Time-dependent Vector Potential Research Articles

Estimates on modulation spaces for Schrödinger operators with time-dependent sub-linear vector potentials

Estimates on modulation spaces for Schrödinger operators with time-dependent sub-linear vector potentials

Hölder stability estimates in determining the time-dependent coefficients of the heat equation from the Cauchy data set

Abstract In this paper, we address stability results in determining the time-dependent scalar and vector potentials appearing in the convection-diffusion equation from the knowledge of the Cauchy data set. We prove Hölder-type stability estimates. The key tool used in this work is the geometric optics solution.

Theoretic impetuses and lengths of Feinberg-Horodecki equation

The exact solution of the Feinberg-Horodecki equation for time-dependent harmonic vector potential has been investigated under a one-dimensional system. The quantized momentum and its corresponding un-normalized wave functions were explicitly obtained. The Fisher information (for time and momentum) and variance (for time and momentum) were calculated using expectation values of time and momentum via Hellman-Feynman Theory (HFT). The time and momentum Shannon entropy were obtained using an existing formula. Numerical results were for time and momentum Fisher information to confirm the Cramer-Rao inequality. Another numerical results were obtained for time and momentum Shannon entropy to confirm Bialynick-Birula, Mycielski (BBM) inequality. The effects of the potential parameters such as mass of the spring and the frequency on the theoretic quantities were fully examined. The new variance inequality was established using the inequalities of Fisher information. The established inequality was confirmed by numerical results which also satisfied the popular Cramer-Rao inequality. The theoretic impetuses for Fisher information, variance and Shannon entropy respectively, were calculated and their variation with some potentials were studied.

Describing the photo-isomerization of a retinal chromophore model with coupled and quantum trajectories.

The exact factorization of the electron-nuclear wavefunction is applied to the study of photo-isomerization of a retinal chromophore model. We describe such an ultrafast nonadiabatic process by analyzing the time-dependent potentials of the theory and by mimicking nuclear dynamics with quantum and coupled trajectories. The time-dependent vector and scalar potentials are the signature of the exact factorization, as they guide nuclear dynamics by encoding the complete electronic dynamics and including excited-state effects. Analysis of the potentials is, thus, essential-when possible-to predict the time-dependent behavior of the system of interest. In this work, we employ the exact time-dependent potentials, available for the numerically exactly solvable model used here, to propagate quantum nuclear trajectories representing the isomerization reaction of the retinal chromophore. The quantum trajectories are the best possible trajectory-based description of the reaction when using the exact-factorization formalism and, thus, allow us to assess the performance of the coupled-trajectory, fully approximate schemes derived from the exact-factorization equations.

Long-lived nonthermal states in pumped one-dimensional systems of hard-core bosons

We study a unitary time evolution of a symmetry-broken state in a form of a charge density wave in a finite system of interacting hard-core bosons, which can be mapped onto the XXZ Heisenberg chain. Moreover, we introduce a spatially-homogenous and time-dependent vector potential that mimics a short laser pulse. We establish the range of amplitudes of the vector potential for which the onset of charge density wave order can be controlled. We propose a protocol that reveals non-thermal long-lived states, which are characterized by a non-zero charge density wave order translated by one lattice site with respect to its initial formation. The life times of these states are large in comparison to all typical times given by the parameters of the system. They increase with the number of lattice sites, but are significantly suppressed by the integrablility breaking perturbations. In view of these findings, we speculate that the long-lived non-thermal states exist in the thermodynamic limit.

Calculation of the pulsed electromagnetic field of a plane annular magnetic current

