Time-periodic Field Research Articles

Stretched-exponential melting of a dynamically frozen state under imprinted phase noise in the ising chain in a transverse field

The concept of dynamical freezing is a phenomenon where a suitable set of local observables freezes under a strong periodic drive in a quantum many-body system. This happens because of the emergence of approximate but perpetual conservation laws when the drive is strong enough. In this work, we probe the resilience of dynamical freezing to random perturbations added to the relative phases between the interfering states (elements of a natural basis) in the time-evolving wave function after each drive cycle. We study this in an integrable Ising chain in a time-periodic transverse field. Our key finding is, that the imprinted phase noise melts the dynamically frozen state, but the decay is “slow”: a stretched-exponential decay rather than an exponential one. Stretched-exponential decays (also known as Kohlrausch relaxation) are usually expected in complex systems with time-scale hierarchies due to strong disorders or other inhomogeneities resulting in jamming, glassiness, or localization. Here we observe this in a simple translationally invariant system dynamically frozen under a periodic drive. Moreover, the melting here does not obliterate the entire memory of the initial state but leaves behind a steady remnant that depends on the initial conditions. This underscores the stability of dynamically frozen states.Graphical abstract

Global weak solutions to a time-periodic body-liquid interaction problem

We prove existence of time-periodic weak solutions to the coupled liquid-structure problem constituted by an incompressible Navier–Stokes fluid interacting with a rigid body of finite size, subject to an undamped linear restoring force. The fluid flow is generated by a uniform, time-periodic velocity field {\boldsymbol V} far from the body. We emphasize that our result is global, in the sense that no restriction is imposed on the magnitude of {\boldsymbol V} and, rather remarkably, the frequency of {\boldsymbol V} is entirely arbitrary. Thus, in particular, it can coincide with any multiple of a natural frequency of vibration of the body so that, with this model, resonance cannot occur. Although based on the classical “invading domains” technique, our approach requires several new ideas. Indeed, due to the lack of sufficient dissipation, it appears quite unfeasible to show the existence of a fixed point of the Poincaré map at the finite-dimensional level along the Galerkin approximant. Therefore, unlike the usual strategy, such a result must be proven directly in a class of weak solutions, and therefore in the infinite-dimensional framework.

Shadows of rotating hairy Kerr black holes coupled to time periodic scalar fields with a nonflat target space

Shadows of rotating hairy Kerr black holes coupled to time periodic scalar fields with a nonflat target space

Dissipative stability and dynamical phase transition in two driven interacting qubits

We examine a two-qubit system influenced by a time-periodic external field while interacting with a Markovian bath. This scenario significantly impacts the temporal coherence characteristics of the system. By solving the evolution equation for the density matrix operator, we determine the characteristic equilibration time and analyze the concurrence parameter-a key metric for quantifying entanglement. Our findings reveal the system’s ability to navigate through a dynamic phase transition. These results pave the way to designing systems of interacting qubits demonstrating robust entanglement under realistic conditions of interaction with the environment.

Parallel-in-Space-and-Time Finite-Element Method for Time-Periodic Magnetic Field Problems With Hysteresis

Parallel-in-Space-and-Time Finite-Element Method for Time-Periodic Magnetic Field Problems With Hysteresis

Bifurcation and dynamics of periodic solutions to the Rayleigh–Plesset equation: Theory and numerical simulation

In this paper, we study the oscillation of a gas-filled spherical bubble immersed in an infinite domain of incompressible liquid under the influence of a time-periodic acoustic field. The oscillation is described by the Rayleigh–Plesset equation, which is derived from the Navier–Stokes equation under the assumptions of spherical symmetry. Taking the initial radius R0, or the initial instantaneous partial pressure Pg0, of the gas-filled bubble as a parameter, we present a saddle–node bifurcation of periodic solutions to the Rayleigh–Plesset equation in the parameter space, provided the mean value of applied pressure is greater than the vapor pressure. Further, we show that the Rayleigh–Plesset equation has two classes of periodic solutions, as R0 (resp. Pg0) tends to +∞, the first class of solutions uniformly diverges to +∞ at the rate of R05 (resp. Pg05/2), while the second class converges to 0 at the rate of R0−5 (resp. Pg0−5/2). As for the case where the density of the liquid ρ is chosen as a parameter, we observe an interesting nonlinear phenomenon that, for some ρ, the Rayleigh–Plesset equation may possess four positive T-periodic solutions: two of them are stable, while the rest of them are unstable. This is quite different from the phenomenon that occurs when R0 (or Pg0) is chosen as a parameter.

