Time-dependent Perturbations Research Articles

Constraining the Gravitational Potential from the Projected Morphology of Extragalactic Tidal Streams

The positions and velocities of stellar streams have been used to constrain the mass and shape of the Milky Way's dark matter halo. Several extragalactic streams have already been detected, though it has remained unclear what can be inferred about the gravitational potential from only 2D photometric data of a stream. We present a fast method to infer halo shapes from the curvature of 2D projected stream tracks. We show that the stream curvature vector must point within 90° of the projected acceleration vector, in the absence of recent time-dependent perturbations. While insensitive to the total magnitude of the acceleration, and therefore the total mass, applying this constraint along a stream can determine halo shape parameters and place limits on disk-to-halo mass ratios. The most informative streams are those with sharp turns or flat segments, since these streams sample a wide range of curvature vectors over a small area (sharp turns) or have a vanishing projected acceleration component (flat segments). We apply our method to low surface brightness imaging of NGC 5907, and find that its dark matter halo is oblate. Our analytic approach is significantly faster than other stream modeling techniques, and indicates which parts of a stream contribute to constraints on the potential. The method enables a measurement of dark matter halo shapes for thousands of systems using stellar stream detections expected from upcoming facilities like Rubin and Roman.

Non-orientable order and non-commutative response in frustrated metamaterials.

From atomic crystals to animal flocks, the emergence of order in nature is captured by the concept of spontaneous symmetry breaking1-4. However, this cornerstone of physics is challenged when broken symmetry phases are frustrated by geometrical constraints. Such frustration dictates the behaviour of systems as diverse as spin ices5-8, confined colloidal suspensions9 and crumpled paper sheets10. These systems typically exhibit strongly degenerated and heterogeneous ground states and hence escape the Ginzburg-Landau paradigm of phase ordering. Here, combining experiments, simulations and theory we uncover an unanticipated form of topological order in globally frustrated matter: non-orientable order. We demonstrate this concept by designing globally frustrated metamaterials that spontaneously break a discrete [Formula: see text] symmetry. We observe that their equilibria are necessarily heteregeneous and extensively degenerated. We explain our observations by generalizing the theory of elasticity to non-orientable order-parameter bundles. We show that non-orientable equilibria are extensively degenerated due to the arbitrary location of topologically protected nodes and lines where the order parameter must vanish. We further show that non-orientable order applies more broadly to objects that are non-orientable themselves, such as buckled Möbius strips and Klein bottles. Finally, by applying time-dependent local perturbations to metamaterials with non-orientable order, we engineer topologically protected mechanical memories11-19, achieve non-commutative responses and show that they carry an imprint of the braiding of the loads' trajectories. Beyond mechanics, we envision non-orientability as a robust design principle for metamaterials that can effectively store information across scales, in fields as diverse as colloidal science8, photonics20, magnetism7 and atomic physics21.

Efficient scheme for time-dependent thermal pure quantum state: Application to the Kitaev model with armchair edges

We consider the time-dependent thermal pure quantum state method and introduce the efficient scheme to evaluate the change in physical quantities induced by the time-dependent perturbations, which has been proposed in our previous paper [H. Taguchi et al., Phys. Rev. B 105, 125137 (2022)]. Here, we treat the Kitaev model to consider the Majorana-mediated spin transport, as an example. We demonstrate how efficient our scheme is to evaluate spin oscillations induced by the magnetic field pulse.

Radial linear stability of nonrelativistic ℓ -boson stars

We study the linear stability of nonrelativistic $\ensuremath{\ell}$-boson stars, describing static, spherically symmetric configurations of the Schr\"odinger-Poisson system with multiple wave functions having the same value of the angular momentum $\ensuremath{\ell}$. In this work we restrict our analysis to time-dependent perturbations of the radial profiles of the $2\ensuremath{\ell}+1$ wave functions, keeping their angular dependency fixed. Based on a combination of analytic and numerical methods, we find that for each $\ensuremath{\ell}$, the ground state is linearly stable, whereas the $n$th excited states possess $2n$ unstable (exponentially in time growing) modes. Our results also indicate that all excited states correspond to saddle points of the conserved energy functional of the theory.

Floquet engineering with quantum optimal control theory

Floquet engineering consists in the modification of physical systems by the application of periodic time-dependent perturbations. The search for the shape of the periodic perturbation that best modifies the properties of a system in order to achieve some predefined metastable target behavior can be formulated as an optimal control problem. We discuss several ways to formulate and solve this problem. We present, as examples, some applications in the context of material science, although the methods discussed here are valid for any quantum system (from molecules and nanostructures to extended periodic and non periodic quantum materials). In particular, we show how one can achieve the manipulation of the Floquet pseudo-bandstructure of a transition metal dichalcogenide monolayer (MoS2).