The work calculates the radiation fields of a plane ring magnetic current in the time domain. Two functions are considered that describe the dependence of the magnetic current on time: the delta function and the unit drop. All calculations are performed in the time domain without using the Fourier transform. First, the time-dependent vector potential is calculated. When writing expressions for the vector potential, the annular magnetic current is represented by the difference between two circular magnetic currents. Then, the magnetic field created by the ring magnetic current is found through the vector potential. Only one φ-th component of the magnetic field is nonzero. Further, from Maxwell's equations through the magnetic field, the components of the electric field of the annular magnetic current are calculated. On the basis of the formulas obtained, various special cases showing the dependence of the emitted field on time and spatial coordinates are considered. The time dependence of the electric field on the ring axis is calculated. It is shown that the Fourier transform of this field leads to a formula known from the literature in the frequency domain for calculating the field on the axis of the ring. The graphs are given showing that near the wave front, the transverse components of the electric and magnetic fields differ only by a factor equal to the wave resistance of the medium (120π for the air medium). The images of the electric field at different times are shown. In the given pictures of the fields, one can observe the movement of the radiation field near the wave front and the formation of a static field in the vicinity of the ring. The analytical expressions obtained in this work can be used to calculate antennas and other structures excited by a coaxial line. They can be used to solve integral equations in the time domain.

Stability estimates for the relativistic Schrödinger equation from partial boundary data

We derive stability estimates for the determination of time-dependent vector and scalar potentials in the relativistic Schrödinger equation from partial boundary data. For the case of space dimensions at least 3, we obtain log–log stability estimates for the determination of vector potentials (modulo gauge equivalence) and log–log–log stability estimates for the determination of scalar potentials from partial boundary data assuming suitable a priori bounds on these potentials.

Dynamically generated synthetic electric fields for photons

Static synthetic magnetic fields give rise to phenomena including the Lorentz force and the quantum Hall effect even for neutral particles, and they have by now been implemented in a variety of physical systems. Moving towards fully dynamical synthetic gauge fields allows, in addition, for backaction of the particles' motion onto the field. If this results in a time-dependent vector potential, conventional electromagnetism predicts the generation of an electric field. Here, we show how synthetic electric fields for photons arise self-consistently due to the nonlinear dynamics in a driven system. Our analysis is based on optomechanical arrays, where dynamical gauge fields arise naturally from phonon-assisted photon tunneling. We study open, one-dimensional arrays, where synthetic magnetic fields are absent. However, we show that synthetic electric fields can be generated dynamically, which, importantly, suppress photon transport in the array. The generation of these fields depends on the direction of photon propagation, leading to a novel mechanism for a photon diode, inducing nonlinear nonreciprocal transport via dynamical synthetic gauge fields.

Nonequilibrium dynamics in the pump-probe spectroscopy of excitonic insulators

We study the nonequilibrium dynamics in the pump-probe spectroscopy of excitonic insulators using the spinless two-orbital model with phonon degrees of freedom in the time-dependent mean-field approximation. We introduce the pulse light as a time-dependent vector potential via the Peierls phase in the Hamiltonian. We find that, in the Bose-Einstein condensation regime where the normal state is semiconducting, the excitonic order is suppressed when the frequency of the pulse light is slightly larger than the band gap, while the order is enhanced when the frequency of the pulse is much larger than the band gap. We moreover find that the excitonic order is completely destroyed in the former situation if the intensity of the pulse is sufficiently strong. In the BCS regime where the normal state is semimetallic, we find that the excitonic order is always suppressed, irrespective of the frequency of the pulse light. The quasiparticle band structure and optical conductivity spectrum after the pumping are also calculated for the instantaneous states.

On the time-dependent Aharonov–Bohm effect

The Aharonov–Bohm effect in the background of a time-dependent vector potential is re-examined for both non-relativistic and relativistic cases. Based on the solutions to the Schrodinger and Dirac equations which contain the time-dependent magnetic vector potential, we find that contrary to the conclusions in a recent paper (Singleton and Vagenas 2013 [4]), the interference pattern will be altered with respect to time because of the time-dependent vector potential.

Breakdown of Polarons in Conducting Polymers at Device Field Strengths

Conducting polymers have become standard engineering materials used in many electronic devices. Despite this, there is a lack of understanding of the microscopic origin of the conducting properties, especially at realistic device field strengths. We present simulations of doped poly(p-phenylene) (PPP) using a Su–Schrieffer–Heeger (SSH) tight-binding model, with the electric field included in the Hamiltonian through a time-dependent vector potential via Peierls substitution of the phase factor. We find that polarons typically break down within less than a picosecond after the field has been switched on, already for electric fields as low as around 1.6 mV/Å. This is a field strength common in many flexible organic electronic devices. Our results challenge the relevance of the polaron as charge carrier in conducting polymers for a wide range of applications.

