Time-independent States Research Articles

Emergence of rogue-like waves in a reaction-diffusion system: Stochastic output from deterministic dissipative dynamics.

Rogue waves are an intriguing nonlinear phenomenon arising across different scales, ranging from ocean waves through optics to Bose-Einstein condensates. We describe the emergence of rogue wave-like dynamics in a reaction-diffusion system that arise as a result of a subcritical Turing instability. This state is present in a regime where all time-independent states are unstable and consists of intermittent excitation of spatially localized spikes, followed by collapse to an unstable state and subsequent regrowth. We characterize the spatiotemporal organization of spikes and show that in sufficiently large domains the dynamics are consistent with a memoryless process.

Nonadiabatic Dynamics in a Laser Field: Using Floquet Fewest Switches Surface Hopping To Calculate Electronic Populations for Slow Nuclear Velocities.

We investigate two well-known approaches for extending the fewest switches surface hopping (FSSH) algorithm to periodic time-dependent couplings. The first formalism acts as if the instantaneous adiabatic electronic states were standard adiabatic states, which just happen to evolve in time. The second formalism replaces the role of the usual adiabatic states by the time-independent adiabatic Floquet states. For a set of modified Tully model problems, the Floquet FSSH (F-FSSH) formalism gives a better estimate for both transmission and reflection probabilities than the instantaneous adiabatic FSSH (IA-FSSH) formalism, especially for slow nuclear velocities. More importantly, only F-FSSH predicts the correct final scattering momentum. Finally, in order to use Floquet theory accurately, we find that it is crucial to account for the interference between wavepackets on different Floquet states. Our results should be of interest to all those interested in laser-induced molecular dynamics.

Nonlinear characteristics of relativistic Pierce diodes in stationary state

Time independent states are explored theoretically for generalized Pierce diode (non-neutral plasma diode with ionic background), which is driven by a cold relativistic electron beam. The region between the electrodes is assumed to be filled uniformly with static ions. Injected beam is monochromatic, i.e., all the electrons are emitted with the same kinetic energy (relativistic). Relativistic effects are explored both for collisionless and collisional systems. The formulation of the model is based on the fluid-Maxwell's equations and it is solved by two methods: in the absence of any dissipative source, Eulerian description is employed, whereas to incorporate the effects of collisional drag Lagrangian formulation is found to be useful. The steady-state solutions are visualized through the “Bursian” and “Non-Bursian” branches in a parametric plane. It is observed that the magnitude of the maximum current density of a Pierce diode increases with the relativistic factor of the injected beam. Other factors like the density of background ions and particle collision also have significant influence on the space-charge-limited flow and other steady state properties. Obtained results are relevant to comprehend the working mechanism of many diode-based instruments such as thermionic energy converters, microwave emitter, Q-machines, etc.

A general approach for the calculation and characterization of x-ray absorption spectra.

We present a general approach for the calculation and assignment of X-ray absorption spectra based on electronic wavepacket propagations performed using explicitly time-dependent electronic structure calculations. Such calculations have the appeal of yielding the entire absorption spectrum for the cost of a single set of electronic wavepacket propagations, obviating the need to explicitly calculate large numbers of core-excited states. The spectrum can either be calculated from the Fourier transform of the time-dependent dipole moment or from the Fourier transform of the wavepacket autocorrelation function. We propose that calculating the absorption spectrum using the latter approach will generally be the preferred option. This method has two important advantages. First, the autocorrelation functions can be obtained for twice the propagation time, resulting in a halving of the computational effort required to calculate the spectrum relative to the time-dependent dipole moment approach. Second, using the tools of filter diagonalisation, the autocorrelation functions may be used to determine the time-independent final core-excited states underlying the peaks of interest in the spectrum. The proposed scheme is validated by calculating and characterizing the X-ray absorption spectra of benzene and trifluoroacetonitrile at the time-dependent second-order algebraic diagrammatic construction level of theory.

Effects of collision on the time-independent states of a non-neutral plasma diode

A theoretical investigation is presented on the steady states of a planar plasma diode where static ions uniformly occupy the inter-electrode region. A cold and purely monochromatic electron beam is injected from the emitter plate, and the emitted electrons are carried to the collector plate through the uniform background of stationary ions. It is considered that the electrons suffer collisions with the other particles (with ions or neutral atoms) during its transportation through the inter-electrode gap. The effects of collisions are incorporated through a simplified one-dimensional model. With the help of Lagrangian description of fluid-Maxwell's equations, time-independent states are explored for arbitrary values of the neutralization parameter. Using the emitter electric field as a characteristic parameter, the steady-state solutions are categorized into “Bursian” and “Non-Bursian” branches in “emitter electric field vs diode gap” parametric space. The Non-Bursian solutions are found to be very sensitive to the dissipative term as they only exist for small, non-zero values of the normalized collision-frequency.