Floquet Engineering of Black Phosphorus upon Below-Gap Pumping.

Time-periodic light field can dress the electronic states and lead to light-induced emergent properties in quantum materials. While below-gap pumping is regarded favorable for Floquet engineering, so far direct experimental evidence of momentum-resolved band renormalization still remains missing. Here, we report experimental evidence of light-induced band renormalization in black phosphorus by pumping at photon energy of 160meV, which is far below the band gap, and the distinction between below-gap pumping and near-resonance pumping is revealed. Our Letter demonstrates light-induced band engineering upon below-gap pumping, and provides insights for extending Floquet engineering to more quantum materials.

Quantum computing Floquet energy spectra

Quantum systems can be dynamically controlled using time-periodic external fields, leading to the concept of Floquet engineering, with promising technological applications. Computing Floquet energy spectra is harder than only computing ground state properties or single time-dependent trajectories, and scales exponentially with the Hilbert space dimension. Especially for strongly correlated systems in the low frequency limit, classical approaches based on truncation break down. Here, we present two quantum algorithms to determine effective Floquet modes and energy spectra. We combine the defining properties of Floquet modes in time and frequency domains with the expressiveness of parametrized quantum circuits to overcome the limitations of classical approaches. We benchmark our algorithms and provide an analysis of the key properties relevant for near-term quantum hardware.

Floquet Theory of Classical Relaxation in Time-Dependent Field

The anomalous transport of particles in the presence of a time-dependent field is considered in the framework of a comb model. This turbulent-like dynamics consists of inhomogeneous time-dependent advection along the x-backbone and Brownian motion along the y-side branches. This geometrically constrained transport leads to anomalous diffusion along the backbone, which is described by a fractional diffusion equation with time-dependent coefficients. The time periodic process leads to localization of the transport and a particular form of relaxation. The analytical approach is considered in the framework of the Floquet theory, which is developed for the fractional diffusion equation with periodic in time coefficients. This physical situation is considered in detail and analytical expressions for both the probability density function and the mean squared displacement are obtained. The new analytical approach is developed in the framework of the fractional Floquet theory that makes it possible to investigate a new class of anomalous diffusion in the presence of time periodic fields.

Free convection of nanofluids in a porous sensible heat storage unit: Combined effect of time periodic heating and external magnetic field

Nanofluids have gained much interest in recent years in heat transfer applications due to their improved thermal properties compared to conventional pure fluids. In many applications, the nanofluid may be subjected to unsteady heating and to the effect of external magnetic field, which can have a considerable effect on the behavior of the nanofluid, especially if the nanoparticles are metallic. In the present study, the flow and heat transfer characteristics of Cu/water nanofluid in a semi-circular cavity are analyzed. The fluid is heated by a heat source located at the bottom wall and having a time-periodic temperature profile. The other walls are adiabatic. Two magnetic sources are located on the top wall. The equations governing the flow and thermal behavior of the nanofluid are presented and converted into the dimensionless form. The equations are then solved by means of the finite volume method. The results are presented in the form of flow and thermal contours, as well as in the variation of the sensible heat, thermal stratification, and Nusselt numbers as functions of time. The impacts of various parameters, namely the temperature frequency, the magnetic number, the porosity, Darcy and Rayleigh numbers, on the results are discussed. In particular, it has been found that the porosity possessed the most important effect on the flow and thermal behaviors of the nanofluid. A 60% increase in Nusselt number is notably observed when the porosity is changed from 0.9 to 0.1.

Dynamical spin-orbit-based spin transistor

Spin-orbit interaction (SOI) has been a key tool to steer and manipulate spin-dependent transport properties in two-dimensional electron gases. Here we demonstrate how spin currents can be created and efficiently read out in nano- or mesoscale conductors with time-dependent and spatially inhomogeneous Rashba SOI. Invoking an underlying non-Abelian SU(2) gauge structure we show how time-periodic spin-orbit fields give rise to spin electric forces and enable the generation of pure spin currents of the order of several hundred nano-Amperes. In a complementary way, by combining gauge transformations with “hidden” Onsager relations, we exploit spatially inhomogeneous Rashba SOI to convert spin currents (back) into charge currents. In combining both concepts, we devise a spin transistor that integrates efficient spin current generation, by employing dynamical SOI, with its experimentally feasible detection via conversion into charge signals. We derive general expressions for the respective spin- and charge conductance, covering large parameter regimes of SOI strength and driving frequencies, far beyond usual adiabatic approaches such as the frozen scattering matrix approximation. We check our analytical expressions and approximations with full numerical spin-dependent transport simulations and demonstrate that the predictions hold true in a wide range from low to high driving frequencies.

