Quantum kinetic equation for nonequilibrium dense systems

Using the density matrix method in the form developed by Zubarev, equations of motion for nonequilibrium quantum systems with continuous short range interactions are derived which describe kinetic and hydrodynamic processes in a consistent way. The T-matrix as well as the two-particle density matrix determining the nonequilibrium collision integral are obtained in the ladder approximation including the Hartree-Fock corrections and the Pauli blocking for intermediate states. It is shown that in this approximation the total energy is conserved. The developed approach to the kinetic theory of dense quantum systems is able to reproduce the virial corrections consistent with the generalized Beth-Uhlenbeck approximation in equilibrium. The contribution of many-particle correlations to the drift term in the quantum kinetic equation for dense systems is discussed.     

Effects of mean-field and pairing correlations on the Bogoliubov quasiparticle resonance

The quasiparticle resonances are investigated by examining three kinds of quasiparticle spectra, i.e., the density of quasiparticle states, the occupation number density, and the pair number density in the continuum Skyrme Hartree-Fock-Bogoliubov theory with the Green's function method. Taking the weakly bound nucleus ~(66)Ca as an example, the quasiparticle resonant energies and widths extracted from these three kinds of quasiparticle spectra are compared. For the narrow resonances, the extracted resonant energy and the width are consistent with each other. However, it is difficult to use the density of quasiparticle states to identify the broad resonances due to the background of nonresonant continuum. By switching off the pairing potential and/or the Hartree-Fock(HF) potential respectively in the calculation of these quasiparticle spectra, the roles of HF mean-field and pairing correlations in the quasiparticle resonances are demonstrated clearly. It turns out that all the quasiparticle resonances corresponding to the deeply bound, weakly bound and positive-energy single-particle resonant states, are mainly contributed by the HF potential. The pairing potential helps to slightly increase the resonant energy and the width. However, the pairing potential is important to make the nucleons occupy the low-lying nonresonant continuum states near the threshold and take part in the pairing correlations here,especially for the partial waves with small angular momentum ?.     

Functional Integral Approach to a Many Fermion System with Bound States

The equation of state for a dense system of interacting Fermions is derived using functional integral technique. To investigate the formation of bound states, a Hubbard-Stratonovich transformation is applied which expresses the action as functional of pair fields. The evaluation of the partition function in lowest orders with respect to the pair fields leads to a result which can be interpreted as the contribution of two-particle states, accounting for density corrections as Pauli blocking and self-energy shift. Comparison is performed with results for the equation of state of hot dense matter (plasmas, nuclear matter) obtained within a Green's function approach.     

Bound States in Coulomb Systems ‐ Old Problems and New Solutions

We analyze the quantum statistical treatment of bound states in Hydrogen considered as a system of electrons and protons. Within this physical picture we calculate analytically isotherms of pressure for Hydrogen in a broad density region and compare to some results from the chemical picture. Our study is restricted to the range of intermediate temperatures 10⁴K < T < 10⁵K and not too high densities n < 10²⁴ protons per cm³, the formation of molecules is neglected. First we resume in detail the two transitions along isotherms: (i) formation of bound states occurring by increasing the density from low to moderate values, (ii) the destruction of bound states in the high density region, modelled here by Pauli‐Fock effects. Avoiding chemical models we will show, why bound states according to a discrete part of the spectra occur only in a valley in the T‐p plane. First we study virial expansions in the canonical ensemble and then in the grand canonical ensemble. We show that in fugacity representations the population of bound states saturates at higher density and that a combination of both representations provides quickly converging equations of state. In the case of degenerate systems we calculated first the density‐dependent energy levels, and find the pressure in Hartree‐Fock‐Wigner approximation showing the prominent role of Pauli blocking and Fock effects in the selfenergy (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Bound and continuum states of a vortex line in a pure type-II superconductor

The Bogoliubov equations for the quasi-particle excitations of an isolated vortex line in a pure type-II superconductor are solved by means of a method due to Bardeenet al. The low lying energy levels of the bound states are found to have the form of Landau levels where the effective field is determined by the pair potential and the magnetic field in the core region of the vortex. From the solutions of the continuum states of high energy simple expressions for the phase shifts are derived. The contributions of the continuum states to the pair potential and the current density are calculated. The pair potential is shown to tend to the BCS gap parameter, and thus to be serf-consistent, at large distances from the vortex axis.     

