A review of the physical basis for the numerical fluid simulation of a large class of laser fusion experiments and of related physics issues is presented. The main emphasis is on processes relevant to the description of the direct-drive approach, employing moderate intensity, short wavelength laser pulses. The rationale for the use of fluid models, and for several simplifications of the resulting MHD equations is addressed with some details. The relevant atomic physics modeling is discussed in connection with the peculiar density-temperature range of laser fusion experiments. Models for the transport of radiation, suprathermal charged particles and neutrons, as well as for laser-matter interaction, are reviewed. A brief survey is also given of the main laser fusion codes. A survey of selected applications of fluid codes to 'model problems' of particular physical aspects of laser fusion, to the simulation of present experiments, and to the design of reactor-size targets is then presented. It is concluded that the basic physical modeling employed by state-of-the-art fluid codes seems to be adequate to the simulation of the class of experiments of interest, as well as to the overall target design. Indeed, results of experiments that are not dominated by fluid instabilities are simulated quite satisfactorily. Also, 2-D simulations have allowed for the first quantitative studies of several fluid instabilities, as well as of the effects of large scale-length non-uniform irradiation. Great progress is instead still needed to perform detailed multi-dimensional simulations capable of dealing simultaneously and self-consistently with both short and large scale-length perturbations.

https://iopscience.iop.org/article/10.1088/0741-3335/29/11/001/pdf

The physical basis for numerical fluid simulations in laser fusion

We investigate the lower bound of concurrence for multipartite quantum mixed states. Analytical lower bounds are derived for some multipartite systems, by establishing functional relations between concurrence and the generalized partial transpositions.

/pdf/estimation-of-concurrence-for-multipartite-mixed-states-22lemwmfio.pdf

Estimation of concurrence for multipartite mixed states

I review some theories of the interaction ofN Rydberg atoms interacting collectively with radiation in microwave cavities. The radiation may be incoherent (black body) radiation or it may be coherent. In the former case theories of the steady state inversion and of the superradiance from initially inverted atoms in low-Q cavities agree well with experimental observations. In the latter case in low-Q cavities ‘phase transitions’ of both first and second order types are predicted and should be observable by monitoring the output of an atomic beam by an atomic ionisation detector. The first order transition which occurs at opposite detunings of the cavity and atoms from the frequency of the coherent driving field is of “optically” bistable type but hysteresis is suppressed by quantum fluctuations which can be large in the cavity field close to the transition. I also review a theory of the spectra from single atoms in cavities ofarbitrary Q containing a few microwave photons. A transition from a single peaked Lorentzian spectrum at low-Q to a double-peaked spectrum forQ≃106 is predicted and peaks representing one or more photon transitions of the Jaynes-Cummings model are also expected to be observable at these or largerQ values. The collective theories are all based onN atom Dicke type models driven by the coherent or incoherent field. Substantial squeezing of the fluorescent radiation field from these Dicke models is also predicted and may be observable with Rydberg atoms.

Photon, quantum and collective, effects from rydberg atoms in cavities

We present results for the solution of the large polaron Fr\"ohlich Hamiltonian in 3 dimensions (3D) and 2 dimensions (2D) obtained via the diagrammatic Monte Carlo (DMC) method. Our implementation is based on the approach by Mishchenko [A. S. Mishchenko et al., Phys. Rev. B 62, 6317 (2000)]. Polaron ground state energies and effective polaron masses are successfully benchmarked with data obtained using Feynman's path integral formalism. By comparing 3D and 2D data, we verify the analytically exact scaling relations for energies and effective masses from $3\mathrm{D}\ensuremath{\rightarrow}2\mathrm{D}$, which provides a stringent test for the quality of DMC predictions. The accuracy of our results is further proven by providing values for the exactly known coefficients in weak- and strong-coupling expansions. Moreover, we compute polaron dispersion curves which are validated with analytically known lower and upper limits in the small-coupling regime and verify the first-order expansion results for larger couplings, thus disproving previous critiques on the apparent incompatibility of DMC with analytical results and furnishing useful reference for a wide range of coupling strengths.

Diagrammatic Monte Carlo study of Fröhlich polaron dispersion in two and three dimensions

The author shows that the propagator of a charged particle in a constant external magnetic field and with a quadratic potential is related to the propagator of a one-dimensional time-dependent forced harmonic oscillator with generalised memory. For special cases, the author evaluates the propagator exactly with the help of a gaussian integral. Results are in agreement with well known results for simple cases.

https://iopscience.iop.org/article/10.1088/0305-4470/17/4/022/pdf

On the propagator of a charged particle in a constant magnetic field and with a quadratic potential

Adequacy of various definitions of polaron effective mass ${m}^{\mathrm{*}}$ is examined. The expression for ${m}^{\mathrm{*}}$ obtained by using the zero-temperature kernel is compared with the zero-temperature limit of the temperature-dependent effective mass obtained by employing the finite-temperature kernel. We find that consistent results are obtained when Saitoh's definition is employed. Our calculations are illustrated for a simple case of weak electron-phonon interaction.

Polaron effective mass.

Path integration of a quadratic action with a generalized memory

Exact propagator for a quadratic lagrangian

https://ris.utwente.nl/ws/files/6435716/Khandekar88on.pdf

On a path integral with a topological constraint

A system of N identical two-level atoms occupying the same site (the Dicke model) interacting with one another and driven by a coherent field is considered. From the known exact steady-state atomic density operator, expressions for the atomic observables, their fluctuations and correlation functions are constructed. Asymptotic analysis is used to obtain the behaviour of these atomic variables with respect to the parameters of the driving field in the thermodynamic limit N → ∞. It is shown that the interplay between the parameters of the interatomic interactions and the driving field leads to a critical behaviour as N → ∞. The conditions under which the atomic system shows either a first order or a second order phase transition with respect to the field variables are discussed.

D.C. Khandekar

Papers

Polaron effective mass.

Path integration of a quadratic action with a generalized memory

Exact propagator for a quadratic lagrangian

On a path integral with a topological constraint

Exact analysis of the critical behaviour in the driven Dicke model of interacting atoms