Collisional Quantum Research Articles

The effect of collisions on the rayleigh-taylor instability in magnetized quantum plasma

Rayleigh-Taylor instability occurs at the interface between light and heavy fluids whenever the heavier fluid is accelerated by the light one. An important issue is the stability conditions of these systems. Various parameters such as density difference between two fluids, density inhomogeneity length, magnetic field, viscosity, collision can affect the stabilization or destabilization of the system. So far, some of these factors have been investigated in the fields of classical and quantum physics. This process has also been studied in both linear and nonlinear states. Here we consider a collisional magnetic inhomogeneous quantum plasma. For the inhomogeneity profile of density as an exponential function, we calculated the second ordinary equation for the disturbed velocity. Since the differential equation does not have an analytical solution, we have calculated the growth rate curve using numerical methods and obtained the disturbed velocity profile in the discontinuity. Then the effects of different parameters such as collision, magnetic field, quantum effects, and density difference of two fluids on the system stabilization are studied. The various branches of the instability growth rate curve and its relationship with the turbulent velocity profile in discontinuity are also discussed.

Propagation of surface plasmons in a quantum collisional semiconductor plasma

In this work, the propagation of surface plasmons in a quantum collisional semiconductor plasma is theoretically investigated using the quantum hydrodynamic model. The general dispersion equation of surface plasmons is deduced and solved in the presence of collisional effects and quantum tunneling of electrons and holes. It is shown that collisions play a significant role in the decay or growth of surface plasmons. Moreover, it is found that the quantum tunneling of electrons and holes increases the phase velocity, the group velocity, and the growth rate of instability. It is also indicated that the growth rate of instability is decreased with the increase of the ratio of hole density to electron density and the ratio of electron effective mass to hole effective mass.

The effect of chirp parameter on laser propagation in collisional quantum plasma

This manuscript investigates the effect of the chirp factor on the relativistic self-focusing of a Gaussian chirped pulse laser in collisional quantum plasmas. Nonlinear equations are derived to describe the propagation of a linear chirped laser frequency; afterward, by considering dielectric function obtained by quantum kinetic equation and BGK collision integral in coordinate space, evolution differential equations of laser beam width are found; and numerically solved by the fourth-order Runge-Kutta method. It studies oscillations of the beam width along the propagation direction for different values of collision frequency, chirp parameter, plasma density, and laser intensity. Numerical analyses show that a laser beam is defocused after focusing on a definite value; nonetheless, the positive chirp parameter could reduce the defocusing and strengthen the self-focusing in collisional quantum plasma. Also, the higher chirp value leads to a smaller oscillation amplitude and a greater oscillation rate. Furthermore, the self-focusing effect becomes stronger by increasing plasma density and laser intensity. These consequences could be beneficial in the improvement of fast ignition experiments.

Collisional open quantum dynamics with a generally correlated environment: Exact solvability in tensor networks

Quantum collision models are receiving increasing attention as they describe many nontrivial phenomena in the dynamics of open quantum systems. In a general scenario of both fundamental and practical interest, a quantum system repeatedly interacts with individual particles or modes, forming a correlated and structured reservoir; however, classical and quantum environment correlations greatly complicate the calculation and interpretation of the system dynamics. Here, we propose an exact solution to this problem based on the tensor network formalism. We find a natural Markovian embedding for the system dynamics, where the role of an auxiliary system is played by virtual indices of the network. The constructed embedding is amenable to an analytical treatment for a number of timely problems such as the system interaction with two-photon wave packets, structured photonic states, and one-dimensional spin chains. We also derive a time-convolution master equation and relate its memory kernel with the environment correlation function, thus revealing a clear physical picture of memory effects in the dynamics. The results advance tensor-network methods in the fields of quantum optics and quantum transport.

Multipartite Correlations in Quantum Collision Models.

Quantum collision models have proved to be useful for a clear and concise description of many physical phenomena in the field of open quantum systems: thermalization, decoherence, homogenization, nonequilibrium steady state, entanglement generation, simulation of many-body dynamics, and quantum thermometry. A challenge in the standard collision model, where the system and many ancillas are all initially uncorrelated, is how to describe quantum correlations among ancillas induced by successive system-ancilla interactions. Another challenge is how to deal with initially correlated ancillas. Here we develop a tensor network formalism to address both challenges. We show that the induced correlations in the standard collision model are well captured by a matrix product state (a matrix product density operator) if the colliding particles are in pure (mixed) states. In the case of the initially correlated ancillas, we construct a general tensor diagram for the system dynamics and derive a memory-kernel master equation. Analyzing the perturbation series for the memory kernel, we go beyond the recent results concerning the leading role of two-point correlations and consider multipoint correlations (Waldenfelds cumulants) that become relevant in the higher-order stroboscopic limits. These results open an avenue for the further analysis of memory effects in collisional quantum dynamics.