Level dynamics and avoided level crossings in driven disordered quantum dots

The statistical properties of the dynamics of energy levels are investigated in the case of two two-dimensional disordered quantum dot models with nearest neighbor hopping subjected to external time-dependent perturbations. While in the first model the external drivings are realized by a continuous variation of the on-site energies, in the second one it is generated by deformations of a parabolic potential. We concentrate on the effects of the potential on the localization properties and investigate the statistics of the energy level velocities and curvatures regarding their typical magnitudes and domain of agreement with the predictions of Random Matrix Theory (RMT) for the Gaussian Orthogonal, Unitary and Symplectic ensembles. Moreover, the statistical properties of the avoided level crossings are investigated in terms of the corresponding Landau-Zener parameters. We find that the strength of the Landau-Zener transitions exhibits universal behavior which also implies universal single-particle dynamics for slow perturbations independent of the disorder and potential strength, the system size and the symmetry class. These results can be verified experimentally by measurements of single-particle energy spectra in quantum dots.

Time dependent quantum perturbations uniform in the semiclassical regime

Time dependent quantum perturbations uniform in the semiclassical regime

Variance Reduction and Noise Source Sampling Techniques for Monte Carlo Simulations of Neutron Noise Induced by Mechanical Vibrations

Neutron noise in nuclear power reactors refers to the small fluctuations around the average neutron flux at steady state resulting from time-dependent perturbations inside the core. The neutron noise equations in the frequency domain can be solved using Monte Carlo simulation codes, which are capable of obtaining reference solutions involving almost no approximations but are hindered by severe issues affecting the statistical convergence: The simultaneous presence of positive and negative particles, which is required by the nature of the complex noise equations, leads to catastrophically large variance in the tallies. In this work, we consider the important case of neutron noise problems induced by mechanical vibrations. First, we derive a new exact sampling strategy for the noise source. Then, building upon our previous findings in other contexts, we show that weight cancellation methods can be highly beneficial in dealing with the presence of negative weights, enabling extremely large gains in the figure of merit. We successfully demonstrate our results on a benchmark configuration consisting of a fuel assembly with a vibrating pin, and we discuss possible pathways for further improvements.

Emergence and manipulation of non-equilibrium Yu-Shiba-Rusinov states

The experimental advances in the study of time-dependent phenomena has opened a new path to investigating the complex electronic structure of strongly correlated and topological materials. Yu-Shiba-Rusinov (YSR) states induced by magnetic impurities in s-wave superconductors provide an ideal candidate system to study the response of a system to time-dependent manipulations of the magnetic environment. Here, we show that by imposing a time-dependent change in the magnetic exchange coupling, by changing the relative alignment of magnetic moments in an impurity dimer, or through a periodic drive of the impurity moment, one can tune the system through a time-dependent quantum phase transition, in which the system undergoes a transition from a singlet to a doublet ground state. We show that the electronic response of the system to external perturbations can be imaged through the time-dependent differential conductance, dI(t)/dV, which, in analogy to the equilibrium case, is proportional to a non-equilibrium local density of states. Our results open the path to visualizing the response of complex quantum systems to time-dependent external perturbations.

Orbital dynamics and histories of satellite galaxies around Milky Way – mass galaxies in the FIRE simulations

ABSTRACT The orbits of satellite galaxies encode rich information about their histories. We investigate the orbital dynamics and histories of satellite galaxies around Milky Way (MW)-mass host galaxies using the FIRE-2 cosmological simulations, which, as previous works have shown, produce satellite mass functions and spatial distributions that broadly agree with observations. We first examine trends in orbital dynamics at z = 0, including total velocity, specific angular momentum, and specific total energy: the time of infall into the MW-mass halo primarily determines these orbital properties. We then examine orbital histories, focusing on the lookback time of first infall into a host halo and pericentre distances, times, and counts. Roughly 37 per cent of galaxies with $M_{\rm star}\lesssim 10^7\, {\rm M}_{\odot }$ were ‘pre-processed’ as a satellite in a lower-mass group, typically $\approx 2.7\, {\rm Gyr}$ before falling into the MW-mass halo. Half of all satellites at z = 0 experienced multiple pericentres about their MW-mass host. Remarkably, for most (67 per cent) of these satellites, their most recent pericentre was not their minimum pericentre: the minimum typically was ∼40 per cent smaller and occurred $\sim 6\, {\rm Gyr}$ earlier. These satellites with growing pericentres appear to have multiple origins: for about half, their specific angular momentum gradually increased over time, while for the other half, most rapidly increased near their first apocentre, suggesting that a combination of a time-dependent MW-mass halo potential and dynamical perturbations in the outer halo caused these satellites’ pericentres to grow. Our results highlight the limitations of idealized, static orbit modelling, especially for pericentre histories.

