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Functional observability and subspace reconstruction in nonlinear systems ; ; Proverbio, Daniele et al in Physical Review Research (2022), 4 Time-series analysis is fundamental for modeling and predicting dynamical behaviors from time- ordered data, with applications in many disciplines such as physics, biology, finance, and engineering ... [more ▼] Time-series analysis is fundamental for modeling and predicting dynamical behaviors from time- ordered data, with applications in many disciplines such as physics, biology, finance, and engineering. Measured time-series data, however, are often low dimensional or even univariate, thus requiring embedding methods to reconstruct the original system’s state space. The observability of a system establishes fundamental conditions under which such reconstruction is possible. However, complete observability is too restrictive in applications where reconstructing the entire state space is not necessary and only a specific subspace is relevant. Here, we establish the theoretic condition to reconstruct a nonlinear functional of state variables from measurement processes, generalizing the concept of functional observability to nonlinear systems. When the functional observability condition holds, we show how to construct a map from the embedding space to the desired functional of state variables, characterizing the quality of such reconstruction. The theoretical results are then illustrated numerically using chaotic systems with contrasting observability properties. By exploring the presence of functionally unobservable regions in embedded attractors, we also apply our theory for the early warning of seizure-like events in simulated and empirical data. The studies demonstrate that the proposed functional observability condition can be assessed a priori to guide time-series analysis and experimental design for the dynamical characterization of complex systems. [less ▲] Detailed reference viewed: 11 (0 UL)Overlap of parafermionic zero modes at a finite distance ; Haller, Andreas ; et al in Physical Review Research (2022) Parafermion bound states (PBSs) are generalizations of Majorana bound states (MBSs) and have been predicted to exist as zero-energy eigenstates in proximitized fractional quantum Hall edge states ... [more ▼] Parafermion bound states (PBSs) are generalizations of Majorana bound states (MBSs) and have been predicted to exist as zero-energy eigenstates in proximitized fractional quantum Hall edge states. Similarly to MBSs, a finite distance between the PBS can split the ground state degeneracy. However, parafermionic modes have a richer exchange statistics than MBSs, so several interaction terms are allowed by the underlying $\mathbb{Z}_{2n}$ symmetry, rendering the effective Hamiltonian governing a pair of PBSs at a finite distance nontrivial. Here, we use a combination of analytical techniques (semiclassical instanton approximation) and numerical techniques (quantum Monte Carlo simulations) to determine the effective coupling Hamiltonian. For this purpose, we go beyond the dilute one-instanton gas approximation and show how finite-size effects can give rise to higher-order parafermion interactions. We find excellent agreement between the analytical results and Monte Carlo simulations. We estimate that these finite-size corrections should be observable in some of the recently proposed experiments to observe PBSs in strongly correlated systems. [less ▲] Detailed reference viewed: 29 (5 UL)Lipid islands on liquid crystal shells Sharma, Anjali ; ; Scalia, Giusy et al in Physical Review Research (2022), 4 By inducing phase separation in lipid monolayers on liquid crystal (LC) shells—thin hollow spheres of LC with water inside and outside—we reveal a rich set of coupled two- and three-dimensional (2D and 3D ... [more ▼] By inducing phase separation in lipid monolayers on liquid crystal (LC) shells—thin hollow spheres of LC with water inside and outside—we reveal a rich set of coupled two- and three-dimensional (2D and 3D) self- organization phenomena enabled by the dual closely spaced internal and external spherical LC-water interfaces. Spindle-shaped 2D islands of condensed lipid monolayer first form at the primary interface where lipids are deposited, later also at the initially unexposed secondary interface, because lipids transfer through the LC. The LCs’ elastic response to the 3D deformation caused by islands moves them from thin to thick regions on the shell and creates an attraction between opposite-side islands, topologically separated by the LCs, until they stack in a sandwich-like manner. We propose that the phase separation may be used for studying liposome adsorption on soft hydrophobic substrates, and to create unconventional colloidal particles with programmed interactions. [less ▲] Detailed reference viewed: 43 (1 UL)Quantum framework for describing retarded and nonretarded molecular interactions in external electric fields Karimpour, Mohammad Reza ; Fedorov, Dmitry ; Tkatchenko, Alexandre in Physical Review Research (2022) Detailed reference viewed: 72 (3 UL)Digitized-counterdiabatic quantum approximate optimization algorithm ; ; et al in Physical Review Research (2022) The quantum approximate optimization algorithm (QAOA) has proved to be an effective classical-quantum algorithm serving multiple purposes, from solving combinatorial optimization problems to finding the ... [more ▼] The quantum approximate optimization