Publications L.G. Suttorp since 1991
(Publications before 1991 are found here )

  • Continued-fraction representation of the Kraus map for non-Markovian reservoir damping,
    A.J. van Wonderen and LGS, Journal of Physics A 51(2018)175304:1-24
    Abstract: Quantum dissipation is studied for a discrete system that linearly interacts with a reservoir of harmonic oscillators at thermal equilibrium. Initial correlations between system and reservoir are assumed to be absent. The dissipative dynamics as determined by the unitary evolution of system and reservoir is described by a Kraus map consisting of an infinite number of matrices. For all Laplace-transformed Kraus matrices exact solutions are constructed in terms of continued fractions that depend on the pair correlation functions of the reservoir. By performing factorizations in the Kraus map a perturbation theory is set up that conserves in arbitrary perturbative order both positivity and probability of the density matrix. The latter is determined by an integral equation for a bitemporal matrix and a finite hierarchy for Kraus matrices. In the lowest perturbative order this hierarchy reduces to one equation for one Kraus matrix. Its solution is given by a continued fraction of a much simpler structure as compared to the non-perturbative case. In the lowest perturbative order our non-Markovian evolution equations are applied to the damped Jaynes-Cummings model. From the solution for the atomic density matrix it is found that the atom may remain in the state of maximum entropy for a significant time span that depends on the initial energy of the radiation field.
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  • Hierarchies of sum rules for squares of spherical Bessel functions,
    LGS and A.J. van Wonderen, Integral Transforms and Special Functions 28 (2017) 156-165
    Abstract: A four-term recurrence relation for squared spherical Bessel functions is shown to yield closed-form expressions for several types of finite weighted sums of these functions. The resulting sum rules, which may contain an arbitrarily large number of terms, are found to constitute three independent hierarchies. Their use leads to an efficient numerical evaluation of these sums.
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  • Modified atomic decay rate near absorptive scatterers at finite temperature,
    LGS and A.J. van Wonderen, Physical Review A 92 (2015) 013843:1-16
    Abstract: The change in the decay rate of an excited atom that is brought about by extinction and thermal-radiation effects in a nearby dielectric medium is determined from a quantummechanical model. The medium is a collection of randomly distributed thermally-excited spherical scatterers with absorptive properties. The modification of the decay rate is described by a set of correction functions for which analytical expressions are obtained as sums over contributions from the multipole moments of the scatterers. The results for the modified decay rate as a function of the distance between the excited atom and the dielectric medium show the influence of absorption, scattering and thermal-radiation processes. Some of these processes are found to be mutually counteractive. The changes in the decay rate are compared to those following from an effective-medium theory in which the discrete scatterers are replaced by a continuum.
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  • Kraus map for non-Markovian quantum dynamics driven by a thermal reservoir,
    A.J. van Wonderen and LGS, Europhysics Letters 102 (2013) 60001:1-6
    Abstract: Starting from unitary dynamics we study the evolution in time of a non-relativistic quantum system that exchanges energy with a thermal reservoir of harmonic oscillators. System and reservoir are assumed to be initially decorrelated. Reservoir correlation functions are factorized by means of a Kraus compliant version of Wick's theorem. As a result, the non-Markovian Kraus map for the system density operator can be completely expressed in terms of system potentials and reservoir pair correlation functions. An infinite hierarchy for the evolution operators of the Kraus map is derived. The system density operator is obtained as a time-ordered exponential containing a non-Markovian counterpart of the standard Markovian generator for dissipative dynamics. We specify a condition on this non-Markovian generator for return to thermal equilibrium. We set up a non-Markovian perturbation theory that preserves both trace and positivity of the system density operator.
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  • Quantized media with absorptive scatterers and modified atomic emission rates,
    LGS and A.J. van Wonderen, Optics Communications 284 (2011) 2943-2948
    Abstract: Modifications in the spontaneous emission rate of an excited atom that are caused by extinction effects in a nearby dielectric medium are analyzed in a quantummechanical model, in which the medium consists of spherical scatterers with absorptive properties. Use of the dyadic Green function of the electromagnetic field near a dielectric sphere leads to an expression for the change in the emission rate as a series of multipole contributions for which analytical formules are obtained. The results for the modified emission rate as a function of the distance between the excited atom and the dielectric medium show the influence of both absorption and scattering processes.