Point sources and stability for an inverse problem for a hyperbolic PDE with space and time dependent coefficients

We study stability aspects for the determination of space and time-dependent lower order perturbations of the wave operator in three space dimensions with point sources. The problems under consideration here are formally determined and we establish Lipschitz stability results for these problems. The main tool in our analysis is a modified version of Bukgheĭm-Klibanov method based on Carleman estimates.

Perturbation theory for fractional evolution equations in a Banach space

A strong inspiration for studying perturbation theory for fractional evolution equations comes from the fact that they have proven to be useful tools in modeling many physical processes. We study fractional evolution equations of order \(\alpha \in (1,2)\) associated with the infinitesimal generator of an operator fractional cosine (sine) function generated by bounded time-dependent perturbations in a Banach space. We show that the fractional abstract Cauchy problem associated with the infinitesimal generator A of a strongly continuous fractional cosine (sine) function remains uniformly well-posed under bounded time-dependent perturbation of A. We also provide some necessary special cases by using the Laplace transform of the generators of the given operator families.

Dynamical analog spacetimes in nonrelativistic flows

Analogue gravity models describe linear fluctuations of fluids as a massless scalar field propagating on stationary acoustic spacetimes constructed from the background flow. In this paper, we establish that this paradigm generalizes to arbitrary order nonlinear perturbations propagating on dynamical analogue spacetimes. Our results hold for all inviscid, spherically symmetric and barotropic non-relativistic flows in the presence of an external conservative force. We demonstrate that such fluids always admit a dynamical description governed by a coupled pair of wave and continuity equations. We provide an iterative approach to solve these equations about any known stationary solution to all orders in perturbation. In the process, we reveal that there exists a dynamical acoustic spacetime on which fluctuations of the mass accretion rate propagate. The dynamical acoustic spacetime is shown to have a well defined causal structure and curvature. In addition, we find a classical fluctuation relation for the acoustic horizon of the spacetime that admit scenarios wherein the horizon can grow as well as recede, with the latter being a result with no known analogue in black holes. As an example, we numerically investigate the Bondi flow accreting solution subject to exponentially damped time dependent perturbations. We find that second and higher order classical perturbations possess an acoustic horizon that oscillates and changes to a new stable size at late times. In particular, the case of a receding acoustic horizon is realized through `low frequency' perturbations. We discuss our results in the context of more general analogue models and its potential implications on astrophysical accretion flows.

The laws of thermodynamics for quantum dissipative systems: A quasi-equilibrium Helmholtz energy approach.

By using the quasi-equilibrium Helmholtz energy, which is defined as the thermodynamic work in a quasi-static process, we investigate the thermal properties of both an isothermal process and a transition process between the adiabatic and isothermal states (adiabatic transition). Here, the work is defined by the change in energy from a steady state to another state under a time-dependent perturbation. In particular, the work for a quasi-static change is regarded as thermodynamic work. We employ a system-bath model that involves time-dependent perturbations in both the system and the system-bath interaction. We conduct numerical experiments for a three-stroke heat machine (a Kelvin-Planck cycle). For this purpose, we employ the hierarchical equations of motion (HEOM) approach. These experiments involve an adiabatic transition field that describes the operation of an adiabatic wall between the system and the bath. Thermodynamic-work diagrams for external fields and their conjugate variables, similar to the P-V diagram, are introduced to analyze the work done for the system in the cycle. We find that the thermodynamic efficiency of this machine is zero because the field for the isothermal processes acts as a refrigerator, whereas that for the adiabatic wall acts as a heat engine. This is a numerical manifestation of the Kelvin-Planck statement, which states that it is impossible to derive the mechanical effects from a single heat source. These HEOM simulations serve as a rigorous test of thermodynamic formulations because the second law of thermodynamics is only valid when the work involved in the operation of the adiabatic wall is treated accurately.

Improved energy estimates for a class of time-dependent perturbed Hamiltonians

We consider time-dependent perturbations which are relatively bounded with respect to the square root of an unperturbed Hamiltonian operator, and whose commutator with the latter is controlled by the full perturbed Hamiltonian. The perturbation is modulated by two auxiliary parameters, one regulates its intensity as a prefactor and the other one controls its time-scale via a regular function, whose derivative is compactly supported in a finite interval. We introduce a natural generalization of energy conservation in the case of time-dependent Hamiltonians: the boundedness of the two-parameter unitary propagator for the physical evolution with respect to the n/2-th power energy norm for all nin mathbb {Z}. We provide bounds of the n/2-th power energy norms, uniformly in time and in the time-scale parameter, for the unitary propagators, generated by the time-dependent perturbed Hamiltonian and by the unperturbed Hamiltonian in the interaction picture. The physically interesting model of Landau-type Hamiltonians with an additional weak and time-slowly-varying electric potential of unit drop is included in this framework.