algorithm (QAOA) has proved to be an effective classical-quantum algorithm serving multiple purposes, from solving combinatorial optimization problems to finding the ground state of many-body quantum systems. Since the QAOA is an Ansatz-dependent algorithm, there is always a need to design Ansätze for better optimization. To this end, we propose a digitized version of the QAOA enhanced via the use of shortcuts to adiabaticity. Specifically, we use a counterdiabatic (CD) driving term to design a better Ansatz, along with the Hamiltonian and mixing terms, enhancing the global performance. We apply our digitized-CD QAOA to Ising models, classical optimization problems, and the P-spin model, demonstrating that it outperforms the standard QAOA in all cases we study. [less ▲] Detailed reference viewed: 22 (2 UL)Super-Heisenberg scaling in Hamiltonian parameter estimation in the long-range Kitaev chain Yang, Jing ; ; Del Campo Echevarria, Adolfo et al in Physical Review Research (2022) In quantum metrology, nonlinear many-body interactions can enhance the precision of Hamiltonian parameter estimation to surpass the Heisenberg scaling. Here, we consider the the estimation of the ... [more ▼] In quantum metrology, nonlinear many-body interactions can enhance the precision of Hamiltonian parameter estimation to surpass the Heisenberg scaling. Here, we consider the the estimation of the interaction strength in linear systems with long-range interactions and using the Kitaev chains as a case study, we establish a transition from the Heisenberg to super-Heisenberg scaling in the quantum Fisher information by varying the interaction range. We further show that quantum control can improve the prefactor of the quantum Fisher information. Our results explore the advantage of optimal quantum control and long-range interactions in many-body quantum metrology. [less ▲] Detailed reference viewed: 18 (1 UL)Benchmarking quantum annealing dynamics: The spin-vector Langevin model ; ; et al in Physical Review Research (2022) The classical spin-vector Monte Carlo (SVMC) model is a reference benchmark for the performance of a quantum annealer. Yet, as a Monte Carlo method, SVMC is unsuited for an accurate description of the ... [more ▼] The classical spin-vector Monte Carlo (SVMC) model is a reference benchmark for the performance of a quantum annealer. Yet, as a Monte Carlo method, SVMC is unsuited for an accurate description of the annealing dynamics in real-time.We introduce the spin-vector Langevin (SVL) model as an alternative benchmark in which the time evolution is described by Langevin dynamics. The SVL model is shown to provide a more stringent test than the SVMC model for the identification of quantum signatures in the performance of quantum annealing devices, as we illustrate by describing the Kibble-Zurek scaling associated with the dynamics of symmetry breaking in the transverse field Ising model, recently probed using D-Wave machines. Specifically, we show that D-Wave data are reproduced by the SVL model. [less ▲] Detailed reference viewed: 23 (1 UL)Probing quantum chaos in multipartite systems ; ; Del Campo Echevarria, Adolfo in Physical Review Research (2022) Understanding the emergence of quantum chaos in multipartite systems is challenging in the presence of interactions. We show that the contribution of the subsystems to the global behavior can be revealed ... [more ▼] Understanding the emergence of quantum chaos in multipartite systems is challenging in the presence of interactions. We show that the contribution of the subsystems to the global behavior can be revealed by probing the full counting statistics of the local, total, and interaction energies. As in the spectral form factor, signatures of quantum chaos in the time domain dictate a dip-ramp-plateau structure in the characteristic function, i.e., the Fourier transform of the eigenvalue distribution. With this approach, we explore the fate of chaos in interacting subsystems that are locally maximally chaotic. Global quantum chaos can be suppressed at strong coupling, as illustrated with coupled copies of random-matrix Hamiltonians and of the Sachdev-Ye-Kitaev model. Our method is amenable to experimental implementation using single-qubit interferometry. [less ▲] Detailed reference viewed: 29 (0 UL)Super-Heisenberg scaling in Hamiltonian parameter estimation in the long-range Kitaev chain Yang, Jing ; ; Del Campo Echevarria, Adolfo et al in Physical Review Research (2021) In quantum metrology, nonlinear many-body interactions can enhance the precision of Hamiltonian parameter estimation to surpass the Heisenberg scaling. Here, we consider the estimation of the interaction ... [more ▼] In quantum metrology, nonlinear many-body interactions can enhance the precision of Hamiltonian parameter estimation to surpass the Heisenberg scaling. Here, we consider the estimation of the interaction strength in linear systems with long-range interactions and using the Kitaev chains as a case study, we establish a transition from the Heisenberg to super-Heisenberg scaling in the quantum Fisher information by varying the interaction range. We further show that quantum control can improve the prefactor of the quantum Fisher information. Our results explore the advantage of optimal quantum control and long-range interactions in many-body quantum metrology. [less ▲] Detailed reference viewed: 51 (7 UL)Delta-kick cooling, time-optimal control of scale-invariant dynamics, and shortcuts to adiabaticity