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  • Atomic decay near a quantized medium of absorbing scatterers,
    LGS and A.J. van Wonderen, Journal of Physics B 43 (2010) 105501:1-12
    Abstract: The decay of an excited atom in the presence of a medium that both scatters and absorbs radiation is studied with the help of a quantum-electrodynamical model. The medium is represented by a half-space filled with a randomly distributed set of non-overlapping spheres, which consist of a linear absorptive dielectric material. The absorption effects are described by means of a quantized damped-polariton theory. It is found that the effective susceptibility of the bulk does not fully account for the medium-induced change in the atomic decay rate. In fact, surface effects contribute to the modification of the decay properties as well. The interplay of scattering and absorption in the total decay rate is discussed.
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  • Sum rules for correlation functions of ionic mixtures in arbitrary dimension $d \geq 2$,
    LGS, Journal of Physics A 41 (2008) 495001:1-18
    Abstract: The correlations in classical multi-component ionic mixtures with spatial dimension $d\geq 2$ are studied by using a restricted grand-canonical ensemble and the associated hierarchy equations for the correlation functions. Sum rules for the first few moments of the two-particle correlation function are derived and their dependence on $d$ is established. By varying $d$ continuously near $d=2$ it is shown how the sum rules for the two-dimensional mixture are related to those for mixtures at higher $d$.
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  • Field quantization in inhomogeneous anisotropic dielectrics with spatio-temporal dispersion,
    LGS, Journal of Physics A 40 (2007) 3697-3719
    Abstract: A quantum damped-polariton model is constructed for an inhomogeneous anisotropic linear dielectric with arbitrary dispersion in space and time. The model Hamiltonian is completely diagonalized by determining the creation and annihilation operators for the fundamental polariton modes as specific linear combinations of the basic dynamical variables. Explicit expressions are derived for the time-dependent operators describing the electromagnetic field, the dielectric polarization and the noise term in the latter. It is shown how to identify bath variables that generate the dissipative dynamics of the medium.
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  • Damping and dispersion of oscillating modes of a multicomponent ionic mixture in a magnetic field,
    G.A.Q. Salvati and LGS, Physica A 371 (2006) 387-408
    Abstract: The collective-mode spectrum of a multicomponent magnetized ionic mixture for small wave number $k$ is studied with the use of magnetohydrodynamics and formal kinetic theory. Apart from the usual thermal and diffusive modes, the spectrum contains a set of four oscillating modes. By evaluating the $k^2$ contributions to the eigenfrequencies, the damping and the dispersion of these oscillating modes are determined. The long-range nature of the Coulomb interactions is shown to imply that Burnett terms with higher-order gradients in the linear phenomenological laws have to be taken into account in order to obtain a full description of all damping and dispersion effects.
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  • Multiple-scattering approach to interatomic interactions and superradiance in inhomogeneous dielectrics,
    M. Wubs, LGS and A. Lagendijk, Physical Review A 70 (2004) 053823/1-17
    Abstract: The dynamics of a collection of resonant atoms embedded inside an inhomogeneous nondispersive and lossless dielectric is described with a dipole Hamiltonian that is based on a canonical quantization theory. The dielectric is described macroscopically by a position-dependent dielectric function and the atoms as microscopic harmonic oscillators. We identify and discuss the role of several types of Green tensors that describe the spatio-temporal propagation of field operators. After integrating out the atomic degrees of freedom, a multiple-scattering formalism emerges in which an exact Lippmann-Schwinger equation for the electric field operator plays a central role. The equation describes atoms as point sources and point scatterers for light. First, single-atom properties are calculated such as position-dependent spontaneous-emission rates as well as differential cross sections for elastic scattering and for resonance fluorescence. Secondly, multi-atom processes are studied. It is shown that the medium modifies both the resonant and the static parts of the dipole-dipole interactions. These interatomic interactions may cause the atoms to scatter and emit light cooperatively. Unlike in free space, differences in position-dependent emission rates and radiative line shifts influence cooperative decay in the dielectric. As a generic example, it is shown that near a partially reflecting plane there is a sharp transition from two-atom superradiance to single-atom emission as the atomic positions are varied.