Snakes and ghosts in a parity-time-symmetric chain of dimers.

We consider linearly coupled discrete nonlinear Schrödinger equations with gain and loss terms and with a cubic-quintic nonlinearity. The system models a parity-time (PT)-symmetric coupler composed by a chain of dimers. We study uniform states and site-centered and bond-centered spatially localized solutions and present that each solution has a symmetric and antisymmetric configuration between the arms. The symmetric solutions can become unstable due to bifurcations of asymmetric ones, that are called ghost states, because they exist only when an otherwise real propagation constant is taken to be complex valued. When a parameter is varied, the resulting bifurcation diagrams for the existence of standing localized solutions have a snaking behavior. The critical gain and loss coefficient above which the PT symmetry is broken corresponds to the condition when bifurcation diagrams of symmetric and antisymmetric states merge. Past the symmetry breaking, the system no longer has time-independent states. Nevertheless, equilibrium solutions can be analytically continued by defining a dual equation that leads to ghost states associated with growth or decay, that are also identified and examined here. We show that ghost localized states also exhibit snaking bifurcation diagrams. We analyze the width of the snaking region and provide asymptotic approximations in the limit of strong and weak coupling where good agreement is obtained.

Implications of the link between the Periodic Table and the Standard Model

The mathematics of quantum physics from the standard model using groups U(1)xSU(2)xSU(3) and the Pauli principle produces two sets of time independent quantum states n(n+1) and n(n-1) where n is the principal quantum number. Oscillations between these states result in a one to one mapping with the Roberts-Janet Nuclear Periodic Table by interpretation of n>0 for condensed matter and n<0 for plasma prior to fusion. The mechanism provides a framework for Periodic Tables for every supernova by excluding mass number. In the lower half of the table occupation by bosons leads to increased energy densities in which an ensemble of outcomes is discussed. An hypothesis of string theory is proposed at the nuclear end of the table merging into quantum loop gravity at the condensed matter at the top end of the table.

Implications of the Link between the Periodic Table and the Standard Model

The mathematics of quantum physics from the standard model using groups U(1)xSU(2)xSU(3) and the Pauli principle produces two sets of time independent quantum states n(n+1) and n(n-1) where n is the principal quantum number. Oscillations between these states result in a one to one mapping with the Roberts-Janet Nuclear Periodic Table by interpretation of n>0 for condensed matter and n<0 for plasma prior to fusion. The mechanism provides a framework for Periodic Tables for every supernova by excluding mass number. In the lower half of the table occupation by bosons leads to increased energy densities in which an ensemble of outcomes is discussed. An hypothesis of string theory is proposed at the nuclear end of the table merging into quantum loop gravity at the condensed matter at the top end of the table.

Dirac potential in the Doebner–Goldin equation

We study a dissipative quantum system which is described by the Doebner–Goldin equation (DGE) model. For time-independent states, the new three-dimensional analytical solutions of the DGE are obtained by binding the vertical relation of velocity and the gradient of density in the system, when the form of a central potential such as hard core or harmonic oscillator is suggested. Through the gauge-invariant parameters which characterize the physical nature of the dissipation, we find a novel set of gauge-invariant parameters which show that the Galilean invariance is broken in this system. Moreover, a subfamily of the DGE can be obtained after a gauge transformation, which describes a dissipative quantum system with the conserved Galilean invariance. It is interesting that this dissipative quantum system is completely equivalent to a charge-monopole system, in which the Dirac potential is supplied with the nonlinear terms and two cases of the velocity potential. Especially, the two gauge potentials given by Wu and Yang emerge from solving the DGE as two cases in our approach. The results not only present some new physical comprehension of the dissipative quantum system, but also might shed light on the Dirac monopole potential, in the sense that the partition into south and north hemisphere is avoided in our new solutions.