assisted by kicks Dupays, Léonce ; ; et al in Physical Review Research (2021) Delta-kick cooling (DKC) is used to compress the momentum distribution of ultracold quantum matter. It combines expansion dynamics with the use of kick pulses, designed via classical methods, that bring ... [more ▼] Delta-kick cooling (DKC) is used to compress the momentum distribution of ultracold quantum matter. It combines expansion dynamics with the use of kick pulses, designed via classical methods, that bring the system to rest.We introduce an exact approach to DKC for arbitrary scale-invariant dynamics of quantum gases, lifting the original restrictions to free evolution and noninteracting systems, to account for the control of atomic clouds in a time-dependent harmonic trap that can be either repulsive (inverted) or confining. We show that DKC assisted by a repulsive potential outperforms the conventional scheme, and that sudden trap-frequency quenches combined with DKC are equivalent to time-optimal bang-bang protocols.We further show that reverse engineering of the scale-invariant dynamics under smooth trap-frequency modulations can be combined with DKC to introduce a new class of shortcuts to adiabaticity assisted by kicks. [less ▲] Detailed reference viewed: 55 (6 UL)Distribution of kinks in an Ising ferromagnet after annealing and the generalized Kibble-Zurek mechanism ; ; et al in Physical Review Research (2021) We consider the annealing dynamics of a one-dimensional Ising ferromagnet induced by a temperature quench in finite time. In the limit of slow cooling, the asymptotic two-point correlator is analytically ... [more ▼] We consider the annealing dynamics of a one-dimensional Ising ferromagnet induced by a temperature quench in finite time. In the limit of slow cooling, the asymptotic two-point correlator is analytically found under Glauber dynamics, and the distribution of the number of kinks in the final state is shown to be consistent with a Poissonian distribution. The mean kink number, the variance, and the third centered moment take the same value and obey a universal power-law scaling with the quench time in which the temperature is varied. The universal power-law scaling of cumulants is corroborated by numerical simulations based on Glauber dynamics for moderate cooling times away from the asymptotic limit, when the kink-number distribution takes a binomial form. We analyze the relation of these results to physics beyond the Kibble-Zurek mechanism for critical dynamics, using the kink-number distribution to assess adiabaticity and its breakdown.We consider linear, nonlinear, and exponential cooling schedules, among which the last provides the most efficient shortcuts to cooling in a given quench time. The nonthermal behavior of the final state is established by considering the trace norm distance to a canonical Gibbs state. [less ▲] Detailed reference viewed: 67 (1 UL)Quantum-mechanical force balance between multipolar dispersion and Pauli repulsion in atomic van der Waals dimers Vaccarelli, Ornella ; Fedorov, Dmitry ; Stoehr, Martin et al in Physical Review Research (2021) Detailed reference viewed: 104 (5 UL)Digitized-counterdiabatic quantum approximate optimization algorithm ; ; et al in Physical Review Research (2021) The quantum approximate optimization algorithm (QAOA) has proved to be an e ective classical-quantum algorithm serving multiple purposes, from solving combinatorial optimization problems to finding the ... [more ▼] The quantum approximate optimization algorithm (QAOA) has proved to be an e ective classical-quantum algorithm serving multiple purposes, from solving combinatorial optimization problems to finding the ground state of many-body quantum systems. Since QAOA is an ansatz-dependent algorithm, there is always a need to design ansatz for better optimization. To this end, we propose a digitized version of QAOA enhanced via the use of shortcuts to adiabaticity. Specifically, we use a counterdiabatic (CD) driving term to design a better ansatz, along with the Hamiltonian and mixing terms, enhancing the global performance. We apply our digitizedcounterdiabatic QAOA to Ising models, classical optimization problems, and the P-spin model, demonstrating that it outperforms standard QAOA in all cases we study. [less ▲] Detailed reference viewed: 33 (2 UL)Universal Hall conductance scaling in non-Hermitian Chern insulators ; Schmidt, Thomas ; in Physical Review Research (2021) We investigate the Hall conductance of a two-dimensional Chern insulator coupled to an environment causing gain and loss. Introducing a biorthogonal linear response theory, we show that sufficiently ... [more ▼] We investigate the Hall conductance of a two-dimensional Chern insulator coupled to an environment causing gain and loss. Introducing a biorthogonal linear response theory, we show that sufficiently strong gain and loss lead to a characteristic nonanalytical contribution to the Hall conductance. Near its onset, this contribution exhibits a universal power law with a power 3/2 as a function of Dirac mass, chemical potential, and gain strength. Our results pave the way for the study of non-Hermitian topology in fermionic transport experiments. [less ▲] Detailed reference viewed: 29 (0 UL)Correlation satellites in optical and loss spectra Cudazzo, Pier Luigi ; in Physical Review Research (2020), 2 Coupling of excitations leads to intriguing effects on the spectra of materials. We propose a cumulant formulation for neutral electronic excitations