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  • The oscillator model for dissipative QED in an inhomogeneous dielectric,
    A.J. van Wonderen and LGS, Journal of Physics A 37 (2004) 11101-11122
    Abstract: The Ullersma model for the damped harmonic oscillator is coupled to the quantised electromagnetic field. All material parameters and interaction strengths are allowed to depend on position. The ensuing Hamiltonian is expressed in terms of canonical fields, and diagonalised by performing a normal-mode expansion. The commutation relations of the diagonalising operators are in agreement with the canonical commutation relations. For the proof we replace all sums of normal modes by complex integrals with the help of the residue theorem. The same technique helps us to explicitly calculate the quantum evolution of all canonical and electromagnetic fields. We identify the dielectric constant and the Green function of the wave equation for the electric field. Both functions are meromorphic in the complex frequency plane. The solution of the extended Ullersma model is in keeping with well-known phenomenological rules for setting up quantum electrodynamics in an absorptive and spatially inhomogeneous dielectric. To establish this fundamental justification, we subject the reservoir of independent harmonic oscillators to a continuum limit. The resonant frequencies of the reservoir are smeared out over the real axis. Consequently, the poles of both the dielectric constant and the Green function unite to form a branch cut. Performing an analytic continuation beyond this branch cut, we find that the long-time behaviour of the quantised electric field is completely determined by the sources of the reservoir. Through a Riemann-Lebesgue argument we demonstrate that the field itself tends to zero, whereas its quantum fluctuations stay alive. We argue that the last feature may have important consequences for application of entanglement and related processes in quantum devices.
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  • Fano diagonalization of a polariton model for an inhomogeneous absorptive dielectric,
    LGS and A.J. van Wonderen, Europhysics Letters 67 (2004) 766-772
    Abstract: The Hamiltonian of a polariton model for an inhomogeneous linear absorptive dielectric is diagonalized by means of Fano's diagonalization method. The creation and annihilation operators for the independent normal modes are explicitly found as linear combinations of the canonical operators. The coefficients in these combinations depend on the tensorial Green function that governs the propagation of electromagnetic waves through the dielectric. The time-dependent electromagnetic fields in the Heisenberg picture are given in terms of the diagonalizing operators. These results justify the phenomenological quantization of the electromagnetic field in an absorptive dielectric.
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  • Field quantization in inhomogeneous absorptive dielectrics,
    LGS and M. Wubs, Physical Review A 70 (2004) 013816/1-18
    Abstract: The quantization of the electromagnetic field in a three-dimensional inhomogeneous dielectric medium with losses is carried out in the framework of a damped-polariton model with an arbitrary spatial dependence of its parameters. The equations of motion for the canonical variables are solved explicitly by means of Laplace transformations for both positive and negative time. The dielectric susceptibility and the quantum noise-current density are identified in terms of the dynamical variables and parameters of the model. The operators that diagonalize the Hamiltonian are found as linear combinations of the canonical variables, with coefficients depending on the electric susceptibility and the dielectric Green function. The complete time dependence of the electromagnetic field and of the dielectric polarization is determined. Our results provide a microscopic justification of the phenomenological quantization scheme for the electromagnetic field in inhomogeneous dielectrics.
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  • Spontaneous-emission rates in finite photonic crystals of plane scatterers,
    M. Wubs, LGS and A. Lagendijk, Physical Review E 69 (2004) 016616/1-17
    Abstract: The concept of a plane scatterer that was developed earlier for scalar waves is generalized so that polarization of light is included. Starting from a Lippmann-Schwinger formalism for vector waves, we show that the Green function has to be regularized before T matrices can be defined in a consistent way. After the regularization, optical modes and Green functions are determined exactly for finite structures built up of an arbitrary number of parallel planes, at arbitrary positions, and where each plane can have different optical properties. The model is applied to the special case of finite crystals consisting of regularly spaced identical planes, where analytical methods can be taken further and only light numerical tasks remain. The formalism is used to calculate position- and orientation-dependent spontaneous-emission rates inside and near the finite photonic crystals. The results show that emission rates and reflection properties can differ strongly for scalar and for vector waves. The finite size of the crystal influences the emission rates. For parallel dipoles close to a plane, emission into guided modes gives rise to a peak in the frequency-dependent emission rate.
