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  • 1. Andersson, L. Mauritz
    et al.
    Aberg, J.
    Karlsson, H. O.
    Goscinski, O.
    Properties of a discretized coherent state representation and the relation to Gabor analysis2002Inngår i: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 35, nr 36, s. 7787-7801Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Properties of a discretized coherent state representation (DCSR) and its connection to Gabor frame analysis are discussed. The DCSR approach was recently shown (Andersson L M 2001 J. Chem. Phys. 115 1158) to yield a practical computational scheme for quantum dynamics, and an iterative scheme for finding the identity operator was proposed. In the present work, we suggest a proof of fast convergence of the iterative scheme for computing the canonical dual to any given countable frame in a Hilbert space. The method of frames is concerned with the use of a non-orthogonal, over-complete set of functions for expansion of an arbitrary function. We also introduce the concept of 'representations of the identity operator' and show how to expand arbitrary vectors using the frame elements, without explicit diagonalization to an orthonormal basis. Numerical examples that illustrate the method are shown.

  • 2. Bourennane, M.
    et al.
    Karlsson, Anders
    KTH, Tidigare Institutioner                               , Mikroelektronik och informationsteknik, IMIT.
    Björk, Gunnar
    KTH, Tidigare Institutioner                               , Mikroelektronik och informationsteknik, IMIT.
    Gisin, N.
    Cerf, N. J.
    Quantum key distribution using multilevel encoding: security analysis2002Inngår i: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 35, nr 47, s. 10065-10076Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We propose an extension of quantum key distribution based on encoding the key into quNits, i.e. quantum states in an N-dimensional Hilbert space. We,estimate both the mutual information between the legitimate parties and the eavesdropper, and the error rate, as a function of the dimension of the Hilbert space. We derive the information gained by an eavesdropper using optimal incoherent attacks and an upper bound on the legitimate party error rate that ensures unconditional security when the eavesdropper uses finite coherent eavesdropping attacks. We also consider realistic systems where we assume that the detector dark count probability is not negligible.

  • 3.
    Essén, Hanno
    KTH, Tidigare Institutioner, Mekanik.
    Magnetohydrodynamic self-consistent exact helical solutions2004Inngår i: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 37, nr 41, s. 9831-9840Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We consider the idealized case of a one-component plasma with aligned fluid velocity and current density. Constant density and pressure as well as zero external magnetic field are also assumed. We show that suitably determined axially symmetric helical current densities within a straight infinite cylinder are exact self-consistent solutions of magnetohydrodynamics. Self-consistent here means that the magnetic field is the field produced by the current density itself. The equation of motion gives a nonlinear differential equation that relates the axial upsilon(z)(rho) and the azimuthal upsilonphi(rho) velocities as functions of radial distance rho. Prescribing one of these gives a specific solution for the other. The solutions can be understood as a set of helix-shaped charged particle trajectories that spiral self-consistently through the magnetic field that they themselves give rise to. Four different specific exact solutions are given: (i) a single particle outside a rectilinear line current, (ii) current on a thin cylinder, (iii) current density with constant angular velocity and (iv) current density with constant axial velocity, both within a cylinder of finite radius.

  • 4. Fu, J.
    et al.
    He, Sailing
    KTH, Tidigare Institutioner                               , Teoretisk elektroteknik.
    Xiao, S. S.
    Analysis of channel-dropping tunnelling processes in photonic crystals with multiple vertical multi-mode cavities2000Inngår i: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 33, nr 43, s. 7761-7771Artikkel i tidsskrift (Fagfellevurdert)
  • 5. Grosse, Harald
    et al.
    Langmann, Edwin
    KTH, Tidigare Institutioner, Fysik.
    Paufler, Cornelius
    KTH, Tidigare Institutioner, Fysik.
    Exact solution of a 1D quantum many-body system with momentum-dependent interactions2004Inngår i: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 37, nr 16, s. 4579-4592Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We discuss a ID quantum many-body model of distinguishable particles with local, momentum-dependent two-body interactions. We show that the restriction of this model to fermions corresponds to the non-relativistic limit of the massive Thirring model. This fermion model can be solved exactly by a mapping to the 1D boson gas with inverse coupling constant. We provide evidence that this mapping is the non-relativistic limit of the duality between the massive Thirring model and the quantum sine-Gordon model. We show that the generalized model with distinguishable particles remains exactly solvable by the (coordinate) Bethe ansatz. Our solution provides a generalization of the above mentioned boson-fermion duality to particles with arbitrary exchange statistics characterized by any irreducible representation of the permutation group.

