Time-Dependent Unitary Transformation Method in the Strong-Field-Ionization Regime with the Kramers-Henneberger Picture

Time evolution operators of a strongly ionizing medium are calculated by a time-dependent unitary transformation (TDUT) method. The TDUT method has been employed in a quantum mechanical system composed of discrete states. This method is especially helpful for solving molecular rotational dynamics in quasi-adiabatic regimes because the strict unitary nature of the propagation operator allows us to set the temporal step size to large; a tight limitation on the temporal step size (δt<<1) can be circumvented by the strict unitary nature. On the other hand, in a strongly ionizing system where the Hamiltonian is not Hermitian, the same approach cannot be directly applied because it is demanding to define a set of field-dressed eigenstates. In this study, the TDUT method was applied to the ionizing regime using the Kramers-Henneberger frame, in which the strong-field-dressed discrete eigenstates are given by the field-free discrete eigenstates in a moving frame. Although the present work verifies the method for a one-dimensional atom as a prototype, the method can be applied to three-dimensional atoms, and molecules exposed to strong laser fields.

Time-Dependent Unitary Transformation Method in the Strong-Field-Ionization Regime With the Kramers-Henneberger Picture

Time evolution operators of a strongly ionizing medium are calculated by a time-dependent unitary transformation (TDUT) method. The TDUT method has been employed in quantum mechanical system composed of discrete states. This method is especially helpful for solving molecular rotational dynamics in quasi-adiabatic regimes because the strict unitary nature of the propagation operator allows us to set the temporal step size large; a tight limitation on the temporal step size ($\delta t &lt;&lt;1$) can be circumvented by the strict unitary nature. On the other hand, in a strongly ionizing system where the Hamiltonian is not Hermitian, the same approach cannot be directly applied because it is demanding to define a set of field-dressed eigenstates. In this study, the TDUT method was applied to the ionizing regime using the Kramers-Henneberger frame, in which the strong-field-dressed discrete eigenstates are given by the field-free discrete eigenstates in a moving frame. Although the present work verifies the method for a one-dimensional atom as a prototype, the method can be applied to three-dimensional atoms, and molecules exposed to strong laser fields.

Anisotropic Born scattering for the qP scalar wavefield using a low-rank symbol approximation

We present a procedure to derive low-rank evolution operators in the mixed space-wavenumber domain for modeling the qP Born-scattered wavefield at perturbations of an anisotropic medium under the pseudo-acoustic approximation. To approximate the full wavefield, this scattered field is then added to the reference wavefield obtained with the corresponding low-rank evolution operator in the background medium. Being built upon a Hamiltonian formulation using the dispersion relation for qP waves, this procedure avoids pseudo-S-wave artifacts and provides a unified approach for linearizing anisotropic pseudo-acoustic evolution operators. Therefore it is immediately applicable to any arbitrary class of anisotropy. As an additional asset, the scattering operators explicitly contain the sensitivity kernels of the Born-scattered wavefield with respect to the anisotropic medium parameters. This enables direct access to important information like its offset dependence or directional characteristics as a function of the individual parameter perturbations. For our numerical tests, we specify the operators for a mildly anisotropic tilted transversly isotropic (TTI) medium. We validate our implementation in a simple model with weak contrasts and simulate reflection data in the BP TTI model to show that the procedure works in a more realistic scenario. The Born-scattering results indicate that our procedure is applicable to strongly heterogeneous anisotropic media. Moreover, we use the analytical capabilities of the kernels by means of sensitivity tests to demonstrate that using two different medium parameterizations leads to different results. The mathematical formulation of the method is such that it allows for an immediate application to least-squares migration in pseudo-acoustic anisotropic media.

Barbashin conditions for uniform instability of evolution operators

"The aim of the present paper is to give some characterization theorems of Barbashin type for the uniform exponential instability and uniform polynomial instability behavior of evolution operators. Also, some examples which illustrate the connections between the concepts presented are given."

A Framework for Implementing Metaheuristic Algorithms Using Intercellular Communication

Metaheuristics (MH) are Artificial Intelligence procedures that frequently rely on evolution. MH approximate difficult problem solutions, but are computationally costly as they explore large solution spaces. This work pursues to lay the foundations of general mappings for implementing MH using Synthetic Biology constructs in cell colonies. Two advantages of this approach are: harnessing large scale parallelism capability of cell colonies and, using existing cell processes to implement basic dynamics defined in computational versions. We propose a framework that maps MH elements to synthetic circuits in growing cell colonies to replicate MH behavior in cell colonies. Cell-cell communication mechanisms such as quorum sensing (QS), bacterial conjugation, and environmental signals map to evolution operators in MH techniques to adapt to growing colonies. As a proof-of-concept, we implemented the workflow associated to the framework: automated MH simulation generators for the gro simulator and two classes of algorithms (Simple Genetic Algorithms and Simulated Annealing) encoded as synthetic circuits. Implementation tests show that synthetic counterparts mimicking MH are automatically produced, but also that cell colony parallelism speeds up the execution in terms of generations. Furthermore, we show an example of how our framework is extended by implementing a different computational model: The Cellular Automaton.

Numerical Simulation of Multistage Bimolecular Photoreactions in Liquids: Algorithms and Software

In this paper we consider the tools for numerical simulation of multistage bimolecular photoreactions assisted by diffusive mobility of reactant molecules in viscous solutions. To describe these processes, the differential encounter theory (DET) is extended to account for the coherent dynamics of certain degrees of freedom (for example, electronic spins of reactants and intermediates). The model involves diffusion of reactants in solution and multistage/multichannel physicochemical processes proceeding both at the level of individual molecules and encounter complexes. Algorithms for numerical solution of model equations are proposed, which are related to evaluation of evolution operators. The algorithm for computing the quantum propagator for the density matrix based on the Trotter splitting is presented. A software package for simulation of multistage photoreactions has been developed using the suggested numerical approaches. The structure of the key software components is presented, examples of the program model construction are presented. A software testing has been carried out, showing good correspondence between the numerical results and exact solutions of the model equations in certain particular cases. As an example, a photoreaction with participation of 9,10-dimethylanthracene and 1,3-dicyanobenzene in acetonitrile solution has been considered, and basic procedures for configuring and simulating multistage bimolecular photoprocesses are shown. An importance of coherent description of the electronic spin evolution at the radical stage is shown.

Datko criteria for uniform instability in Banach spaces

The main objective of this paper is to present some necessary and sufficient conditions of Datko type for the uniform exponential and uniform polynomial instability concepts for evolution operators in Banach spaces.