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  • Multipole interaction between atoms and their photonic environment,
    M. Wubs, LGS and A. Lagendijk, Physical Review A 68 (2003) 013822/1-16
    Abstract: Macroscopic field quantization is presented for a nondispersive photonic dielectric environment, both in the absence and presence of guest atoms. Starting with a minimal-coupling Lagrangian, a careful look at functional derivatives shows how to obtain Maxwell's equations before and after choosing a suitable gauge. A Hamiltonian is derived with a multipolar interaction between the guest atoms and the electromagnetic field. Canonical variables and fields are determined and in particular, the field canonically conjugate to the vector potential is identified by functional differentiation as minus the full displacement field. An important result is that inside the dielectric a dipole couples to a field that is neither the (transverse) electric nor the macroscopic displacement field. The dielectric function is different from the bulk dielectric function at the position of the dipole, so that local-field effects must be taken into account.
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  • Time correlations in a confined magnetized free-electron gas,
    LGS, Journal of Physics A 36 (2003) 8223-8247
    Abstract: The time-dependent pair correlation functions for a degenerate ideal quantum gas of charged particles in a uniform magnetic field are studied on the basis of equilibrium statistics. In particular, the influence of a flat hard wall on the correlations is investigated, both for a perpendicular and a parallel orientation of the wall with respect to the field. The coherent and incoherent parts of the time-dependent structure function in position space are determined from an expansion in terms of the eigenfunctions of the one-particle Hamiltonian. For the bulk of the system, the intermediate scattering function and the dynamical structure factor are derived by taking successive Fourier transforms. In the vicinity of the wall the time-dependent coherent structure function is found to decay faster than in the bulk. For coinciding positions near the wall the form of the structure function turns out to be independent of the orientation of the wall. Numerical results are shown to corroborate these findings.
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  • Correlations in a confined magnetized free-electron gas,
    M.M. Kettenis and LGS, Journal of Physics A 34 (2001) 7991-8013.
    Abstract: Equilibrium quantum statistical methods are used to study the pair correlation function for a magnetized free-electron gas in the presence of a hard wall that is parallel to the field. With the help of a path-integral technique and a Green function representation, the modifications in the correlation function caused by the wall are determined both for a non-degenerate and for a completely degenerate gas. In the latter case the asymptotic behaviour of the correlation function for large position differences in the direction parallel to the wall and perpendicular to the field, is found to change from Gaussian in the bulk to algebraic near the wall.
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  • Magnetohydrodynamics for a multicomponent ionic mixture,
    G.A.Q. Salvati and LGS, Physica A 299 (2001) 378-404.
    Abstract: The magnetohydrodynamical equations for a multi-component magnetized ionic mixture are used to derive the spectrum of collective modes for small wave numbers. The results are compared with those from formal kinetic theory , which is based on the microscopic balance equations and a projection-operator formalism. The comparison leads to a set of Green-Kubo-type expressions for the phenomenological coefficients occurring in the magnetohydrodynamical treatment.
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  • Transient QED effects in absorbing dielectrics,
    M. Wubs and LGS, Physical Review A 63 (2001) 043809/1-14.
    Abstract: The spontaneous-emission rate of a radiating atom reaches its time-independent equilibrium value after an initial transient regime. In this paper, we consider the associated relaxation effects of the spontaneous-decay rate of atoms in dispersive and absorbing dielectric media for atomic-transition frequencies near material resonances. A quantum mechanical description of such media is furnished by a damped-polariton model in which absorption is taken into account through coupling to a bath. We show how all field and matter operators in this theory can be expressed in terms of the bath operators at an initial time. The consistency of these solutions for the field and matter operators are found to depend on the validity of certain velocity sum rules. The transient effects in the spontaneous-decay rate are studied with the help of several specific models for the dielectric constant, which are shown to follow from the general theory by adopting particular forms of the bath coupling constant.
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  • Path-decomposition and edge effects in a magnetized electron gas,
    LGS, J. de Physique IV Proc. 10 (2000) 461-464.