  • 6.
    Hallnäs, Martin
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Teoretisk fysik, Matematisk fysik.
    Langmann, Edwin
    KTH, Skolan för teknikvetenskap (SCI), Teoretisk fysik, Matematisk fysik.
    Explicit formulae for the eigenfunctions of the N-body Calogero model2006Inngår i: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 39, nr 14, s. 3511-3533Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We consider the quantum Calogero model, which describes N non-distinguishable quantum particles on the real line confined by a harmonic oscillator potential and interacting via two-body interactions proportional to the inverse square of the inter-particle distance. We elaborate a novel solution algorithm which allows us to obtain fully explicit formulae for its eigenfunctions, arbitrary coupling parameter and particle number. We also show that our method applies, with minor changes, to all Calogero models associated with classical root systems.

  • 7.
    Hallnäs, Martin
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Teoretisk fysik, Matematisk fysik.
    Langmann, Edwin
    KTH, Skolan för teknikvetenskap (SCI), Teoretisk fysik, Matematisk fysik.
    Paufler, Cornelius
    KTH, Skolan för teknikvetenskap (SCI), Teoretisk fysik, Matematisk fysik.
    Generalized local interactions in 1D: solutions of quantum many-body systems describing distinguishable particles2005Inngår i: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 38, nr 22, s. 4957-4974Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    As is well known, there exists a four-parameter family of local interactions in 1D. We interpret these parameters as coupling constants of delta-type interactions which include different kinds of momentum-dependent terms, and determine all cases leading to many-body systems of distinguishable particles which are exactly solvable by the coordinate Bethe ansatz. We find two such families of systems, one with two independent coupling constants deforming the well-known delta-interaction model to non-identical particles, and the other with a particular one-parameter combination of the delta and (the so-called) delta-prime interaction. We also find that the model of non-identical particles gives rise to a somewhat unusual solution of the Yang-Baxter relations. For the other model we write down explicit formulae for all eigenfunctions.

  • 8.
    He, Sailing
    et al.
    KTH, Tidigare Institutioner                               , Teoretisk elektroteknik.
    Xiao, S. S.
    Shen, L. F.
    He, J. P.
    Fu, J.
    A new finite-difference time-domain method for photonic crystals consisting of nearly-free-electron metals2001Inngår i: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 34, nr 45, s. 9713-9721Artikkel i tidsskrift (Fagfellevurdert)
  • 9. Heydari, H.
    et al.
    Björk, Gunnar
    KTH, Skolan för informations- och kommunikationsteknik (ICT), Mikroelektronik och tillämpad fysik, MAP.
    Complex multi-projective variety and entanglement2005Inngår i: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 38, nr 14, s. 3203-3211Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    In this paper, we will show that a vanishing generalized concurrence of a separable state can be seen as an algebraic variety called the Segre variety. This variety defines a quadric space which gives a geometric picture of separable states. For pure, bi- and three-partite states the variety equals the generalized concurrence. Moreover, we generalize the Segre variety to a general multipartite state by relating to a quadric space defined by two-by-two subdeterminants.

  • 10.
    Heydari, Hoshang
    et al.
    KTH, Tidigare Institutioner, Mikroelektronik och informationsteknik, IMIT.
    Björk, Gunnar
    KTH, Tidigare Institutioner, Mikroelektronik och informationsteknik, IMIT.
    Entanglement measure for general pure multipartite quantum states2004Inngår i: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 37, nr 39, s. 9251-9260Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We propose an explicit formula for a measure of entanglement of pure multipartite quantum states. We discuss the mathematical structure of the measure and give a brief explanation of its physical motivation. We apply the measure on some pure, tripartite, qubit states and demonstrate that, in general, the entanglement can depend on what actions are performed on the various subsystems, and specifically if the parties in possession of the subsystems cooperate or not. We also give some simple but illustrative examples of the entanglement of four-qubit and m-qubit states.

  • 11. Klimov, A. B.
    et al.
    Sanchez-Soto, L. L.
    de Guise, H.
    Björk, Gunnar
    KTH, Tidigare Institutioner, Mikroelektronik och informationsteknik, IMIT.
    Quantum phases of a qutrit2004Inngår i: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 37, nr 13, s. 4097-4106Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We consider various approaches to treat the phases of a qutrit. Although it is possible to represent qutrits in a convenient geometrical manner by resorting to a generalization of the Poincare sphere, we argue that the appropriate way of dealing with this problem is through phase operators associated with the algebra su(3). The rather unusual properties of these phases are caused by the small dimension of the system and are explored in detail. We also examine the positive operator-valued measures that can describe the qutrit phase properties.

