Adiabatic Limit Research Articles

Electronic and nuclear flux analysis on nonadiabatic electron transfer reaction: A view from single-configuration adiabatic born-huang representation.

A detailed flux analysis on nonadiabatically coupled electronic and nuclear dynamics in the intramolecular electron transfer of LiF is presented. Full quantum dynamics both of electrons and nuclei within two-state model has uncovered interesting features of the individual fluxes (current of probability density) and correlation between them. In particular, a spatiotemporal oscillatory pattern of electronic flux has been revealed, which reflects the coherence coming from spatiotemporal differential overlap between nuclear wavepackets running on covalent and ionic potential curves. In this regard, a theoretical analogy between the nonadiabatic transitions and the Rabi oscillation is surveyed. We also present a flux-flux correlation between the nuclear and electronic motions, which quantifies the extent of deviation of the actual electronic and nuclear coupled dynamics from the Born-Oppenheimer adiabatic limit, which is composed only of a single product of the adiabatic electronic and nuclear wavefunctions. © 2018 Wiley Periodicals, Inc.

Experimental Demonstration of Dynamical Input Isolation in Nonadiabatically Modulated Photonic Cavities

Modulated optical cavities have been proposed and demonstrated for applications in communications, laser frequency stabilization, microwave-to-optical conversion and frequency comb generation. However, most studies are restricted to the adiabatic regime, where either the maximum excursion of the modulation or the modulation frequency itself is below the linewidth of the cavity. Here, using a fiber ring resonator with an embedded electro-optic phase modulator, we investigate the nonadiabatic regime. By strongly driving the modulator at frequencies that are significantly smaller than the free-spectral range of the ring resonator, but well beyond the linewidth of the resonator, we experimentally observe counterintuitive behavior predicted in a recent theoretical study by Minkov et al. [APL Photonics 2, 076101 (2017)], such as the complete suppression of drop-port transmission even when the input laser wavelength is on resonance with the optical cavity. This can be understood as dynamical isolation of the cavity from the input light. We also show qualitative differences in the steady-state responses of the system between the adiabatic and nonadiabatic limits. Our experiments probe a seldom explored regime of operation that is promising for applications in integrated photonic systems with current state-of-the-art technology.

Numerical inverse estimation of the thermal diffusivity and the adiabatic limit temperature of three types of unfired clay bricks using flash method and global minimization algorithm

Clay is an ecological building material used widely in constructions especially in rural areas. In this work an experimental study has been carried out to estimate the apparent thermal diffusivity and adiabatic limit temperature of three types of unfired clay brick using flash method. The three samples were prepared with the same water proportion (picked between the plasticity and the liquidity limits) and exposed to the same drying conditions. The thermal diffusivity and adiabatic limit temperature were estimated using numerical global minimization procedures of the quadratic distance between the theoretical model and the experimental thermogram. The theoretical model is derived from a numerical inversion of Laplace transform using Gaver-Stehfest method. An approach based on the independence between the sensitivity coefficients and the magnitude of these coefficients(Beck criterion)is presented in order to examine the simultaneous estimation of the different parameters related to the theoretical model from the experimental data. For all samples tested, the results show that the estimated parameters give a good agreement between the experimental data and the theoretical model.

Longitudinal momentum of the electron at the tunneling exit

The longitudinal momentum of the electron at the tunneling exit is a useful quantity to make sense of the tunneling ionization process. It was usually assumed to be zero from a classical argument, but recent experiments show that it must be nonzero in order to explain the measured electron momentum distributions. In this article we show that the flow momentum of the probability fluid is a sensible quantum mechanical definition for tunneling-exit momentum, and it can be (and in general is) nonzero at the tunneling exit point where the kinetic energy is zero by definition. We show that this longitudinal momentum is nonzero even in the static or adiabatic limit, and this nonzero momentum is a purely quantum mechanical effect determined by the shape of the wave function in the vicinity of the tunneling exit point. Nonadiabaticity or finite wavelength may increase this momentum substantially, and the detailed value depends on both the atomic and the laser parameters.

Time-dependent Markovian quantum master equation

We construct a quantum Markovian Master equation for a driven system coupled to a thermal bath. The derivation utilizes an explicit solution of the propagator of the driven system. This enables the validity of the Master equation to be extended beyond the adiabatic limit. The Non-Adiabatic Master Equation (NAME) is derived employing the weak system-bath coupling limit. The NAME is valid when a separation of timescales exists between the bath dynamics and the external driving. In contrast to the adiabatic Master equation, the NAME leads to coupled equations of motion for the population and coherence. We employ the NAME to solve the example of an open driven time-dependent harmonic oscillator. For the harmonic oscillator the NAME predicts the emergence of coherence associated with the dissipation term. As a result of the non-adiabatic driving the thermalization rate is suppressed. The solution is compared with both numerical calculations and the adiabatic Master equation.