    Abstract: The influence of boundaries on the properties of a magnetized free-electron gas is discussed with the help of a path-integral representation for the temperature Green function. By using a suitable decomposition of the paths the profiles of the excess particle density and the current density are analysed. The asymptotic behaviour of these profiles towards the bulk is found to depend sensitively on the degree of degeneracy.
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  • Path-decomposition expansion and edge effects in a confined magnetized free-electron gas,
    M.M. Kettenis and LGS, Journal of Physics A 32 (1999) 8209-8223.
    Abstract: Path-integral methods can be used to derive a `path-decomposition expansion' for the temperature Green function of a magnetized free-electron gas confined by a hard wall. With the help of this expansion the asymptotic behaviour of the profiles for the excess particle density and the electric current density far from the edge is determined for arbitrary values of the magnetic field strength. The asymptotics are found to depend sensitively on the degree of degeneracy. For a non-degenerate electron gas the asymptotic profiles are essentially Gaussian (albeit modulated by a Bessel function), on a length scale that is a function of the magnetic field strength and the temperature. For a completely degenerate electron gas the asymptotic behaviour is again proportional to a Gaussian, with a scale that is the magnetic length in this case. The prefactors are polynomial and logarithmic functions of the distance from the wall, which depend on the number of filled Landau levels n. As a consequence, the Gaussian asymptotic decay sets in at distances that are large compared with the magnetic length multiplied by square root n.
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  • Statistics of quantum-electrodynamical plasmas in external magnetic fields,
    LGS, in: Strongly Coupled Coulomb Systems , eds. G.J. Kalman e.a., (Plenum Press, 1998) 705-708.
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  • Generalized master equation for systems in nonideal cavities with squeezed baths,
    R.W.F. van der Plank and LGS, European Physical Journal D 3 (1998) 183-193.
    Abstract: The master equation for the density operator of a system in a lossy cavity, which is coupled to a squeezed bath, is generalized so as to include the effects of an enhanced loss through a mirror of finite transmittivity. As compared to the standard master equation, which is valid for a nearly-perfect cavity, the generalized master equation is found to contain additional terms that account for an effective squeezed-light mixing at the nonideal mirror and for the interplay of the photon loss and the interaction within the cavity. As an example, the new master equation is used to study the influence of the enhanced losses on the photon statistics of a localized degenerate parametric oscillator. It is found that considerable changes in the photon distribution can occur as soon as the quality of the mirror becomes less than perfect.
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  • Charge and current density profiles of a degenerate magnetized free-electron gas near a hard wall,
    M.M. Kettenis and LGS, Journal of Physics A 31 (1998) 6547-6560.
    Abstract: The charge and current densities of a completely degenerate free-electron gas in a uniform magnetic field are found to have a damped oscillatory spatial dependence near a wall that is parallel to the magnetic field. For large distances from the wall the behaviour of the associated profile functions are analysed by means of systematic asymptotic expansions. Both densities are shown to decay to their bulk values through a Gaussian tail, with prefactors that depend algebraically and logarithmically on the distance from the wall.
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  • Spontaneous emission from an atom in a nonideal cavity: application of a generalized master equation,
    R.W.F. van der Plank and LGS, Physical Review A 54 (1996) 2464-2473.
    Abstract: The decay of an excited two-level atom in a cavity with mirrors of finite transmittivity is studied with the help of a generalized multimode master equation that has been established recently. The time evolution of the decaying atom is obtained by accounting for the interaction with infinitely many quasimodes. The analytical and numerical results are compared with those of the standard multimode master equation and of a universe-mode approach.
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  • Edge effects in magnetoplasmas,
    LGS, in: Strongly Coupled Plasma Physics, World Scientific (1996) 381-386.
    Abstract: Edge effects in magnetized charged-particle systems are discussed with the help of a multiple-reflection expansion for the Green function. The profiles of the density and the electric current are determined both for the non-degenerate and the highly degenerate case. The asymptotic form of the profiles near the bulk is found to be exponentially decaying in both cases.
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  • Generalization of damping theory for cavities with mirrors of finite transmittivity,
    R.W.F. van der Plank and LGS, Physical Review A 53 (1996) 1791-1800.