  • 12.
    Langmann, Edwin
    KTH, Tidigare Institutioner, Fysik.
    Exactly solvable models for 2D interacting fermions2004Inngår i: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 37, nr 2, s. 407-423Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    I discuss many-body models for correlated fermions in two space dimensions which can be solved exactly using group theory. The simplest example is a model of a quantum Hall system: two-dimensional (2D) fermions in a constant magnetic field and a particular non-local four-point interaction. It is exactly solvable due to a dynamical symmetry corresponding to the Lie algebra gl(infinity) circle plus gl(infinity). There is an algorithm to construct all energy eigenvalues and eigenfunctions of this model. The latter are, in general, many-body states with spatial correlations. The model also has a non-trivial zero temperature phase diagram. I point out that this QH model can be obtained from a more realistic one using a truncation procedure generalizing a similar one leading to mean field theory. Applying this truncation procedure to other 2D fermion models I obtain various simplified models of increasing complexity which generalize mean field theory by taking into account non-trivial correlations but nevertheless are treatable by exact methods.

  • 13.
    Langmann, Edwin
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Teoretisk fysik, Matematisk fysik.
    Laptev, Ari
    KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).
    Paufler, Cornelius
    Singular factorizations, self-adjoint extensions and applications to quantum many-body physics2006Inngår i: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 39, nr 5, s. 1057-1071Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We study self-adjoint operators defined by factorizing second-order differential operators in first-order ones. We discuss examples where such factorizations introduce singular interactions into simple quantum-mechanical models such as the harmonic oscillator or the free particle on the circle. The generalization of these examples to the many-body case yields quantum models of distinguishable and interacting particles in one dimensions which can be solved explicitly and by simple means. Our considerations lead us to a simple method to construct exactly solvable quantum many-body systems of Calogero-Sutherland type.

  • 14.
    Lenells, Jonatan
    Lund University, Sweden .
    Conservation laws of the Camassa-Holm equation2005Inngår i: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 38, nr 4, s. 869-880Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    We use the bi-Hamiltonian structure of the Camassa-Holm equation to show that its conservation laws Hn[m] are homogeneous with respect to the scaling m → λm. Moreover, a direct argument is presented proving that H-1, H-2,..., are of local character. Finally, simple representations of the conservation laws in terms of their variational derivatives are derived and used to obtain a constructive scheme for computation of the Hns.

  • 15.
    Lu, X.
    et al.
    KTH, Skolan för industriell teknik och management (ITM), Energiteknik, Tillämpad termodynamik och kylteknik.
    Tervola, P.
    Viljanen, M.
    A new analytical method to solve the heat equation for a multi-dimensional composite slab2005Inngår i: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 38, nr 13, s. 2873-2890Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A novel analytical approach has been developed for heat conduction in a multi-dimensional composite slab subject to time-dependent boundary changes of the first kind. Boundary temperatures are represented as Fourier series. Taking advantage of the periodic properties of boundary changes, the analytical solution is obtained and expressed explicitly. Nearly all the published works necessitate searching for associated eigenvalues in solving such a problem even for a one-dimensional composite slab. In this paper, the proposed method involves no iterative computation such as numerically searching for eigenvalues and no residue evaluation. The adopted method is simple which represents an extension of the novel analytical approach derived for the one-dimensional composite slab. Moreover, the method of 'separation of variables' employed in this paper is new. The mathematical formula for solutions is concise and straightforward. The physical parameters are clearly shown in the formula. Further comparison with numerical calculations is presented.

  • 16. Salo, J.
    et al.
    Friberg, Ari T.
    KTH, Tidigare Institutioner                               , Mikroelektronik och informationsteknik, IMIT.
    Salomaa, M. M.
    Orthogonal X waves2001Inngår i: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 34, nr 43, s. 9319-9327Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Nondiffracting pulses are spatially and temporally localized wave fields that undergo no diffractive spreading under propagation through homogeneous media. We introduce an orthogonality condition for nondiffracting pulses and present an orthogonal set of X waves which possess temporal spectra of the form (polynomial in omega) x e(-alpha omega). The newly introduced Bessel-X pulses and X-wave transforms are discussed in the framework of the orthogonal X-wave bases.