Linear response of entanglement entropy from holography

For time-independent excited states in conformal field theories, the entanglement entropy of small subsystems satisfies a ‘first law’-like relation, in which the change in entanglement is proportional to the energy within the entangling region. Such a law holds for time-dependent scenarios as long as the state is perturbatively close to the vacuum, but is not expected otherwise. In this paper we use holography to investigate the spread of entanglement entropy for unitary evolutions of special physical interest, the so-called global quenches. We model these using AdS-Vaidya geometries. We find that the first law of entanglement is replaced by a linear response relation, in which the energy density takes the role of the source and is integrated against a time-dependent kernel with compact support. For adiabatic quenches the standard first law is recovered, while for rapid quenches the linear response includes an extra term that encodes the process of thermalization. This extra term has properties that resemble a time-dependent ‘relative entropy’. We propose that this quantity serves as a useful order parameter to characterize far-from-equilibrium excited states. We illustrate our findings with concrete examples, including generic power-law and periodically driven quenches.

Radiation Pressure Cooling as a Quantum Dynamical Process.

One of the most fundamental problems in optomechanical cooling is how small the thermal phonon number of a mechanical oscillator can be achieved under the radiation pressure of a proper cavity field. Different from previous theoretical predictions, which were based on an optomechanical system's time-independent steady states, we treat such cooling as a dynamical process of driving the mechanical oscillator from its initial thermal state, due to its thermal equilibrium with the environment, to a stabilized quantum state of higher purity. We find that the stabilized thermal phonon number left in the end actually depends on how fast the cooling process could be. The cooling speed is decided by an effective optomechanical coupling intensity, which constitutes an essential parameter for cooling, in addition to the sideband resolution parameter that has been considered in other theoretical studies. The limiting thermal phonon number that any cooling process cannot surpass exhibits a discontinuous jump across a certain value of the parameter.

Time-independent states of a non-neutral plasma diode when emitted electrons are partially turned around by a transverse magnetic field

An analytical study is presented on the steady states of a plasma diode that is uniformly occupied by infinitely massive ions of constant density and driven by a cold electron beam in the presence of an external transverse magnetic field. In contrast to our previous work [Pramanik et al., Phys. Plasmas 23, 062118 (2016)], here, we investigate the case when electrons are reflected back to the emitter by the magnetic field for arbitrary values of the neutralization parameter. Using the emitter electric field as a characteristic parameter, the steady-state solutions have been evaluated for the specific values of the diode gap, applied voltage, neutralization parameter, and magnetic field strength. It was found that unlike vacuum diodes (e.g., the Bursian diode), steady state solutions also exist for negative values of the emitter field strength. In case of the Bursian diode, only a single type of solutions (Bursian branches) was observed. However, for the Pierce diode, the new family of solutions appeared along with the Bursian ones. In the absence of the external magnetic field as well as when it is weak, the potential distribution shows a wavy nature. However, when the Larmor radius was ten times the beam Debye length, the wavy potential profile and non-Bursian branches disappeared. Based on this phenomenon, a non-neutral diode can be used to operate fast electronic switches.

Scalar products of state vectors in totally asymmetric exactly solvable models on a ring

We consider exactly solvable, totally asymmetric models of the low-dimensional nonequilibrium physics on a ring, namely, the totally asymmetric simple exclusion process and the totally asymmetric simple zero range process. The quantum inverse method allows us to calculate the scalar products of state vectors of the models and to represent the answers in the determinantal form. It is shown that the eigenvectors of the models form a complete orthogonal basis. The projections of state vectors on stationary, time independent states are studied. Bibliography: 39 titles.

Radiation-induced resistance oscillation and instability in GaAS/AlGaAS heterostructure under transverse magnetic fields

This paper studies dynamics of a modulation-doped GaAs/AlGaAs heterostructure under transverse magnetic fields and microwave radiations. It finds that negative differential conductivity, due to the real-space electron transfer and delayed dielectric relaxation of the interface potential barrier, can lead to complex behaviours when a relatively small magnetic field is applied. Quasiperiodicity, frequency-locking and the routes from period-doubling to chaos are found. Under a large magnetic field, however, two time-independent homogeneous steady states exist; and the longitudinal resistance of the system shows an interesting oscillation with period tuned by the ratio of microwave radiation frequency ω to the cyclotron frequency ωc and local minima at ω/ωc = integer + 1/4.