    Abstract: Standard damping theory is generalized to incorporate the effects of finite mirror transmittivity. The correction to the standard Langevin equation for the quasimode annihilation operator is determined in first order in the transmittivity of the mirrors. From the Langevin equation an effective master equation is derived. As an example, we study the decay of a single two-level atom at a fixed position in a nonideal cavity. For this case we find a modification of the damped Rabi oscillations, which depends on the atomic position.
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  • Boundary effects in a magnetized free-electron gas: Green function approach,
    P. John and LGS, Journal of Physics A 28 (1995) 6087-6097.
    Abstract: A Green function approach to the boundary effects of a free-electron gas in a magnetic field is presented. It is shown that truncation of the multiple-reflection expansion for the Green function of a confined system is not justified if a magnetic field is present, even for a system with flat boundaries. Using the full expansion we calculate the profiles for the particle density, the current density and the components of the pressure tensor near the boundary.
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  • Output photon statistics for a beam splitter with input squeezed light,
    R.W.F. van der Plank and LGS, Optics Communications 112 (1994) 145-150.
    Abstract: The mixing of (quadrature-) squeezed states by a lossless beam splitter is studied. Two generating functions describing the outgoing-photon distribution are calculated. With the use of these generating functions the distribution is determined explicitly for some special cases.
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  • Boundary effects in the pressure of a confined magnetized electron gas,
    P. John and LGS, Physica A 210 (1994) 237-256.
    Abstract: The role of boundary effects in the pressure of a magnetized quantum plasma is determined by evaluating the spatial dependence of the mechanical pressure tenser for several simplified model systems, namely for a non-interacting magnetized electron gas in either a slab geometry or in a harmonic confining potential. From the pressure profiles it is shown that the bulk and surface values of the pressure are related in such a way that an earlier result on the difference between the thermodynamic and the mechanical pressure in a magnetized quantum plasma is confirmed.
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  • Pressure and compressibility in a quantum one-component plasma,
    P. John and LGS, Journal of Physics A 27 (1994) 6053-6065.
    Abstract: With the help of scaling methods, a general relation is established between the thermodynamic pressure and the mechanical pressure tensor of an equilibrium one-component plasma in a magnetic field. The mechanical pressure tenser is shown to be anisotropic. A general proof of the compressibility sum rule for a magnetized quantum plasma is presented. Finally, fourth-order wavenumber inequalities for the static charge correlation function are derived.
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  • Fluctuations properties and collective modes of quantum plasmas in a magnetic field,
    LGS, in: Strongly Coupled Plasma Physics, University of Rochester Press (1993) 105-108.
    Abstract: A complete set of equilibrium fluctuation formulas for the charge density, the momentum density and the energy density of a magnetized one-component quantum plasma is presented. The derivation is based on the use of equations of motion for Fourier-transformed imaginary-time Green functions. The resulting formulas depend both on the strength and the orientation of the magnetic field. They are a basic ingredient for the derivation of the collective-mode spectrum in the long-wavelength limit. Projection-operator methods are used to establish explicit expressions for the mode frequencies of a magnetized quantum plasma up to second order in the wave number.
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  • Pressure and compressibility of a quantum plasma in a magnetic field,
    LGS, Contributions in Plasma Physics 33 (1993) 503-512.
    Abstract: The equilibrium pressure tensor that occurs in the momentum balance equation for a quantum plasma in a magnetic field is shown to be anisotropic. Its relation to the pressure that follows from thermodynamics is elucidated. A general proof of the compressibility rule for a magnetized quantum plasma is presented.
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  • Collective modes of the quantum one-component plasma in a magnetic field,
    P. John and LGS, Physica A 197 (1993) 613-628.
    Abstract: The authors derive the collective modes of a quantum one-component plasma in a magnetic field by using a projection operator technique. With the help of these modes the long-time behaviour of the time correlation functions for the charge density, the current density and the energy density is determined in the limit of small wavenumbers.