  • 17.
    Shen, Jian Qi
    et al.
    KTH, Tidigare Institutioner (före 2005), Teoretisk elektroteknik. KTH, Tidigare Institutioner (före 2005), Alfvénlaboratoriet. Centre for Optical and Electromagnetic Research, Joint Research Centre of Photonics of the Royal Institute of Technology, Sweden and Zhejiang University, Hangzhou Yuquan 310027, People's Republic of China.
    He, Sailing
    KTH, Tidigare Institutioner (före 2005), Teoretisk elektroteknik. KTH, Tidigare Institutioner (före 2005), Alfvénlaboratoriet. Centre for Optical and Electromagnetic Research, Joint Research Centre of Photonics of the Royal Institute of Technology, Sweden and Zhejiang University, Hangzhou Yuquan 310027, People's Republic of China.
    ADDENDUM, Backward waves and negative refractive indices in gyrotropic chiral media (vol 39, pg 457, 2006)2006Inngår i: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 39, nr 48, s. 15057-15057Artikkel i tidsskrift (Fagfellevurdert)
  • 18.
    Shen, Jianqi
    et al.
    KTH, Skolan för elektro- och systemteknik (EES), Centra, Alfvénlaboratoriet.
    He, Sailing
    KTH, Skolan för elektro- och systemteknik (EES), Centra, Alfvénlaboratoriet.
    Backward waves and negative refractive indices in gyrotropic chiral media2006Inngår i: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 39, s. 457-466Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The possibility of the backward waves and negative refractive indices of the gyrotropic chiralmaterials is studied, and the impedances of the eigenmodes arederived. Since the gyrotropic parameters in the permittivity and permeabilitytensors favour the realization of the negative refractive index in the gyrotropicchiral material, the negatively refracting medium can be achieved even far offthe resonances of the permittivity and permeability. A potential effect of the field quantization in a compact subwavelength cavity resonator containing thegyrotropic chiral material is suggested.

  • 19.
    Thylwe, Karl-Erik
    KTH, Skolan för teknikvetenskap (SCI), Mekanik.
    Generalization of the amplitude-phase S-matrix formula for coupled scattering states2005Inngår i: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 38, nr 46, s. 10007-10013Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    The amplitude-phase method is generalized to coupled Schrodinger scattering states with a common angular momentum quantum number. A pair of expontentail-type amplitude-phase solutions u(j)((+/-))(r)exp[+/- i phi(j)(r)] for each channel is obtained, containing a common complex scalar phase function phi(j)(r) and two (column) vector amplitudes u(j)((+/-))(r). The amplitude functions satisfy certain nonlinear generalized Milne equations and the scalar product of the two amplitudes determines the derivative of the common phase function. Fundamental amplitude-phase matrix solutions that are proportional to Jost-like Schrodinger matrix solutions are constructed. It is shown how a generalized amplitude-phase S-matrix formula can be derived from Wronskian relations involving the two amplitude-phase matrix solutions and a regular matrix solution.

  • 20.
    Thylwe, Karl-Erik
    KTH, Skolan för teknikvetenskap (SCI), Mekanik.
    Improved amplitude-phase method for complex angular momentum analysis2005Inngår i: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 38, nr 33, s. 7363-7375Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    An amplitude-phase formula for the S matrix using two Milne solutions and the regular Schrodinger solution is derived. The formula is particularly useful in the analysis of Regge poles located far out in the complex e-plane, particularly for discontinuous scattering potentials. Numerical applications for an attractive square-well potential and an inverse-power potential similar to r(-4) are presented.

  • 21.
    Thylwe, Karl-Erik
    KTH, Skolan för teknikvetenskap (SCI), Mekanik.
    Multi-state complex angular momentum residues2006Inngår i: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 39, nr 38, s. 11895-11899Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    A relation between a multi-state complex angular momentum (CAM) pole residue and the corresponding CAM-state wavefunction is derived for a real symmetric potential matrix. The result generalizes a residue formula available for single-channel atomical collision systems and it is based on a diagonalization of the S matrix together with the use of exact Wronskian relations.