Stochastic Collisional Quantum Thermometry.

We extend collisional quantum thermometry schemes to allow for stochasticity in the waiting time between successive collisions. We establish that introducing randomness through a suitable waiting time distribution, the Weibull distribution, allows us to significantly extend the parameter range for which an advantage over the thermal Fisher information is attained. These results are explicitly demonstrated for dephasing interactions and also hold for partial swap interactions. Furthermore, we show that the optimal measurements can be performed locally, thus implying that genuine quantum correlations do not play a role in achieving this advantage. We explicitly confirm this by examining the correlation properties for the deterministic collisional model.

Linear and nonlinear low-frequency collisional quantum Buneman Instability in electron-positron-ion Plasmas

The linear and nonlinear low-frequency collisional quantum Buneman instability in electronpositron- ion plasmas have been studied. Buneman instability in low frequency three species quantum plasma has been investigated using the approach of the quantum hydrodynamic model. The one-dimensional low-frequency collisional model is revisited by introducing the Bohm potential term in the momentum equation along with the role of the positron. Low-frequency Buneman instability which arises by one stream of particles drifting over another is investigated in the presence of the positron. Different plasma configurations based on the relative velocities of streaming particles are analyzed and it is observed that positron content enhances the instability in classical limits. Further, we found that in pure quantum limits the instability growth rate is decreased by increasing the positron concentration. The present work is very useful for the nonlinear problems in Quantum Coulomb systems.

Vortices in a strongly coupled collisional quantum plasma embedded in an external magnetic field

Abstract Vortex motion of a cylindrical quantum plasma containing degenerate inertialess electrons and strongly correlated, non-degenerate inertial ions is studied. The electron exchange–correlation and ion–neutral collisional effects are taken into consideration, along with vertical external magnetic field and radial electric field. Considering generalized viscoelastic momentum equation for strongly coupled ions in quasi-crystalline state, variation of different rotational characteristics along radial distance are discussed numerically. Existence of shear rotation is observed near both the core and the periphery of the vortex, which is found to be modified by ion–ion correlation, quantum effects of the degenerate electrons, the ion–neutral collision, as well as by the magnetic field. It is noticed that electron exchange–correlation potential and quantum diffraction play major roles in modifying the rotational characteristics. Vorticity and the rate of increment of enstrophy with respect to radial distance, diminish to zero towards the periphery of the vortex. Also, it is noted that the ion–neutral collision may be responsible for reducing the increment of enstrophy.

Optical Ferris wheels as a platform for collisional quantum gates

We show how optical Ferris wheel light fields can be exploited for the generation of internal-state-dependent optical lattices. We furthermore demonstrate how these lattices can be employed for the realization of controllable collisional gates. By employing realistic and experimentally accessible parameters, we demonstrate the potential of such gates, taking advantage of the extraordinary properties of optical Ferris wheels for efficient and scalable quantum computation.

Influence of varying magnetic field on nonlinear wave excitations in collisional quantum plasmas

Abstract The nonlinear wave excitations arising from the spatially varying magnetic field in the quantum plasma environment are investigated in the frame work of quantum hydrodynamic model. In the weakly nonlinear, dispersive and dissipative limit it is shown that the varying magnetic field and collision-induced excitations can be described by a modified form of Korteweg-de Vries–Burgers’ type model equation. It is found that the dissipation terms (Burgers’ and collisional term) arise due to spatially varying magnetic field and the ion-neutral collisions. The numerical solutions of this equation predict that the localized soliton solutions decay algebraically due to the combined effect of varying magnetic field and collision by radiating oscillatory pulses behind the propagating soliton.

Conditional wave theory of environmental interactions with a quantum particle

We present an alternative formulation of quantum decoherence theory using conditional wave theory (CWT), which was originally developed in molecular physics (also known as exact factorisation methods). We formulate a CWT of a classic model of collisional decoherence of a free particle with environmental particles treated in a long-wavelength limit. In general, the CWT equation of motion for the particle is non-linear, where the non-linearity enters via the CWT gauge fields. For Gaussian wave packets the analytic solutions of the CWT equations are in exact agreement with those from the density matrix formalism. We show that CWT gauge terms that determine the dynamics of the particle's marginal wave function are related to a Taylor series expansion of the particle's reduced density matrix. Approximate solutions to these equations lead to a linear-time approximation that reproduces the ensemble width in the limits of both short and long times, in addition to reproducing the long-term behaviour of the coherence length. With this approximation, the non-linear equation of motion for the particle's marginal wave function can be written in the form of the logarithmic Schr\"odinger equation. The CWT formalism may lead to computationally efficient calculations of quantum decoherence, since it involves working with wave-function level terms instead of evolving a density matrix via a master equation.