which opens the way to describe effects such as double ... [more ▼] Coupling of excitations leads to intriguing effects on the spectra of materials. We propose a cumulant formulation for neutral electronic excitations which opens the way to describe effects such as double plasmon satellites or exciton-exciton coupling. Our approach starts from the GW+Bethe-Salpeter approximation to many-body perturbation theory which is based on a quasiparticle picture, and it adds coupling of excitations through a consistent inclusion of dynamically screened interactions. This requires one to consider scattering contributions that are usually neglected. The result is formulated in a way that highlights essential physics, that can be implemented as a postprocessing tool in first-principles codes, and that suggests which kind of materials and measurements should exhibit strong effects. This is illustrated using a model. [less ▲] Detailed reference viewed: 127 (8 UL)Superadiabatic thermalization of a quantum oscillator by engineered dephasing Dupays, Léonce ; ; Del Campo Echevarria, Adolfo et al in Physical Review Research (2020), 2 Fast nonadiabatic control protocols known as shortcuts to adiabaticity have found a plethora of applications, but their use has been severely limited to speeding up the dynamics of isolated quantum ... [more ▼] Fast nonadiabatic control protocols known as shortcuts to adiabaticity have found a plethora of applications, but their use has been severely limited to speeding up the dynamics of isolated quantum systems. We introduce shortcuts for open quantum processes that make possible the fast control of Gaussian states in nonunitary processes. Specifically, we provide the time modulation of the trap frequency and dephasing strength that allow preparing an arbitrary thermal state in a finite time. Experimental implementation can be done via stochastic parametric driving or continuous measurements, readily accessible in a variety of platforms. [less ▲] Detailed reference viewed: 41 (3 UL)Discrimination of thermal baths by single-qubit probes ; ; et al in Physical Review Research (2020) Nonequilibrium states of quantum systems in contact with thermal baths help distinguishing between environments with different temperatures or different statistics. We extend these studies to a more ... [more ▼] Nonequilibrium states of quantum systems in contact with thermal baths help distinguishing between environments with different temperatures or different statistics. We extend these studies to a more generic problem that consists in discriminating between two baths with disparate constituents at unequal temperatures. Notably there exist temperature regimes in which the presence of coherence in the initial state preparation is beneficial for the discrimination capability. We also find that nonequilibrium states are not universally optimal and detail the conditions in which it becomes advantageous to wait for complete thermalization of the probe. These concepts are illustrated in a linear-optical simulation. [less ▲] Detailed reference viewed: 51 (1 UL)Dynamic tuning of the director field in liquid crystal shells using block copolymers ; ; et al in Physical Review Research (2020), 2(3), 033160 When an orientationally ordered system, like a nematic liquid crystal (LC), is confined on a self-closing spherical shell, topological constraints arise with intriguing consequences that depend critically ... [more ▼] When an orientationally ordered system, like a nematic liquid crystal (LC), is confined on a self-closing spherical shell, topological constraints arise with intriguing consequences that depend critically on how the LC is aligned in the shell. We demonstrate reversible dynamic tuning of the alignment, and thereby the topology, of nematic LC shells stabilized by the nonionic amphiphilic block copolymer Pluronic F127. Deep in the nematic phase, the director (the average molecule orientation) is tangential to the interface, but upon approaching the temperature TNI of the nematic-isotropic transition, the director realigns to normal. We link this to a delicate interplay between an interfacial tension that is nearly independent of director orientation, and the configuration-dependent elastic deformation energy of an LC confined in a shell. The process is primarily triggered by the heating-induced reduction of the nematic order parameter, hence realignment temperatures differ by several tens of degrees between LCs with high and low TNI, respectively. The temperature of realignment is always lower on the positive-curved shell outside than at the negative-curved inside, yielding a complex topological reconfiguration on heating. Complementing experimental investigations with mathematical modeling and computer simulations, we identify and investigate three different trajectories, distinguished by their configurations of topological defects in the initial tangential-aligned shell. Our results uncover a new aspect of the complex response of LCs to curved confinement, demonstrating that the order of the LC itself can influence the alignment and thereby the topology of the system. They also reveal the potential of amphiphilic block copolymer stabilizers for enabling continuous tunability of LC shell configuration, opening doors for in-depth studies of topological dynamics as well as novel applications in, e.g., sensing and programed soft actuators. [less ▲] Detailed reference viewed: 73 (0 UL) |
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