Pseudospin-selective Floquet band engineering in black phosphorus

Time-periodic light field has emerged as a control knob for manipulating quantum states in solid-state materials1-3, cold atoms4 and photonic systems5 through hybridization with photon-dressed Floquet states6 in the strong-coupling limit, dubbed Floquet engineering. Such interaction leads to tailored properties of quantum materials7-11, for example, modifications of the topological properties of Dirac materials12,13 and modulation of the optical response14-16. Despite extensive research interests over the past decade3,8,17-20, there is no experimental evidence of momentum-resolved Floquet band engineering of semiconductors, which is a crucial step to extend Floquet engineering to a wide range of solid-state materials. Here, on the basis of time and angle-resolved photoemission spectroscopy measurements, we report experimental signatures of Floquet band engineering in a model semiconductor, black phosphorus. On near-resonance pumping at a photon energy of 340-440 meV, a strong band renormalization is observed near the band edges. In particular, light-induced dynamical gap opening is resolved at the resonance points, which emerges simultaneously with the Floquet sidebands. Moreover, the band renormalization shows a strong selection rule favouring pump polarization along the armchair direction, suggesting pseudospin selectivity for the Floquetband engineering as enforced by the lattice symmetry. Our work demonstrates pseudospin-selective Floquet band engineering in black phosphorus and provides important guiding principles for Floquet engineering of semiconductors.

Weak Nonlinear Oscillatory Double Diffusive Convection in a Viscoelastic Fluid-Saturated Porous Layer Under Gravity Modulation

A thermal instability caused by buoyancy force is investigated in an initially quiescent indefinitely extended horizontal porous layer saturated with non - Newtonian fluid. The characteristics of fluid motion are explained by using Modified Darcy’s law. Here, we considered the time periodic gravity field, and its effect on the system has been investigated. For the oscillatory mode of convection, a weakly non-linear stability analysis has been performed to evaluate Heat and Mass transfers in terms of the Nusselt number and Sherwood Number. To compute the results, the complex non-autonomous Ginzburg – Landau equation is used. It has been studied how viscoelastic fluid relaxation and retardation times impacts on heat and mass transmission. Further, the research confirms that heat and mass transfer can be successfully regulates by a technique that is external to the system. Finally, it has been discovered that excessive stability delays the onset of convection, hence increasing in the heat and mass transmission.

Fe3O4-SiO2 Mesoporous Core/Shell Nanoparticles for Magnetic Field-Induced Ibuprofen-Controlled Release.

Hybrid magnetic nanoparticles made up of an iron oxide, Fe3O4, core and a mesoporous SiO2 shell with high magnetization and a large surface area were proposed as an efficient drug delivery platform. The core/shell structure was synthesized by two seed-mediated growth steps combining solvothermal and sol-gel approaches and using organic molecules as a porous scaffolding template. The system presents a mean particle diameter of 30(5) nm (9 nm magnetic core diameter and 10 nm silica shell thickness) with superparamagnetic behavior, saturation magnetization of 32 emu/g, and a significant AC magnetic-field-induced heating response (SAR = 63 W/gFe3O4, measured at an amplitude of 400 Oe and a frequency of 307 kHz). Using ibuprofen as a model drug, the specific surface area (231 m2/g) of the porous structure exhibits a high molecule loading capacity (10 wt %), and controlled drug release efficiency (67%) can be achieved using the external AC magnetic field for short time periods (5 min), showing faster and higher drug desorption compared to that of similar stimulus-responsive iron oxide-based nanocarriers. In addition, it is demonstrated that the magnetic field-induced drug release shows higher efficiency compared to that of the sustained release at fixed temperatures (47 and 53% for 37 and 42 °C, respectively), considering that the maximum temperature reached during the exposure to the magnetic field is well below (31 °C). Therefore, it can be hypothesized that short periods of exposure to the oscillating field induce much greater heating within the nanoparticles than in the external solution.