Collisional Quantum Thermometry.

We introduce a general framework for thermometry based on collisional models, where ancillas probe the temperature of the environment through an intermediary system. This allows for the generation of correlated ancillas even if they are initially independent. Using tools from parameter estimation theory, we show through a minimal qubit model that individual ancillas can already outperform the thermal Cramer-Rao bound. In addition, due to the steady-state nature of our model, when measured collectively the ancillas always exhibit superlinear scalings of the Fisher information. This means that even collective measurements on pairs of ancillas will already lead to an advantage. As we find in our qubit model, such a feature may be particularly valuable for weak system-ancilla interactions. Our approach sets forth the notion of metrology in a sequential interactions setting, and may inspire further advances in quantum thermometry.

Collisional Quantum Dynamics for MgH- (1Σ+) With He as a Buffer Gas: Ionic State-Changing Reactions in Cold Traps.

We present in this paper a detailed theoretical and computational analysis of the quantum inelastic dynamics involving the lower rotational levels of the MgH− (X1Σ+) molecular anion in collision with He atoms which provide the buffer gas in a cold trap. The interaction potential between the molecular partner and the He (1S) gaseous atoms is obtained from accurate quantum chemical calculations at the post-Hartree-Fock level as described in this paper. The spatial features and the interaction strength of the present potential energy surface (PES) are analyzed in detail and in comparison with similar, earlier results involving the MgH+ (1Σ) cation interacting with He atoms. The quantum, multichannel dynamics is then carried out using the newly obtained PES and the final inelastic rats constants, over the range of temperatures which are expected to be present in a cold ion trap experiment, are obtained to generate the multichannel kinetics of population changes observed for the molecular ion during the collisional cooling process. The rotational populations finally achieved at specific temperatures are linked to state-selective laser photo-detachment experiments to be carried out in our laboratory.All intermediate steps of the quantum modeling are also compared with the behavior of the corresponding MgH+ cation in the trap and the marked differences which exist between the collisional dynamics of the two systems are dicussed and explained. The feasibility of the present anion to be involved in state-selective photo-detachment experiments is fully analyzed and suggestions are made for the best performing conditions to be selected during trap experiments.

Nonplanar ion acoustic waves in collisional quantum plasma

The dynamics of nonlinear ion acoustic waves (IAWs) is studied in homogeneous, unmagnetized, collisional quantum plasma consisting of electrons and ions in bounded nonplanar (cylindrical/spherical) geometries. By using the reductive perturbation method, the nonplanar Kakutani and Kawahara equation is derived to investigate the nonlinear quantum IAW profiles. The dissipation is introduced by taking into account the collision among the plasma constituents in presence of quantum diffraction effect. Numerically, the effects of various plasma parameters, such as, the collisional parameter (η), the quantum diffraction parameter H, have been examined on the propagation of nonplanar IAW structures in quantum plasma. It is shown that in nonplanar geometry, plasma parameters play a vital role on the basic features of nonlinear structures (viz. amplitude, width, speed, and so on). It is also found that the properties of IAW structures in nonplanar geometry significantly differ from those in planar geometry.

Propagation of surface waves in a spin 1/2 magnetized collisional quantum plasma half-space

The quantum magnetohydrodynamics model, including the correction terms of the Bohm potential, quantum pressure, collision and intrinsic spin of electrons, is employed to investigate the propagation of surface waves in a semi-bounded spin 1/2 magnetized collisional quantum plasma. The parametric equation method is used to derive the highly nonlinear dispersion relation. Furthermore, the exact dispersion relation is solved numerically. It is shown that the external magnetic field increases the group and phase velocities of the surface waves in both collisionless and collisional quantum plasma, while the spin contribution leads to a decrease in the phase velocity. In the collisional quantum plasma, the damping rate of the surface waves is increased by the external magnetic field and the spin of the electrons.