On the Dynamics through a Conical Intersection.

Conical intersections represent critical topological features of potential energy surfaces and open ultrafast nonradiative deactivation channels for photoexcited molecules. In the following, we investigate how this funneling picture is transposed in the eyes of the exact factorization formalism for a 2D model system. The exact factorization of the total molecular wave function leads to the fundamental concept of time-dependent potential energy surface and time-dependent vector potential, whose behavior during a dynamics through a conical intersection has up to now remained unexplored. Despite the fact that these quantities might be viewed as time-dependent generalizations of the adiabatic potential energy surfaces and the nonadiabatic coupling vectors, characteristic quantities appearing in the Born-Oppenheimer framework, we observe that they do not exhibit particular topological features in the region of conical intersection but still reflect the complex dynamics of the nuclear wavepacket.

PCTDSE: A parallel Cartesian-grid-based TDSE solver for modeling laser–atom interactions

We present a parallel Cartesian-grid-based time-dependent Schrödinger equation (TDSE) solver for modeling laser–atom interactions. It can simulate the single-electron dynamics of atoms in arbitrary time-dependent vector potentials. We use a split-operator method combined with fast Fourier transforms (FFT), on a three-dimensional (3D) Cartesian grid. Parallelization is realized using a 2D decomposition strategy based on the Message Passing Interface (MPI) library, which results in a good parallel scaling on modern supercomputers. We give simple applications for the hydrogen atom using the benchmark problems coming from the references and obtain repeatable results. The extensions to other laser–atom systems are straightforward with minimal modifications of the source code. Program summaryProgram title: PCTDSECatalogue identifier: AFBM_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AFBM_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: BSD 3 - ClauseNo. of lines in distributed program, including test data, etc.: 398662No. of bytes in distributed program, including test data, etc.: 6355779Distribution format: tar.gzProgramming language: Fortran 2003.Computer: Distributed memory machines.Operating system: Unix-like system.RAM: Depends on the size of the Cartesian gridClassification: 2.1, 2.2, 2.5.External routines: 2DECOMP&FFT; FFTW; MPINature of problem:Simulate the single-electron dynamics of atoms under the strong fields of modern lasers according to the time-dependent Schrödinger equation.Solution method:The package solves the TDSE in the FFT-split-operator method, employing the split-operator method to approximate the time evolution operator and fast Fourier transforms to calculate the spatial derivatives.Restrictions:The code is restricted to problems where the atoms are in the single-active-electron approximation and the lasers are in the dipole approximation. It is also limited by the CPU time and memory that one can afford.Unusual features:We adopt the parallel strategy where the Cartesian grid is distributed among processors using a 2D decomposition, which has no limitation for large-scale simulations.Running time:The running time depends on the size of the grid, the number of time step, the number of processors, and the choice of the processor grid, ranging from a few hours to several days.

Time-dependent massless Dirac fermions in graphene

Using the Lewis–Riesenfeld method of invariants we construct explicit analytical solutions for the massless Dirac equation in 2+1 dimensions describing quasi-particles in graphene. The Hamiltonian of the system considered contains some explicit time-dependence in addition to one resulting from being minimally coupled to a time-dependent vector potential. The eigenvalue equations for the two spinor components of the Lewis–Riesenfeld invariant are found to decouple into a pair of supersymmetric invariants in a similar fashion as the known decoupling for the time-independent Dirac Hamiltonians.

Photodetachment of Si− by mid-infrared few-cycle femtosecond laser pulses

The Kelydsh model originally developed for infinitely long periodic laser pulses is extended to a spin polarized model to consider direct photodetachment of negative ions with half-filled np3 valence shells by few-cycle laser pulses without taking into account rescattering effects. The theory is applied to study above threshold detachment of Si− negative ions by intense short infrared pulses but is expected to be inherent of any half-filled p subshell negative ion. Photoelectron momentum maps of the direct electrons of Si− are presented. These are found to exhibit a distinctive threshold structure of concentric elliptical rings where the separation of these rings is dependent on the quantized frequency components of the few-cycle laser pulse. Photoelectron angular distributions (PADs) predicted by short duration laser pulses are calculated and threshold effects associated with channel closings are observed as the laser-field frequency and intensity pass through critically induced ponderomotive potential channel closures. Enhanced structures of the PADs in the vicinity near threshold show that the detachment process does not follow the Wigner law. This is a because the photon energy is not conserved in a few-cycle pulse in contrast to a long periodic pulse. In the energy spectra interference effects are observable as multiphoton peaked structures whose positions are dependent on the ponderomotive threshold shifts determined by the nature of the time-dependent vector potential. Additionally we show that carrier envelope phase effects manipulate all emission spectra considered.

