Theory of quantum control landscapes: Overlooked hidden cracks

Why does controlling quantum phenomena appear easy to achieve? Why do effective quantum controls appear easy to find? Why is chemical synthesis and property optimization easier than expected? How to explain the commonalities across the optimal control applications in quantum mechanics, chemistry, material science, biological evolution and engineering? The theory of quantum control landscapes (QCL) is developed by Prof. Rabitz and his colleagues to address these puzzling questions. Unfortunately, the obtained conclusions are subject of gross misinterpretations which are spread in hundreds of published papers. We investigate, summarize and report several previously unknown subtleties of the QCL theory which have far-reaching implications for nearly all practical applications.Comment: The explanation of why the key result of the paper B. Russell, H. Rabitz, R.-B. Wu, J. Phys. A: Math. Theor. 50, 205302 (2017) [ arXiv:1608.06198 ] is wrong is significantly simplified and complemented by a demonstrative example. Various changes were introduced to fully adapt all parts of presentation for readers unfamiliar with differential topology. 5 pages, 3 figure

One-dimensional model of cosmological perturbations: direct integration in the Fourier space

We propose a method of calculation of the power spectrum of cosmological perturbations by means of a direct numerical integration of hydrodynamic equations in the Fourier space for a random ensemble of initial conditions with subsequent averaging procedure. This method can be an alternative to the cosmological N-body simulations. We test realizability of this method in case of one-dimensional motion of gravitating matter pressureless shells. In order to test the numerical simulations, we found an analytical solution which describes one-dimensional collapse of plane shells. The results are used to study a nonlinear interaction of different Fourier modes.Comment: 12 pages, 3 figure

Quantum optimal environment engineering for efficient photoinduced charge separation

The possibility to induce predetermined coherent quantum dynamics by controlling only the dissipative environmental parameters (such as temperature and pressure) is studied using the combined optimal control and environment engineering frameworks. As an example, we consider the problem of transforming an optically excited donor state into free charge carriers via intermediate higher-lying bridge state(s), with a view to solar energy conversion. In this context, vibrational bath engineering allows to promote fast, directional charge transfer and to suppress recombinative losses.Comment: 6 pages, 5 figure

Wigner representation of the rotational dynamics of rigid tops

We propose a methodology to design Wigner representations in phase spaces with nontrivial topology having evolution equations with desired mathematical properties. As an illustration, two representations of molecular rotations are developed to facilitate the analysis of molecular alignment in moderately intense laser fields, reaction dynamics, scattering phenomena and dissipative processes.Comment: 15 pages, 1 figur

Structure of optimal policies in quantum control

Using the Pontryagin maximum principle, the generic structure of optimal policies is deduced for typical quantum control tasks involving coherent lasers, magnetic fields and reservoir engineering. In addition, the periodic optimization is considered for the first time in view of prospective applications. We proved that nearly all optimal policies are actively constrained by technical bounds on control parameter but reduce to entirely bang-bang sequences only in special cases, such as the environmental control by random collisions. The results allow to arguably refute two generally accepted and concurring conjectures regarding the structure of optimal controls.Comment: The following major changes were made compared to the previous version. 1) The original literature review (which dates back to 2009-2012) is updated. 2) Incorrect theorem 2 is removed. 3) Mistakes in treating branch points in the proof of theorem 1 are fixed. 4) The detailed discussions on the physical meaning of each formal mathematical result are added. 12 pages, 3 figures, 2 table

Role of control constraints in quantum optimal control

The problems of optimizing the value of an arbitrary observable of the two-level system at both a fixed time and the shortest possible time is theoretically explored. Complete identification and classification along with comprehensive analysis of globally optimal control policies and traps (i.e. policies which are locally but not globally optimal) is presented. The central question addressed is whether the control landscape remains trap-free if control constraints of the inequality type are imposed. The answer is astonishingly controversial, namely, although formally it is always negative, in practice it is positive provided that the control time is fixed and chosen long enough.Comment: 14 pages, 11 figure

Qualitative types of cosmological evolution in hydrodynamic models with barotropic equation of state

We study solutions of the Friedmann equations in case of the homogeneous isotropic Universe filled with a perfect fluid. The main points concern the monotony properties of the solutions, the possibility to extend the solutions on all times and occurrence of singularities. We present a qualitative classification of all possible solutions in case of the general smooth barotropic equation of state of the fluid, provided the speed of sound is finite. The list of possible scenarios includes analogs of the "Big Rip" in the future and/or in the past as well as singularity free solutions and oscillating Universes. Extensions of the results to the multicomponent fluids are discussed.Comment: 7 pages, 5 figure

Small viscosity method and criteria for shock wave existence in relativistic magnetic hydrodynamics

We obtain criteria for shock wave (SW)existence in relativistic magnetic hydrodynamics with no suppositions about convexity of the equation of state. Method of derivation involves consideration of a continuous SW profile in presence of Landau-Lifshitz relativistic viscosity tensor with both non-zero viscosity coefficients.Comment: 15 pages including 3 figure

Ultra-Relativistic Expansion of Ideal Fluid with Linear Equation of State

We study solutions of the relativistic hydrodynamical equations, which describe spherical or cylindrical expansion of ideal fluid. We derived approximate solutions involving two arbitrary functions, which describe asymptotic behavior of expanding fireballs in ultra-relativistic limit. In case of a sufficiently stiff linear equation of state the solution may be represented in form of an asymptotic series.Comment: 10 page

Symmetry and Exact Solutions of the Maxwell and SU(2) Yang-Mills Equations

We give the overview of solution techniques for the general conformally-invariant linear and nonlinear wave equations centered around the idea of dimensional reductions by their symmetry groups. The efficiency of these techniques is demonstrated on the examples of the SU(2) Yang-Mills and the vacuum Maxwell equations. For the Yang-Mills equations we have derived the most general form of the conformally-invariant solution and construct a number of their new analytical non-Abelian solutions in explicit form. We have completely solved the problem of symmetry reduction of the Maxwell equations by subgroups of the conformal group. This yields twelve multi-parameter families of their exact solutions, a majority of which are new and might be of considerable interest for applications.Comment: 81 pages, LaTe