Saha Equation,Single and Two Particle States

Single and two particle properties in a dense plasma are discussed in connection with their role in the mass action law for a partially ionized plasma. The two particle bound states are nearly density independent, while the continuum is essentially shifted. The single particle states are damped, and their energy has a negative shift and a parabolic behaviour for small momenta.     

The single-particle interaction in nuclear matter via the relativistic Dirac-Brueckner approach

Within the relativistic Dirac-Brueckner approach and starting from a one-boson-exchange interaction, the nucleon selfenergy is calculated above the nuclear-matter Fermi sea. The effects of Pauli blocking and energy dispersion are studied. At low energy we see a dominance of the Pauli blocking whereas at nucleon energies up to 250 MeV the dispersive effect still has a very large influence on the single-particle interaction. From the selfenergy a Schrödinger optical potential is deduced, for which the DB results nicely agree with empirical values. The density dependence of this optical potential compares well with earlier calculations.     

Three- and Four-Body Correlations in Nuclear Matter

 Few-nucleon correlations in nuclear matter at finite densities and temperatures are explored. Using the Dyson-equation approach leads to effective few-body equations that include self-energy corrections and Pauli blocking factors in a systematic way. Examples given are the nucleon-deuteron in-medium reaction rates, few-body bound states including the α-particle, and α-particle condensation. Received October 17, 2001; accepted for publication November 12, 2001     

在热密物质中的J/Ψ分解

用误差函数形式的禁闭位加上库仑形式的单胶子位研究了（ｃｃ）和（ｂｂ）质量谱，并用热场动力学近似研究了在有限温度和有限密度下的Ｄｅｂｙｅ屏蔽质量，得到在热密物质中Ｊ／Ψ分解的临界温度和临界能量密度．     

J/ψ Dissociation in Hot and Dense Matter

The energy spectra of heavy quark bound states are analyzed using the error-function-type potential and the one-gluon-exchange Coulomb-type force. The Debye screening mass at finite temperature and density is studied in the thermofield dynamics approach. The critical temperature and cridcal energy density for J/ψ dissociation in hot and dense matter are obtained.     

Metastable States in Parametrically Excited Multimode Hamiltonian Systems

 Consider a linear autonomous Hamiltonian system with m time periodic bound state solutions. In this paper we study their dynamics under time almost periodic perturbations which are small, localized and Hamiltonian. The analysis proceeds through a reduction of the original infinite dimensional dynamical system to the dynamics of two coupled subsystems: a dominant m-dimensional system of ordinary differential equations (normal form), governing the projections onto the bound states and an infinite dimensional dispersive wave equation. The present work generalizes previous work of the authors, where the case of a single bound state is considered. Here, the interaction picture is considerably more complicated and requires deeper analysis, due to a multiplicity of bound states and the very general nature of the perturbation's time dependence. Parametric forcing induces coupling of bound states to continuum radiation modes, of bound states directly to bound states, as well as coupling among bound states, which is mediated by continuum modes. Our analysis elucidates these interactions and we prove the metastability (long life time) and eventual decay of bound states for a large class of systems. The key hypotheses for the analysis are: appropriate local energy decay estimates for the unperturbed evolution operator, restricted to the continuous spectral part of the Hamiltonian, and a matrix Fermi Golden rule condition, which ensures coupling of bound states to continuum modes. Problems of the type considered arise in many areas of application including ionization physics, quantum molecular theory and the propagation of light in optical fibers in the presence of defects. Received: 13 March 2002 / Accepted: 2 January 2003 Published online: 14 April 2003 Communicated by J.L. Lebowitz     

Pressure ionization in laser-fusion target simulation

Accurate simulation of high density target implosion requires material properties (ionization, pressure, energy, opacity and transport coefficients) at densities where bound electrons are significantly perturbed by neighboring atoms. In modern laser-fusion simulation codes, this data is supplied by tables and/or calculated from a Stromgren model for ionization equilibrium. Improvements have been made in the Stromgren average-atom model which aim at assuring thermodynamic consistency and obtaining better agreement with more elaborate calculations. Arbitrary degeneracy is allowed for the free electrons. Consistent Coulomb contributions to pressure and continuum lowering are obtained. A new pressure ionization scheme merges bound electrons into the continuum as a smooth function of density and the corresponding contribution to pressure is calculated. Results are shown for aluminum.     