Dynamical competition between quantum Hall and quantum spin Hall effects

In this paper we investigate the occurrence of quantum phase transitions in topological systems out of equi- librium. More specifically, we consider graphene with a sizable spin-orbit coupling, irradiated by circularly- polarized light. In the absence of light, the spin-orbit coupling drives a quantum spin Hall phase where edge currents with opposite spins counter-propagate. On the other hand, the light generates a time-dependent vector potential, which leads to a hopping parameter with staggered time-dependent phases around the benzene ring. The model is a dynamical version of the Haldane model, which considers a static staggered flux with zero total flux through each plaquette. Since the light breaks time-reversal symmetry, a quantum Hall phase protected by an integer topological invariant arises. By numerically solving the complete problem, with spin-orbit coupling and light, and investigating different values of the driving frequency {\omega}, we show that the spectrum exhibits non-trivial gaps not only at zero energy, but also at {\omega}/2. This additional gap is created by photon resonances between the valence and conduction band of graphene, and the symmetry of the spectrum forces it to lie at {\omega}/2. By increasing the intensity of the irradiation, the topological state in the zero energy gap undergoes a dynamical phase transition from a quantum spin Hall to a quantum Hall phase, whereas the gap around {\omega}/2 remains in the quantum Hall regime.

Revealing the time-dependent polarization of ultrashort pulses with sub-cycle resolution.

We report on the first experiments characterizing the complete time-dependent 2D vector potential of a few-cycle laser pulse. The instantaneous amplitude and orientation of the electric field is determined with sub-cycle resolution, directly giving access to the polarization state of the pulse at any instant in time. This is achieved by performing an attosecond streaking experiment using a reaction microscope, where the full pulse characterization is performed directly in the target region.

Stability estimate for the relativistic Schrödinger equation with time-dependent vector potentials

We consider the relativistic Schrödinger equation with a time dependent vector and scalar potential on a bounded cylindrical domain. Using a geometric optics ansatz we establish a logarithmic stability estimate for the recovery of vector and scalar potentials.

Mixed quantum-classical dynamics from the exact decomposition of electron-nuclear motion

We present a novel mixed quantum-classical approach to the coupled electron-nuclear dynamics based on the exact factorisation of the electron-nuclear wave function, recently proposed in Abedi A., Maitra N. T. and Gross E. K. U., Phys. Rev. Lett., 105 (2010) 123002. In this framework, the correct classical limit of the nuclear dynamics is worked out by taking the classical limit of the exact time-dependent Schrödinger equation satisfied by the nuclear wave function. The effect of the time-dependent scalar and vector potentials, representing the exact electronic back-reaction on the nuclear subsystem, is consistently derived within the classical approximation. We examine with an example the performance of the proposed mixed quantum-classical scheme in comparison with exact calculations.

Photon induced tunneling of electron through a graphene electrostatic barrier

The influence of an external intense laser field on the tunneling transport (ballistic) of the Dirac fermions through a monolayer graphene electrostatic barrier is studied in the framework of the Floquet approach for a continuous wave, linearly polarized, monochromatic laser. The Klein tunneling is shown to be suppressed by the irradiation of a strong laser field, arising due to breaking of chiral symmetry. The symmetric nature of the field free angular transmission spectrum around the normal to the well-barrier interface is destroyed due to the additional coupling between the pseudo-spin and the time dependent vector potential. The energy distribution of the tunneling spectrum displays Fano resonance which is absent for a laser assisted conventional electrostatic barrier but similar to the case of quantum well structures, providing an optical tool to identify field free quasi bound states inside the graphene nanostructures.