Observations on holographic aspects of four-dimensional asymptotically flat mathcal{N} = 2 black holes

In this note, we explore holographic attributes of four-dimensional near-extremal Reissner-Nordstrom black hole solutions in ungauged mathcal{N} = 2 supergravity theories at the two-derivative level by recasting them as a specific first-order deformation in solution space, associated with an infinitesimal Harrison transformation, of black holes in an AdS2 space-time. Specifically, we use this link to exhibit how bulk properties, such as mass and entropy, of four-dimensional near-extremal black holes are holographically encoded in the one-dimensional boundary theory dual to gravity in an infinitesimally deformed AdS2 space-time. We do so for the case of four-dimensional near-extremal black holes that arise as deformations in solution space of BPS black holes by changing the non-extremality parameter. For these near-extremal black holes, we further show that the nAdS2 attractor mechanism can be recast as a specific deformation of the BPS flow equations in four dimensions. Additionally, we also discuss time-dependent perturbations of the four-dimensional near-extremal Reissner-Nordstrom solutions from a two-dimensional point of view.

Stability and bifurcation phenomena in asymptotically Hamiltonian systems

The influence of time-dependent perturbations on an autonomous Hamiltonian system with an equilibrium of center type is considered. It is assumed that the perturbations decay at infinity in time and vanish at the equilibrium. In this case the stability and the long-term behaviour of trajectories depend on nonlinear and non-autonomous terms of equations. The paper investigates bifurcations associated with a change of Lyapunov stability of the equilibrium and the emergence of new attracting or repelling states in the perturbed non-autonomous system. The dependence of bifurcations on the structure of perturbations is discussed.

Exploring Functional Materials by Understanding Beam‐Sample Interactions

AbstractUltra‐low‐dose electron diffraction is performed with a double metal cyanide catalyst (DMC) to understand how electron irradiation stimulates structural alterations in functional materials. The commonly fading diffraction patterns with dose accumulation depend on the irradiated area and the beam current even when below 50 femto Amperes. Heat generation is observed and modeled by statistical, inelastic scattering events to describe how phonon excitations modulate radiation hardness. Specifically, the characteristic 1/e‐decay of Bragg intensities from DMC is delayed from 6 to 30 eÅ−2 at room temperature, which is comparable to the effect of embedding radiation soft matter in ice. DMC's radiation hardness is enhanced by a latency dose that forms during a phase transformation. This unifying model predicts that a critical dose rate exists for any material that varies between 0.1 and 104 eÅ−2s−1 because of a material dependent competition of heat generation and spread. It shows that Brillouin scattering causes time dependent perturbations in electron irradiated solids that trigger time‐temperature‐transformations on a time scale of nanoseconds to microseconds at room temperature, which is not included in traditional models describing the decay of Bragg intensities by radiolysis.

Phase and frequency linear response theory for hyperbolic chaotic oscillators.

We formulate a linear phase and frequency response theory for hyperbolic flows, which generalizes phase response theory for autonomous limit cycle oscillators to hyperbolic chaotic dynamics. The theory is based on a shadowing conjecture, stating the existence of a perturbed trajectory shadowing every unperturbed trajectory on the system attractor for any small enough perturbation of arbitrary duration and a corresponding unique time isomorphism, which we identify as phase such that phase shifts between the unperturbed trajectory and its perturbed shadow are well defined. The phase sensitivity function is the solution of an adjoint linear equation and can be used to estimate the average change of phase velocity to small time dependent or independent perturbations. These changes in frequency are experimentally accessible, giving a convenient way to define and measure phase response curves for chaotic oscillators. The shadowing trajectory and the phase can be constructed explicitly in the tangent space of an unperturbed trajectory using co-variant Lyapunov vectors. It can also be used to identify the limits of the regime of linear response.

Spherically symmetric perturbations of a Schwarzschild black hole in torsion bigravity

Time-dependent spherically-symmetric perturbations of Schwarzschild black holes are studied within torsion bigravity, i.e., within generalized Einstein-Cartan theories where the dynamical torsion carries massive spin-2 excitation. We reduce linearized perturbations to a Zerilli-like equation. The structure of the potential entering the latter Zerilli-like equation has two important consequences. First, in order to avoid the presence of singularities in generic perturbations, one must restrict the range (or inverse mass) of the spin-2 excitation to be (essentially) smaller than the radius of the considered black hole. Second, we then show that the Schwarzschild black hole is linearly stable against spherically-symmetric perturbations.