Study of theS-matrix near bound states in the continuum

The behaviour ofS-matrix for potentials generating bound states in continuum in the neighbourhood of the positive bound state energies is studied. It is shown that unlike the case of usual negative energy bound states, theS-matrix does not have a pole at the positive bound state energy but becomes unity at the energy corresponding to bound states in continuum. Calculations ofS-waveS-matrix for a local potential constructed by Stillinger and Herrick and a separable nonlocal potential constructed by the present authors verify these results. Our results indicate that the bound states embedded in continuum constructedvia the von Neumann and Wigner procedure cannot be interpreted as resonances with zero width.     

Nature and properties of a repulsive Fermi gas in the upper branch of the energy spectrum

We generalize the Noziéres-Schmitt-Rink method to study the repulsive Fermi gas in the absence of molecule formation, i.e., in the so-called "upper branch." We find that the system remains stable except close to resonance at sufficiently low temperatures. With increasing scattering length, the energy density of the system attains a maximum at a positive scattering length before resonance. This is shown to arise from Pauli blocking which causes the bound states of fermion pairs of different momenta to disappear at different scattering lengths. At the point of maximum energy, the compressibility of the system is substantially reduced, leading to a sizable uniform density core in a trapped gas. The change in spin susceptibility with increasing scattering length is moderate and does not indicate any magnetic instability. These features should also manifest in Fermi gases with unequal masses and/or spin populations.     

Radiation Emission of Fast Electrons in Collisions with “Ion‐Sphere” in Dense Plasmas

Radiative emission of fast electrons in collision with an “ion‐sphere” electron distribution in dense plasmas is under consideration. The electron structure of the ion sphere is calculated ab initio using self‐consistent solution of both bound and free electron distribution inside the sphere. Two radiation channels are included: emission of the colliding electron itself in static potential (conventional or static Bremsstrahlung) and the emission of “ion sphere” medium due to its polarization by the colliding electron (polarization Bremsstrahlung). The last one is calculated in the frame of local plasma density approximation. Interference between conventional and polarization Bremsstrahlung is taken into account. It is shown that spectral cross section of the process has characteristic features depending on plasma density and ionization stage of plasma ions. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Some aspects of redundant states in nucleon-nucleus scattering solutions with antisymmetrization

Redundant states are known to appear as solutions to the scattering equation when an incident particle is antisymmetrized with respect to a target nucleus represented by a Slater determinant. Using criteria which have been found to characterize a potential which produces a continuum bound state (CBS), we demonstrate that a redundant solution can be identified as a CBS which appears at every positive energy. This identification provides a procedure for isolating and removing that portion of the potential responsible for redundant states. The remaining portion of the potential generates solutions to the original scattering equation which we demonstrate to be orthogonal to the redundant states which have been eliminated.     

Nonautonomous Hamiltonians

We present a theory of resonances for a class of nonautonomous Hamiltonians to treat the structural instability of spatially localized and time-periodic solutions associated with an unperturbed autonomous Hamiltonian. The mechanism of instability is radiative decay, due to resonant coupling of the discrete modes to the continuum modes by the time-dependent perturbation. This results in a slow transfer of energy from the discrete modes to the continuum. The rate of decay of solutions is slow and hence the decaying bound states can be viewed as metastable. The ideas are closely related to the authors' work on (i) a time-dependent approach to the instability of eigenvalues embedded in the continuous spectra, and (ii) resonances, radiation damping, and instability in Hamiltonian nonlinear wave equations. The theory is applied to a general class of Schrödinger equations. The phenomenon of ionization may be viewed as a resonance problem of the type we consider and we apply our theory to find the rate of ionization, spectral line shift, and local decay estimates for such Hamiltonians.     

Particle-hole state densities for statistical multi-step compound reactions

An analytical relation is derived for the density of particle-hole bound states applying the equidistant-spacing approximation and the Darwin-Fowler statistical method. The Pauli exclusion principle as well as the finite depth of the potential well are taken into account. The set of densities needed for calculations of multi-step compound reactions is completed by deriving the densities of accessible final states for escape and damping.     

Dimers, Effective Interactions, and Pauli Blocking Effects in a Bilayer of Cold Fermionic Polar Molecules

We consider a bilayer setup with two parallel planes of cold fermionic polar molecules when the dipole moments are oriented perpendicular to the planes. The binding energy of two-body states with one polar molecule in each layer is determined and compared to various analytic approximation schemes in both coordinate- and momentum-space. The effective interaction of two bound dimers is obtained by integrating out the internal dimer bound state wave function and its robustness under analytical approximations is studied. Furthermore, we consider the effect of the background of other fermions on the dimer state through Pauli blocking, and discuss implications for the zero-temperature many-body phase diagram of this experimentally realizable system.