Statistical mechanics of time independent nondissipative nonequilibrium states

We examine the question of whether the formal expressions of equilibrium statistical mechanics can be applied to time independent nondissipative systems that are not in true thermodynamic equilibrium and are nonergodic. By assuming that the phase space may be divided into time independent, locally ergodic domains, we argue that within such domains the relative probabilities of microstates are given by the standard Boltzmann weights. In contrast to previous energy landscape treatments that have been developed specifically for the glass transition, we do not impose an a priori knowledge of the interdomain population distribution. Assuming that these domains are robust with respect to small changes in thermodynamic state variables we derive a variety of fluctuation formulas for these systems. We verify our theoretical results using molecular dynamics simulations on a model glass forming system. Nonequilibrium transient fluctuation relations are derived for the fluctuations resulting from a sudden finite change to the system's temperature or pressure and these are shown to be consistent with the simulation results. The necessary and sufficient conditions for these relations to be valid are that the domains are internally populated by Boltzmann statistics and that the domains are robust. The transient fluctuation relations thus provide an independent quantitative justification for the assumptions used in our statistical mechanical treatment of these systems.

The Pierce-diode approximation to the single-emitter plasma diode

The possibility of modeling fast processes in the collisionless single-emitter plasma diode (Knudsen diode with surface ionization, KDSI) by means of the Pierce-diode is studied. The KDSI is of practical importance in that it is an almost exact model of thermionic energy converters (TICs) in the collisionless regime and can also be used to model low-density Q-machines. At high temperatures, the Knudsen TIC comes close to the efficiency of the Carnot cycle and hence is the most promising converter of thermal to electric energy. TICs can be applied as component parts in high-temperature electronics. It is shown that normalizations must be chosen appropriately in order to compare the plasma characteristics of the two models: the KDSI and the Pierce-diode. A linear eigenmode theory of the KDSI is developed. For both nonlinear time-independent states and linear eigenmodes without electron reflection, excellent agreement is found between the analytical potential distributions for the Pierce-diode and the corresponding numerical ones for the KDSI. For the states with electron reflection, the agreement is satisfactory in a qualitative sense. A full classification of states of both diodes for the regimes with and without electron reflection is presented. The effect of the thermal spread in electron velocities on the potential distributions and the (ε,η) diagrams is analyzed. Generally speaking, the methodology developed is usefully applicable to a variety of systems in which the electrons have beam-like distributions.

Steady states of a microwave-irradiated modulation-doped heterostructure under perpendicular magnetic field

We present a theoretical model and study dynamics of the modulation-doped GaAs/Al x Ga 1− x As heterostructure under a perpendicular magnetic field and microwave radiation. We propose a mechanism, which is based on the nonlinear dynamics of real-space electron transfer and delayed dielectric relaxation of the interface potential barrier resulting from the space charge in the doped AlGaAs layer. Static analysis specifies the negative differential conductance region when the dc bias voltage varies. The self-sustained oscillations and bistability between oscillationary and stationary states are predicted. Varying with the microwave irradiation amplitude and the perpendicular magnetic field, the routes from period-doubling to chaos, quasiperiodicity, and frequency-locking are found. In addition varying with the microwave irradiation frequency can lead to time-independent homogeneous steady states spatially and result in a longitudinal resistance oscillation with period tuned by the ratio of microwave radiation frequency ω to the cyclotron frequency ω c and local minima at ω / ω c = integer + 1 / 4 .

Seasonal Variability of Teleconnection Patterns

Abstract The seasonal variability of 300-hPa global streamfunction fields taken from a 40-yr period of reanalyzed observations starting on 1 January 1958 and from long 497- and 900-yr general circulation model (GCM) datasets forced by sea surface temperatures (SSTs) is examined and analyzed in terms of empirical orthogonal functions (EOFs), principal oscillation patterns (POPs), and particularly finite-time principal oscillation patterns (FTPOPs). The FTPOPs are the eigenvectors of the propagator, over a 1-yr period covering the annual cycle, that has been constructed by fitting a linear stochastic model with a time-dependent matrix operator to atmospheric fluctuations based on the daily or twice-daily 300-hPa streamfunction datasets. The leading FTPOPs are large-scale teleconnection patterns and by construction they are the empirical analogs of finite-time normal modes (FTNMs) of linear instability theory. Hence, by comparing FTPOPs to FTNMs, the study provides insight into the ability of linear theory to explain seasonal and intraseasonal variability in the structure and growth rates of large-scale disturbances. The study finds that the leading FTPOP teleconnection patterns have similar seasonal cycles of relative growth rates and amplitudes to the leading FTNMs of the barotropic vorticity equation with 300-hPa basic states that change with the annual cycle; the largest amplitudes of both theoretical and empirical modes occur in late boreal winter or early spring, and minimum amplitudes in boreal autumn, with the GCM-based FTPOPs having additional secondary maxima in early boreal summer. In each month, there are leading POPs and EOFs that closely resemble the leading FTPOPs. Also, the growth rates of leading FTNMs and FTPOPs during each season are generally similar to those of respective leading normal modes and POPs calculated for that season. Thus the perturbations are reacting to the seasonally varying basic state faster than the state is changing and this appears to explain why linear planetary wave models with time-independent basic states can be useful. Nevertheless, intermodal interference effects, as well as intramodal interference effects, between the eastward and westward propagating components of single traveling modes, can play important roles in the evolution of FTPOPs and FTNMs, particularly in boreal spring. This study has examined the roles of internal instability and interannual SST variability in the behavior of leading FTPOPs and has also used comparisons of FTPOPs and FTNMs for GCM simulations with and without interannually varying SSTs to assess the role of internal instability and SST variations in organizing interannual atmospheric variability. The comparison indicates that both factors are significant. The results found here also support a close relationship between the boreal spring predictability barrier of some models of climate prediction over the tropical Pacific Ocean and the amplitudes of large-scale instabilities and teleconnection patterns of the atmospheric circulation.