Simulating vibronic spectra via Matsubara-like dynamics: Coping with the sign problem.

Measuring vibronic spectra probes dynamical processes in molecular systems. When interpreted via suitable theoretical tools, the experimental data provides comprehensive information about the system in question. For complex many-body problems, such an approach usually requires the formulation of proper classical-like approximations, which is particularly challenging if multiple electronic states are involved. In this work, we express the imaginary-time shifted time correlation function and, thus, the vibronic spectrum in terms of the so-called Matsubara dynamics, which combines quantum statistics and classical-like dynamics. By applying the Matsubara approximation in the adiabatic limit, we derive a formal generalization of the existing Matsubara dynamics formalism to multiple potential energy surfaces (PESs), which, however, does not feature all the defining properties of its single-PES counterpart though suffering equally from the sign problem. The mathematical analysis for two shifted harmonic oscillators suggests a new modified method to practically simulate the standard correlation function via Matsubara-like dynamics. Importantly, this modified method samples the thermal Wigner function without suffering from the sign problem and yields an accurate approximation to the vibronic absorption spectrum, not only for the harmonic system but also for the anharmonic one.

Thermal State with Quadratic Interaction

We consider the perturbative construction, proposed in [37], for a thermal state $\Omega_{\beta,\lambda V\{f\}}$ for the theory of a real scalar Klein-Gordon field $\phi$ with interacting potential $V\{f\}$. Here $f$ is a spacetime cut-off of the interaction $V$ and $\lambda$ is a perturbative parameter. We assume that $V$ is quadratic in the field $\phi$ and we compute the adiabatic limit $f\to 1$ of the state $\Omega_{\beta,\lambda V\{f\}}$. The limit is shown to exist, moreover, the perturbative series in $\lambda$ sums up to the thermal state for the corresponding (free) theory with potential $V$. In addition, we exploit the same methods to address a similar computation for the non-equilibrium steady state (NESS) [59] recently constructed in [25].

Three-Dimensional Chiral Lattice Fermion in Floquet Systems.

We show that the Nielsen-Ninomiya no-go theorem still holds on a Floquet lattice: there is an equal number of right-handed and left-handed Weyl points in a three-dimensional Floquet lattice. However, in the adiabatic limit, where the time evolution of the low-energy subspace is decoupled from the high-energy subspace, we show that the bulk dynamics in the low-energy subspace can be described by Floquet bands with extra left- or right-handed Weyl points, despite the no-go theorem. Assuming adiabatic evolution of two bands, we show that the difference of the number of right-handed and left-handed Weyl points equals twice the winding number of the adiabatic Floquet operator over the Brillouin zone. Based on these findings, we propose a realization of purely left- or right-handed Weyl particles on a 3D lattice using a Hamiltonian obtained through dimensional reduction of a four-dimensional quantum Hall system. We argue that the breakdown of the adiabatic approximation on the surface facilitates unusual closed orbits of wave packets in an applied magnetic field, which traverse alternatively through the low-energy and high-energy sector of the spectrum.

Opto-Mechanics Driven Fast Martensitic Transition in Two-Dimensional Materials.

Diffusional phase-change materials, such as Ge-Sb-Te alloys, are used in rewritable nonvolatile memory devices. But the continuous pursuit of readout/write speed and reduced energy consumption in miniaturized devices calls for an optically driven, diffusionless phase change scheme in ultrathin materials. Inspired by optical tweezers, in this work, we illustrate theoretically and computationally that a linearly polarized laser pulse with selected frequency can drive an ultrafast diffusionless martensitic phase transition of two-dimensional ferroelastic materials such as SnO and SnSe monolayers, where the unit-cell strain is tweezed as a generalized coordinate that affects the anisotropic dielectric function and electromagnetic energy density. At laser power of 2.0 × 1010 and 7.7 × 109 W/cm2, the transition potential energy barrier vanishes between two 90°-orientation variants of ferroelastic SnO and SnSe monolayer, respectively, so displacive domain switching can occur within picoseconds. The estimated adiabatic thermal limit of energy input in such optomechanical martensitic transition (OMT) is at least 2 orders of magnitude lower than that in Ge-Sb-Te alloy.