Nonlinear interaction between surface plasmons and ion oscillations in a semi-bounded collisional quantum plasma

In this paper, we have investigated the nonlinear interaction between high-frequency surface plasmons and low-frequency ion oscillations in a semi-bounded collisional quantum plasma. By coupling the nonlinear Schrodinger equation and quantum hydrodynamic model, and taking into account the ponderomotive force, the dispersion equation is obtained. By solving this equation, it is shown that there is a modulational instability in the system, and collisions and quantum forces play significant roles on this instability. The quantum tunneling increases the phase and group velocities of the modulated waves and collisions increase the growth rate of the modulational instability. It is also shown that the effect of quantum forces and collisions is more significant in high modulated wavenumber regions.

Energy exchange in strongly coupled plasmas with electron drift

In this paper, the generalized viscoelastic collisional quantum hydrodynamic model is employed in order to investigate the linear dielectric response of a quantum plasma in the presence of strong electron-beam plasma interactions. The generalized Chandrasekhar's relativistic degeneracy pressure together with the electron-exchange and Coulomb interaction effects are taken into account in order to extend current research to a wide range of plasma number density relevant to big planetary cores and astrophysical compact objects. The previously calculated shear viscosity and the electron-ion collision frequencies are used for strongly coupled ion fluid. The effect of the electron-beam velocity on complex linear dielectric function is found to be profound. This effect is clearly interpreted in terms of the wave-particle interactions and their energy-exchange according to the sign of the imaginary dielectric function, which is closely related to the wave attenuation coefficient in plasmas. Such kinetic effect is also shown to be in close connection with the stopping power of a charged-particle beam in a quantum plasma. The effect of many independent plasma parameters, such as the ion charge-state, electron beam-velocity, and relativistic degeneracy, is shown to be significant on the growing/damping of plasma instability or energy loss/gain of the electron-beam.

Relativistic Gaussian laser beam self-focusing in collisional quantum plasmas

AbstractPropagation of Gaussian X-ray laser beam is presented in collisional quantum plasma and the beam width oscillation is studied along the propagation direction. It is noticed that due to energy absorption in collisional plasma, the laser energy drops to an amount less than the critical value of the self-focusing effect and consequently, the laser beam defocuses. It is found that the oscillation amplitude of the laser spot size enhances while passing through collisional plasma. For the greater values of collision frequency, the beam width oscillates with higher amplitude and defocuses in a shallower plasma depth. Also, it is realized that in a dense plasma environment, the laser self-focusing occurs earlier with the higher oscillation amplitude, smaller laser spot size and more oscillations.

Distinct optical properties of relativistically degenerate matter

In this paper, we use the collisional quantum magnetohydrodynamic (CQMHD) model to derive the transverse dielectric function of a relativistically degenerate electron fluid and investigate various optical parameters, such as the complex refractive index, the reflection and absorption coefficients, the skin-depth and optical conductivity. In this model we take into accounts effects of many parameters such as the atomic-number of the constituent ions, the electron exchange, electron diffraction effect and the electron-ion collisions. Study of the optical parameters in the solid-density, the warm-dense-matter, the big-planetary core, and the compact star number-density regimes reveals that there are distinct differences between optical characteristics of the latter and the former cases due to the fundamental effects of the relativistic degeneracy and other quantum mechanisms. It is found that in the relativistic degeneracy plasma regime, such as found in white-dwarfs and neutron star crusts, matter possess a much sharper and well-defined step-like reflection edge beyond the x-ray electromagnetic spectrum, including some part of gamma-ray frequencies. It is also remarked that the magnetic field intensity only significantly affects the plasma reflectivity in the lower number-density regime, rather than the high density limit. Current investigation confirms the profound effect of relativistic degeneracy on optical characteristics of matter and can provide an important plasma diagnostic tool for studying the physical processes within the wide scope of quantum plasma regimes be it the solid-density, inertial-confined, or astrophysical compact stars.

Space-charge waves in magnetized and collisional quantum plasma columns confined in carbon nanotubes

We study the dispersion relation of electrostatic waves propagating in a column of quantum magnetized collisional plasma embraced completely by a metallic single-walled carbon nanotubes. The analysis is based on the quantum linearized hydrodynamic formalism of collective excitations within the quasi-static approximation. It is shown when the electronic de Broglie's wavelength of the plasma is comparable in the order of magnitude to the radius of the nanotube, the quantum effects are quite meaningful and our model anticipates one acoustical and two optical space-charge waves which are positioned into three propagating bands. With increasing the nanotube radius, the features of the acoustical branch remain unchanged, yet two distinct optical branches are degenerated and the classical behavior is recovered. This study might provide a platform to create new finite transverse cross section quantum magnetized plasmas and to devise nanometer dusty plasmas based on the metallic carbon nanotubes in the absence of either a drift or a thermal electronic velocity and their existence could be experimentally examined.