Oscillatory thermocapillary convection in open cylindrical annuli. Part 1. Experiments under microgravity

We report results from microgravity experiments on thermocapillary convection in open annuli with outer radius $R_{o}{\,=\,}40\,\hbox{mm}$ and inner radius $R_{i}{\,=\,}20\,\hbox{mm}$ of various aspect ratios $Ar$. The measurements are from more than 230 equilibrated states in the $Ar$–Marangoni-number space. We found time-independent and oscillatory states and report some selected oscillation and Fourier spectra from thermocouple measurements. We measured the critical temperature difference $\uDelta T^{\hspace*{1pt}c}$ for the onset of temperature oscillations in the range $1{\,\le\,}Ar{\,\le\,}8$. We report supercritical oscillation periods and attribute the oscillations in the larger $Ar$ range to hydrothermal waves. This conclusion is supported by the values of the oscillation periods and of the critical Marangoni numbers in that $Ar$ range. The hydrothermal waves exhibit an internal corotating multicellular pattern. For the smaller $Ar$ and near the threshold we report $m$-fold temperature patterns on the free surface with $m$ decreasing for decreasing $Ar$. At $4\uDelta T^{\hspace*{1pt}c}$ these patterns become very irregular. Most of the findings are in accordance with the numerical results reported in Part 2 (Sim et al. (2003)). The experimental $\uDelta T^{\hspace*{1pt}c}$ are higher and the experimental periods $\tau^{c}$ are smaller than the numerical values for Biot number $Bi{\,=\,}0$. However, analysis of the experimental free-surface thermal boundary conditions shows that there was heat input to the free surface. Good agreement with numerical results for $\uDelta T^{\hspace*{1pt}c}$ and $\tau^{\hspace*{1pt}c}$ is obtained with $Bi{\,\ne\,}0$ (heat input).

Optimization of the Fixed Global Observing Network in a Simple Model

An exact closed form expression for the infinite time analysis and forecast error covariances of a Kalman filter is used to investigate how the locations of fixed observing platforms such as radiosonde stations affect global distributions of analysis and forecast error variance. The solution pertains to a system with no model error, time-independent nondefective unstable dynamics, time-independent observation operator, and time-independent observation error covariance. As far as the authors are aware, the solutions are new. It is shown that only nondecaying normal modes (eigenvectors of the dynamics operator) are required to represent the infinite time error covariance matrices. Consequently, once a complete set of nondecaying eigenvectors has been obtained, the solution allows for the rapid assessment of the error-reducing potential of any observational network that bounds error variance. Atmospherically relevant time-independent basic states and their corresponding tangent linear propagators are obtained with the help of a (T21L3) quasigeostrophic global model. The closed form solution allows for an examination of the sensitivity of the error variances to many different observing configurations. It is also feasible to determine the optimal location of one additional observation given a fixed observing network, which, through repetition, can be used to build effective observing networks. Effective observing networks result in error variances several times smaller than other types of networks with the same number of column observations, such as equally spaced or land-based networks. The impact of the observing network configuration on global error variance is greater when the observing network is less dense. The impact of observations at different pressure levels is also examined. It is found that upper-level observations are more effective at reducing globally averaged error variance, but midlevel observations are more effective at reducing forecast error variance at and downstream of the baroclinic regions associated with midlatitude jets.