Bulk-edge correspondence for Floquet topological phases in honeycomb nanoribbon

Possibility of having different topological phases by time-periodic external field encourages people who wish to manipulate the properties of the materials as their will for the various kinds of systems including a honeycomb nanoribbon. We study bulk-edge correspondence by looking at the change in the value of the first Chern number of a specific band, which reflects the bulk properties, together with the change of associated edge states in quasienergy spectrum when the honeycomb nanoribbon is exposed to circularly polarized laser field. Various topological phase transitions are observed as the intensity of the laser field is raised up and we classify them in two categories. In the first category, when the frequency is sufficiently high, the system undergoes simple transition from trivial phase to topological one, reflected by the sudden jump in the value of Chern number from 0 to 1 and the appearance of two crossing edge states in the spectrum. Whereas, in the second category where the frequency is low enough, anomalous transitions are drawn, having several nonzero values of Chern number, and band folding prevails, often disappearing depending on the laser intensities. The results confirm the bulk-edge correspondence in periodically driven systems and will contribute to future material designs.

Transport properties of vertical heterostructures under light irradiation

Electronic and transport properties of bilayer heterostructure under light irradiation are of fundamental interest to improve functionality of optoelectronic devices. We theoretically study the modification of transport properties of bilayer graphene and bilayer heterostructures under a time-periodic external light field. The bulk electronic and transport properties are studied in a Landauer-type configuration by using the nonequilibrium Green's function formalism. To illustrate the behavior of the differential conductance of a bilayer contact under light illumination, we consider tight-binding models of bilayer graphene and graphene/hexagonal boron-nitride heterostructures. The non-adiabatic driving induces sidebands of the original band structure and opening of gaps in the quasienergy spectrum. In transport properties, the gap openings are manifested in a suppression of the differential conductance. In addition to suppression, an external light field induces an enhancement of the differential conductance if photoexcited electrons tunnel into or out of a Van~Hove singularity.

A Boundary Element Procedure for 3D Electromagnetic Transmission Problems with Large Conductivity

We consider the scattering of time-periodic electromagnetic fields by metallic obstacles, or the eddy current problem. In this interface problem, different sets of Maxwell equations must be solved both in the obstacle and outside it, while the tangential components of both electric and magnetic fields are continuous across the interface. We describe an asymptotic procedure, applied for large conductivity, which reflects the skin effect in metals. The key to our method is a special integral equation procedure for the exterior boundary value problems corresponding to perfect conductors. The asymptotic procedure leads to a great reduction in complexity for the numerical solution, since it involves solving only the exterior boundary value problems. Furthermore, we introduce a FEM/BEM coupling procedure for the transmission problem and consider the implementation of Galerkin’s elements for the perfect conductor problem, and present numerical experiments.

Effect of Magnetic Field on Corcyra cephalonica Eggs for Parasitization by Trichogramma chilonis

This study evaluated the effect of permanent magnetic field on Corcyra cephalonica Stainton eggs and effect on parasitisation by the egg parasitoid Trichogramma chilonis Ishii. Corcyra eggs were exposed to magnetic field for different time periods. It was observed that three hours magnetized eggs were significantly more preferred for parasitisation and revealed maximum adult emergence (76.23%, 98.67%) than non-magnetized Corcyra eggs (63.50%, 85.96%). When UV irradiated Corcyra eggs were kept under magnetic field for parasitisation, with increase in the time of exposure to magnetic field, parasitisation also increases along with adult emergence (89.85%, 97.16%) up to 3 hr. Then, it gradually decreases as compared with control (86.80%, 94.54%). Thus, 3 hr magnetized Corcyra eggs prevent the emergence of larva and was preferred by Trichogramma for maximum parasitisation and adult emergence.

Light-induced emergent phenomena in 2D materials and topological materials

Light-matter interaction in 2D and topological materials provides a fascinating control knob for inducing emergent, non-equilibrium properties and achieving new functionalities in the ultrafast time scale (from fs to ps). Over the past decade, intriguing light-induced phenomena, e.g., Bloch-Floquet states and photo-induced phase transitions, have been reported experimentally, but many still await experimental realization. In this Review, we discuss recent progress on the light-induced phenomena, in which the light field could act as a time-periodic field to drive Floquet states, induce structural and topological phase transitions in quantum materials, couple with spin and various pseudospins, and induce nonlinear optical responses that are affected by the geometric phase. Perspectives on the opportunities of proposed light-induced phenomena as well as open experimental challenges are also discussed.

Long Time Behaviour of a Local Perturbation in the Isotropic XY Chain Under Periodic Forcing

We study the isotropic XY quantum spin chain with a time-periodic transverse magnetic field acting on a single site. The asymptotic dynamics is described by a highly resonant Floquet–Schrödinger equation, for which we show the existence of a periodic solution if the forcing frequency is away from a discrete set of resonances. This in turn implies the state of the quantum spin chain to be asymptotically a periodic function synchronised with the forcing, also at arbitrarily low non-resonant frequencies. The behaviour at the resonances remains a challenging open problem.