Quantization of the Hall conductivity in the Harper-Hofstadter model

We study the robustness of the quantization of the Hall conductivity in the Harper-Hofstadter model towards the details of the protocol with which a longitudinal uniform driving force $F_x(t)$ is turned on. In the vector potential gauge, through Peierls substitution, this involves the switching-on of complex time-dependent hopping amplitudes $\mathrm{e}^{-\frac{i}{\hbar}\mathcal{A}_x(t)}$ in the $\hat{\mathbf{x}}$-direction such that $\partial_t \mathcal{A}_x(t)=F_x(t)$. The switching-on can be sudden, $F_x(t)=\theta(t) F$, where $F$ is the steady driving force, or more generally smooth $F_x(t)=f(t/t_{0}) F$, where $f(t/t_{0})$ is such that $f(0)=0$ and $f(1)=1$. We investigate how the time-averaged (steady-state) particle current density $j_y$ in the $\hat{\mathbf{y}}$-direction deviates from the quantized value $j_y \, h/F = n$ due to the finite value of $F$ and the details of the switching-on protocol. Exploiting the time-periodicity of the Hamiltonian $\hat{H}(t)$, we use Floquet techniques to study this problem. In this picture the (Kubo) linear response $F\to 0$ regime corresponds to the adiabatic limit for $\hat{H}(t)$. In the case of a sudden quench $j_y \, h/F$ shows $F^2$ corrections to the perfectly quantized limit. When the switching-on is smooth, the result depends on the switch-on time $t_{0}$: for a fixed $t_{0}$ we observe a crossover force $F^*$ between a quadratic regime for $F<F^*$ and a {\em non-analytic} exponential $\mathrm{e}^{-\gamma/|F|}$ for $F>F^*$. The crossover $F^*$ decreases as $t_{0}$ increases, eventually recovering the topological robustness. These effects are in principle amenable to experimental tests in optical lattice cold atomic systems with synthetic gauge fields.

Dynamics of polar polarizable rotors acted upon by unipolar electromagnetic pulses: From the sudden to the adiabatic regime.

We study, analytically as well as numerically, the dynamics that arises from the interaction of a polar polarizable rigid rotor with single unipolar electromagnetic pulses of varying length, Δτ, with respect to the rotational period of the rotor, τ r . In the sudden, non-adiabatic limit, Δτ ≪ τ r , we derive analytic expressions for the rotor's wavefunctions, kinetic energies, and field-free evolution of orientation and alignment. We verify the analytic results by solving the corresponding time-dependent Schrödinger equation numerically and extend the temporal range of the interactions considered all the way to the adiabatic limit, Δτ > τ r , where general analytic solutions beyond the field-free case are no longer available. The effects of the orienting and aligning interactions as well as of their combination on the post-pulse populations of the rotational states are visualized as functions of the orienting and aligning kick strengths in terms of population quilts. Quantum carpets that encapsulate the evolution of the rotational wavepackets provide the space-time portraits of the resulting dynamics. The population quilts and quantum carpets reveal that purely orienting, purely aligning, or even-break combined interactions each exhibit sui generis dynamics. In the intermediate temporal regime, we find that the wavepackets as functions of the orienting and aligning kick strengths show resonances that correspond to diminished kinetic energies at particular values of the pulse duration.

Stochastic resonance in an underdamped triple-well potential system

In this paper, stochastic resonance (SR) in an underdamped triple-well potential system driven by Gaussian white noise and a parametric harmonic excitation is investigated. The analytical expressions of the output signal-to-noise ratio (SNR), together with the mean first-passage times (MFPTs), are derived for the triple-well potential system involving damping in adiabatic limit. The effects of noise intensity, damping coefficient and triple-well potential on MFPTs and SNR are analyzed. The results suggest the existence of two critical damping values, giving rise to the onset and the disappearance of SR, respectively. Since the system is unstable in weak damping regime, emergence of SR is prohibited. Under the weak noise level, SNR exhibits a prominent resonance-like behavior at the optimal value of damping coefficient. Moreover, the two nonlinear stiffness coefficients of restoring force play an opposite role in the enhancement of SR. Thus, the SR effect significantly depends on the change of the two-side potential wells. Particularly, the appropriate choice of triple-well potential function and damping coefficient can improve the response of the system to an external periodic excitation according to the damping-induced resonance effect. Finally, the numerical results confirm the effectiveness of the theoretical analyses.

Intrinsic ratchets: A Hamiltonian approach

An asymmetric Brownian particle subjected to an external time-dependent force may acquire a net drift velocity, and thus operate as a motor or ratchet, even if the external force is represented by an unbiased time-periodic function or by a zero-centered noise. For an adequate description of such ratchets, a conventional Langevin equation linear in the particle's velocity is insufficient, and one needs to take into account the first nonlinear correction to the dissipation force which emerges beyond the weak coupling limit. We derived microscopically the relevant nonlinear Langevin equation by extending the standard projection operation technique beyond the weak coupling limit. The particle is modeled as a rigid cluster of atoms and its asymmetry may be geometrical, compositional (when a cluster is composed of atoms of different types), or due to a combination of both factors. The drift velocity is quadratic in the external force's amplitude and increases with decreasing the force's frequency (for a periodic force) and inverse correlation time (for a fluctuating force). The maximum value of the drift velocity is independent on the particle's mass and achieved in the adiabatic limit, i.e. for an infinitely slow change of the external field.