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  • Equilibrium fluctuations formulas for the quantum one-component plasma in a magnetic field,
    P. John and LGS, Physica A 192 (1993) 280-304.
    Abstract: The authors derive a complete set of equilibrium fluctuation formulae for the charge density, the current density and the energy density of the quantum one-component plasma in a magnetic field. The derivation is based on the use of imaginary-time-dependent Green functions and their Kubo transforms. It is shown how the fluctuation formulae involving Kubo-transformed quantities can be established directly, even in the absence of a detailed knowledge of the full imaginary-time dependence of the Green functions. The resulting fluctuation formulae for the Kubo transforms are found to have a considerably simpler structure than those for the equal-imaginary-time observables.
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  • Second-moment sum rules for correlation functions in a classical ionic mixture,
    LGS, in: Physics of Nonideal Plasmas, eds. W. Ebeling e.a., Teubner (1992) 73-80.
    Abstract: The complete set of second-moment sum rules for the correlation functions of arbitrarily high order describing a classical multi-component ionic mixture in equilibrium is derived from the grand-canonical ensemble. The connection of these sum rules with the large-scale behaviour of fluctuations in an ionic mixture is pointed out.
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  • Asymptotic behavior of correlation functions for electric potential and field fluctuations in a classical one-component plasma,
    LGS, Journal of Statistical Physics 66 (1992) 1343-1357.
    Abstract: The correlations of the electric potential fluctuations in a classical one-component plasma are studied for large distances between the observation points. The two-point correlation function for these fluctuations is known to decay slowly for large distances, even if exponential clustering holds for the charge correlation functions. In this paper the asymptotic behavior of the general k-point electric potential correlation functions is analyzed. Each of these correlation functions can be split into a reducible part, which is given by a sum of products of lower-order correlation functions, and a remaining irreducible part. It is shown, on the basis of an exponential clustering hypothesis for the charge correlation functions, that for all k>or=3D3 the irreducible parts of the electric potential correlation functions decay faster than any inverse power of the distance, if one or more of the observation points move far away from the others. Hence, the two-point electric potential correlation function is the only one with a slow algebraic decay. The same statement holds for the correlation functions of the electric field fluctuations.
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  • Dispersive optical bistability in a nonideal Fabry-Perot cavity II. Numerical results on side-mode instabilities,
    A.J. van Wonderen and LGS, Zeitschrift fur Physik B 83 (1991) 143-151.
    Abstract: For pt.I see ibid., vol.83, p.135 (1991). Instabilities in the nearest side-modes are predicted for dispersive optical bistability in a nonideal Fabry-Perot cavity. The results are based on a linear stability analysis of the Maxwell-Bloch equations. This analysis leads to a boundary value problem for a four-dimensional set of linear differential equations, which the authors have solved numerically. The findings show that the instability spectrum strongly depends on the detuning parameters and on the transmission coefficient of the cavity mirrors. If the atomic detuning gradually increases, instability domains are found to merge. If moreover the cavity detuning grows, instabilities spread along the upper branch of the bistability curve, even for high values of the medium response time. The authors have made a comparison between our results and recent experimental data, the outcome of which is satisfactory from a qualitative point of view. Finally, they show that the side-mode instabilities for dispersive optical bistability in a Fabry-Perot cavity are incorrectly predicted, if a so-called equivalent ring cavity is adopted as a model.
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  • Dispersive optical bistability in a nonideal Fabry-Perot cavity I. Stability analysis of the Maxwell-Bloch equations,
    A.J. van Wonderen and LGS, Zeitschrift fur Physik B 83 (1991) 135-142.
    Abstract: A stability analysis is performed for optical bistability in a Fabry-Perot cavity with mirrors of arbitrary transmission coefficient. The mixed absorptive and dispersive regime is covered. In order to describe the system we use the Maxwell-Bloch equations formulated in terms of slowly varying envelopes. Standing-wave effects are completely taken into account by refraining from a truncation of the harmonic expansions for the polarization and the inversion density. The authors represent the solutions of the linearized Bloch hierarchy in terms of Chebyshev polynomials depending on the stationary electric field envelopes. In this way, they reduce the stability problem to a four-dimensional set of linear differential equations. Together with a couple of boundary conditions these equations govern the spatial behaviour of the deviations of the forward and the backward electric field envelopes. The final stability problem becomes much simpler in the uniform-field limit and in the adiabatic limit. If one chooses the stationary backward electric field equal to zero one recovers results that were derived earlier for the case of a ring cavity.
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  • (Publications before 1991 are found here. )