  • 22.
    Thylwe, Karl-Erik
    KTH, Tidigare Institutioner                               , Mekanik.
    Note on invariants for uncoupled Ermakov systems2002Inngår i: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 35, nr 19, s. 4359-4362Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Several invariants for an Ermakov system consisting of a parametric oscillator and a Milne oscillator in one dimension are derived. This system appears in amplitude-phase analysis of parametric oscillator solutions. First- and second-order invariants for such a system are derived using the Wronskian relations of a fundamental pair of parametric oscillator solutions. In this way Wronskian invariants of the parametric oscillator system alone imply Ermakov-Lewis type invariants for the combined Ermakov system, as well as invariants for the Milne oscillator alone.

  • 23.
    Thylwe, Karl-Erik
    KTH, Tidigare Institutioner, Mekanik.
    Scattering S-matrix derived from invariants of the Ermakov-Lewis type2004Inngår i: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 37, nr 44, s. L589-L591Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    An amplitude-phase formula for the S-matrix due to a central potential is derived. The derivation makes use of invariants of the Ermakov-Lewis type.

  • 24.
    Thylwe, Karl-Erik
    KTH, Skolan för teknikvetenskap (SCI), Mekanik.
    The barrier transmission problem treated by the amplitude-phase method and expressed in terms of an invariant of the Ermakov-Lewis type2005Inngår i: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 38, nr 1, s. 235-243Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Transmission and reflection of a quantal particle by a single-hump potential barrier are analysed by means of an amplitude-phase decomposition of the wavefunction on both sides of the barrier. The amplitude-phase analysis of the wavefunction provides a particular invariant of the Ermakov-Lewis type, which originates in the matching process. The transmission and reflection coefficients turn out to be simple functions of this invariant. Numerical calculations of the invariant for an Eckart-Epstein potential barrier provide very accurate results.

  • 25.
    Thylwe, Karl-Erik
    et al.
    KTH, Tidigare Institutioner                               , Mekanik.
    Korsch, H. J.
    Harmonic oscillator subject to parametric pulses: an amplitude (Milne) oscillator approach2001Inngår i: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 34, nr 16, s. 3497-3510Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    harmonic oscillator subject to a parametric pulse is examined. The aim of the paper is to present a new theory for analysing transitions caused by parametric pulses. The new theoretical notions which are introduced relate the pulse parameters in a direct way with transition matrix elements. The harmonic-oscillator transitions are expressed in terms of the asymptotic properties of a companion oscillator, the Milne (amplitude) oscillator. A traditional phase-amplitude decomposition of the harmonic-oscillator solutions results in the so-called Milne's equation fur the amplitude, and the phase is determined by an exact relation to the amplitude. This approach is extended in the present analysis with new relevant concepts and parameters for pulse dynamics of classical and quantal systems. The amplitude oscillator has a particularly nice numerical behaviour. In the case of strong pulses it does not possess any of the fast oscillations induced by the pulse on the original harmonic oscillator. Furthermore, the new dynamical parameters introduced in this approach are closely related to the relevant characteristics of the pulse. The relevance to quantum mechanical problems such as reflection and transmission from a localized well and the mechanical problem of controlling vibrations is illustrated.

  • 26.
    Thylwe, Karl-Erik
    et al.
    KTH, Tidigare Institutioner                               , Mekanik.
    Korsch, H. J.
    On pulse-induced transition amplitudes in a two-state quantum system without level crossings2002Inngår i: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 35, nr 34, s. 7507-7523Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    An exact dynamical parametrization of pulse-induced transition amplitudes in a Rosen-Zener- or Nikitin-type two-level system is constructed. The three dynamical parameters are closely related to the shape of the interaction pulse and are convenient to calculate. The Milne equation with a complex coefficient function is essential for these calculations. Its complex solution is non-oscillatory and makes the computation of transition probabilities efficient. The paper reviews the quantum calculations for the rectangular pulse, which has well-defined duration and strength. By comparing transition matrix elements from a rectangular pulse with those of a general symmetric pulse, we introduce effective strength and effective duration for a general pulse. It is also possible to define an equivalent rectangular pulse, with respect to the transition probabilities, for each general pulse.

  • 27.
    Thylwe, Karl-Erik
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Mekanik.
    Sokolovski, D.
    An amplitude-phase approach to calculating Regge-pole positions and residues2005Inngår i: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 38, nr 23, s. 5305-5313Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    New amplitude-phase formulae for Regge-pole positions and residues are derived. The derivation makes use of certain invariants of the En-nakov-Lewis type. The formulas allow calculation to be made on the real r-axis, with an additional flexibility to optimize its numerical aspects.

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