Relative Entropy and Entropy Production for Equilibrium States in pAQFT

We analyze the relative entropy of certain KMS states for scalar self-interacting quantum field theories over Minkowski backgrounds that have been recently constructed by Fredenhagen and Lindner in [FL14] in the framework of perturbative algebraic quantum field theory. The definition we are using is a generalization of the Araki relative entropy to the case of field theories. In particular, we shall see that the analyzed relative entropy is positive in the sense of perturbation theory, hence, even if the relative modular operator is not at disposal in this context, the proposed extension is compatible with perturbation theory. In the second part of the paper we analyze the adiabatic limits of these states showing that also the density of relative entropy obtained dividing the relative entropy by the spatial volume of the region where interaction takes place is positive and finite. In the last part of the paper we discuss the entropy production for states obtained by an ergodic mean (time average) of perturbed KMS states evolved with the free evolution recently constructed by the authors of the present paper. We show that their entropy production vanishes even if return to equilibrium [Ro73, HKT74] does not hold. This means that states constructed in this way are thermodynamically simple, namely they are not so far from equilibrium states.

Coulomb Corrections in Photoelectron Spectra in the Adiabatic Limit

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Upper critical magnetic field in superconducting Dirac semimetal

Temperature dependence of the upper critical field Hc2 of the Dirac semimetal (DSM) with phonon-mediated pairing is considered within the semiclassical approximation. The low-temperature dependence deviates from conventional BCS superconductor with parabolic dispersion relation (Werthamer N. R., Helfand E. and Hohenberg P. C., Phys. Rev., 147 (1966) 295; Helfand E. and Werthamer N. R., Phys. Rev. Lett., 13 (1964) 686) even for large adiabaticity parameter, , where μ is the chemical potential and Ω the Debye frequency. In particular the “reduced field”, ratio of zero-temperature Hc2 to the derivative at critical temperature, , depends on γ and can be extended beyond the adiabatic limit. The reduced magnetic field ratio is universal (independent of the chemical potential, interaction strength, etc.) and smaller than the Werthamer ratio for clean superconductors: for DSM, for parabolic band. The results are in good agreement compared with recent experiments on TaP.

Engineering chiral and topological orbital magnetism of domain walls and skyrmions

Electrons that are slowly moving through chiral magnetic textures can effectively be described as if they were influenced by electromagnetic fields emerging from the real-space topology. This adiabatic viewpoint has been very successful in predicting physical properties of chiral magnets. Here, based on a rigorous quantum-mechanical approach, we unravel the emergence of chiral and topological orbital magnetism in one- and two-dimensional spin systems. We uncover that the quantized orbital magnetism in the adiabatic limit can be understood as a Landau-Peierls response to the emergent magnetic field. Our central result is that the spin–orbit interaction in interfacial skyrmions and domain walls can be used to tune the orbital magnetism over orders of magnitude by merging the real-space topology with the topology in reciprocal space. Our findings point out the route to experimental engineering of orbital properties of chiral spin systems, thereby paving the way to the field of chiral orbitronics.

The Adiabatic Limit of the Connection Laplacian

We study the behaviour of Laplace-type operators H on a complex vector bundle E → M in the adiabatic limit of the base space. This space is a fibre bundle M → B with compact fibres and the limit corresponds to blowing up directions perpendicular to the fibres by a factor 1/e. Under a gap condition on the fibre-wise eigenvalues we prove existence of effective operators that provide asymptotics to any order in e for H (with Dirichlet boundary conditions), on an appropriate almost-invariant subspace of L²(E).

Gradient flow line near birth–death critical points

Near a birth–death critical point in a one-parameter family of gradient flows, there are precisely two Morse critical points of index difference one on the birth side. This paper gives a self-contained proof of the folklore theorem that these two critical points are joined by a unique gradient trajectory up to time-shift. The proof is based on the Whitney normal form, a Conley index construction, and an adiabatic limit analysis for an associated fast–slow differential equation.

Direct measurement of astrophysical factor S(E) and screening potential for [formula omitted] reaction at low energy

As Beryllium is an important element in primary nucleosynthesis, its nuclear reaction cross-sections induced by charged projectiles need to be measured precisely. The astrophysical S(Ei) factors were measured in the ultra-low energy range from Elab=18 to 100 keV in 2-keV increments (42 points). Both the astrophysical S(E) curve (Sbare(0)=16.2±1.8MeVb) and the screening energy (Us=545±98eV) were deduced. In regard to astrophysical applications of the Sbare(E) curve, the present results are consistent with Zahnow's direct measurement. For the long-standing problem of ‘abnormal’ screening effect, our screening energy result also agrees with that obtained using the Trojan-horse method (Us=676±86eV) but smaller than Zahnow's value (900±50eV), although all results are much larger than that obtained in the adiabatic limit (∼264 eV).