment and finite chain exact diagonalizations studies. The upper critical magnetic field corresponding to the transition into a fully polarized state has been also determined. It has been shown that the very presence of the staggered component of the magnetic field vapes out the composite (C1) in favour of the composite gapped (C2) phase., Comment: 13 pages, 8 figures, will be appear in Phys. Rev. E

Swarm Robotics is an emerging field of adapting the phenomenon of natural swarms to robotics. It is a study of robots that are aimed to mimic natural swarms, like ants and birds, to form a system that is scalable, flexible, and robust. These robots show self-organization, autonomy, cooperation, and coordination amongst themselves. The cost and design complexity factor is aimed to keep low, hence trying to form systems that are very much similar to natural swarms. The robots operate without any central entity to control them, and the communication amongst the robots can either be direct (robot-to-robot) or indirect (robot-to-environment). Swarm robotics has a wide range of application fields, from simple household tasks to military missions. This paper reviews the swarm robotics approach from its history to its future. It discusses the basic idea of swarm robotics, its important features, simulators, projects, real life applications and some future ideas.

We consider the dynamics of maximal quantum Fisher information (MQFI) after sudden quenches for the one-dimensional transverse-field Ising model. Our results show, the same as Loschmidt echo, there is a universality for the revival times i.e., they do not depend on the initial state and the size of the quench and are given by integer multiples of $T_{rev} \simeq \frac{N}{2v_{max }}$, where $N$ is the system size and $v_{max }$ is the maximal group velocity of quasiparticles. Critically enhanced and decreased at revival and decay times as $T_{rev} \equiv T_{dec} $ are characterized by quenching from the order and disorder phases into the quantum phase transition respectively, that can be utilized to detect the quantum critical point (QCP). In some quenches crossed from the QCP, nonanalytic behaviors appear at some times due to the turning of the local observable from one direction to another because of identifying the maximum value. We name this phenomenon \textit{the dynamical MQFI transitions}, occurring at the critical times $t_c$. Interestingly, although no Fisher zero exists in the dynamics of MQFI, the first critical time emerged from the dynamical quantum phase transition is equal to the first time whose the logarithm of MQFI is minimum. In addition, we unveil the long-time run of MQFI indicates a signature of a nonequilibrium quantum phase transition at the QCP. We also discuss the probability of arising of macroscopic superpositions in the nonequilibrium dynamics of the system., Comment: 10 pages, 8 figures, will appear in Phys. Rev. B

We prove that for a dense set of irrational numbers $\alpha$, the analytic centraliser of the map $e^{2\pi i \alpha} z+ z^2$ near $0$ is trivial. We also prove that some analytic circle diffeomorphisms in the Arnold family, with irrational rotation numbers, have trivial centralisers. These provide the first examples of such maps with trivial centralisers., Comment: 13 Pages, No figures

In this paper we study the geometry of the attractors of holomorphic maps with an irrationally indifferent fixed point. We prove that for an open set of such holomorphic systems, the local attractor at the fixed point has Hausdorff dimension two, provided the asymptotic rotation at the fixed point is of sufficiently high type and does not belong to Herman numbers. As an immediate corollary, the Hausdorff dimension of the Julia set of any such rational map with a Cremer fixed point is equal to two. Moreover, we show that for a class of asymptotic rotation numbers, the attractor satisfies Karpi\'{n}ska's dimension paradox. That is, the the set of end points of the attractor has dimension two, but without those end points, the dimension drops to one., Comment: 42 pages, 4 figures

Ergodicity sits at the heart of the connection between statistical mechanics and dynamics of a physical system. By fixing the initial state of the system into the ground state of the Hamiltonian at zero temperature and tuning a control parameter, we consider the occurrence of the ergodicity with quench dynamics in the one-dimensional (1D) spin-1/2 XY model in a transverse magnetic field. The ground-state phase diagram consists of two ferromagnetic and paramagnetic phases. It is known the magnetization in this spin system is non-ergodic. We set up two different experiments as we call them single and double quenches and test the dynamics of the magnetization along the $Z$-axis and the spin-spin correlation function along the $X$-axis which are the order parameters of the zero-temperature phases . Our exact results reveal that for single quenches at zero-temperature, the ergodicity depends on the initial state and the order parameter. Interestingly on the other setup, a double quench on a cyclic path, ergodicity is completely broken for starting from the phase corresponding to the order parameter. Otherwise, it depends on the first quenched point, and the quench time $T$ when the model spent before a second quench in the way back which gives an ability to controlling the ergodicity in the system. Therefore, and contrary to expectations, in the mentioned model the ergodicity can be observed with probing quench dynamics at zero-temperature. Our results provide further insight into the zero-temperature dynamical behavior of quantum systems and their connections to the ergodicity phenomenon., Comment: 12 pages, 8 figures