TY - JOUR AU - Apagyi, Barnabás TI - Determination of α – α interaction from experiment JF - JOURNAL OF MATHEMATICAL CHEMISTRY J2 - J MATH CHEM VL - 60 PY - 2022 IS - 9 SP - 1739 EP - 1749 PG - 11 SN - 0259-9791 DO - 10.1007/s10910-022-01382-3 UR - https://m2.mtmt.hu/api/publication/33056353 ID - 33056353 N1 - Export Date: 18 August 2022 Correspondence Address: Apagyi, B.; Department of Theoretical Physics, Hungary; email: apagyi@gmail.com Funding Agency and Grant Number: Budapest University of Technology and Economics Funding text: Open access funding provided by Budapest University of Technology and Economics. AB - Fixed-energy quantum inversion method is applied to determine model independent alpha-particle scattering potentials within the energy range between 0 and 50 MeV. Only experimentally allowed even phase shifts are used in the calculation. Detailed results exhibited at low and higher energies show up a large interaction domain, a thin strong Pauli-blocking part and a smooth merging region between the colliding particles. Overall agreement between input and re-calculated phase shifts justifies the procedure. LA - English DB - MTMT ER - TY - JOUR AU - Scheid, W AU - Apagyi, Barnabás TI - Quantum inversion with elastic phase shifts to discrete different energies JF - INTERNATIONAL JOURNAL OF MODERN PHYSICS E-NUCLEAR PHYSICS J2 - INT J MOD PHYS E VL - 23 PY - 2014 IS - 11 PG - 11 SN - 0218-3013 DO - 10.1142/S0218301314500773 UR - https://m2.mtmt.hu/api/publication/2882736 ID - 2882736 AB - We consider the inverse quantum scattering problem with phase shifts of different discrete energies belonging to a real energy-independent radial potential for elastic scattering. The solution of this problem is essential for atomic and nuclear physics. The two procedures investigated are based on the modified Newton-Sabatier method. The first procedure leads to angular-momentum dependent potentials with poles. The second one carries out an inversion at a fixed energy by varying the phase shifts of the other energies and leads finally to the correct energy-independent potential. LA - English DB - MTMT ER - TY - JOUR AU - Pálmai, Tamás Vencel AU - Apagyi, Barnabás TI - The inverse scattering problem at fixed energy based on the Marchenko equation for an auxiliary Sturm-Liouville operator JF - JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL J2 - J PHYS A-MATH THEOR VL - 46 PY - 2013 IS - 4 PG - 11 SN - 1751-8113 DO - 10.1088/1751-8113/46/4/045303 UR - https://m2.mtmt.hu/api/publication/2696590 ID - 2696590 AB - A new approach is proposed to the solution of the quantum mechanical inverse scattering problem at a fixed energy. The method relates the fixed energy phase shifts to those arising in an auxiliary Sturm–Liouville problem via the interpolation theory of the Weyl–Titchmarsh m-function. Then a Marchenko equation is solved to obtain the potential. As an illustration test results are shown including the reconstructions of the piecewise constant and Coulomb-type potentials. A byproduct of the new framework is a demonstration of the connection found between the Gelfand–Levitan and Marchenko formalisms. LA - English DB - MTMT ER - TY - JOUR AU - Csire, Gábor AU - Apagyi, Barnabás TI - Macroscopic quantum superpositon states of two-component Bose-Einstein condensates JF - PHYSICAL REVIEW A J2 - PHYS REV A VL - 85 PY - 2012 IS - 3 SN - 2469-9926 DO - 10.1103/PhysRevA.85.033613 UR - https://m2.mtmt.hu/api/publication/2284190 ID - 2284190 AB - We examine a two-component Bose-Einstein condensate in a double-well potential. We propose a model for the creation of many-particle macroscopic quantum superposition states. The effect of dissipation on the formation of these states is also investigated with the Monte Carlo wave-function technique. © 2012 American Physical Society. LA - English DB - MTMT ER - TY - JOUR AU - Pálmai, Tamás Vencel AU - Apagyi, Barnabás TI - Fixed energy potentials through an auxiliary inverse eigenvalue problem JF - INVERSE PROBLEMS J2 - INVERSE PROBL VL - 28 PY - 2012 IS - 8 PG - 19 SN - 0266-5611 DO - 10.1088/0266-5611/28/8/085007 UR - https://m2.mtmt.hu/api/publication/2688568 ID - 2688568 AB - An inverse scattering method based on an auxiliary inverse Sturm-Liouville problem recently proposed by Horvath and Apagyi (2008 Mod. Phys. Lett. B 22 2137) is examined in various aspects and developed further to (re) construct spherically symmetric fixed energy potentials of compact support realized in the three-dimensional Schrodinger equation. The method is generalized to obtain a family of inverse procedures characterized by two parameters originating, respectively, from the Liouville transformation and the solution of the inverse Sturm-Liouville problem. Both parameters affect the bound states arising in the auxiliary inverse spectral problem and one of them enables us to reduce their number which is assessed by a simple method. Various solution techniques of the underlying moment problem are proposed including the exact Cauchy matrix inversion method, usage of spurious bound state and assessment of the number of bound states. Examples include (re) productions of potentials from phase shifts known theoretically or derived from scattering experiments. LA - English DB - MTMT ER - TY - JOUR AU - Pálmai, Tamás Vencel AU - Apagyi, Barnabás TI - Quantum Mechanical Inverse Scattering Problem at Fixed Energy: A Constructive Method JF - METHODS AND APPLICATIONS OF ANALYSIS J2 - METHODS APPL ANAL VL - 18 PY - 2011 IS - 1 SP - 93 EP - 104 PG - 12 SN - 1073-2772 DO - 10.4310/MAA.2011.v18.n1.a6 UR - https://m2.mtmt.hu/api/publication/2680543 ID - 2680543 LA - English DB - MTMT ER - TY - JOUR AU - Pálmai, Tamás Vencel AU - Apagyi, Barnabás TI - Interlacing of positive real zeros of Bessel functions JF - JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS J2 - J MATH ANAL APPL VL - 375 PY - 2011 IS - 1 SP - 320 EP - 322 PG - 3 SN - 0022-247X DO - 10.1016/j.jmaa.2010.09.024 UR - https://m2.mtmt.hu/api/publication/2680538 ID - 2680538 LA - English DB - MTMT ER - TY - JOUR AU - Werner, Scheid AU - Apagyi, Barnabás TI - DISCUSSION OF QUANTUM INVERSE SCATTERING PROBLEMS FOR COUPLED CHANNELS AT FIXED ENERGY JF - INTERNATIONAL JOURNAL OF MODERN PHYSICS E-NUCLEAR PHYSICS J2 - INT J MOD PHYS E VL - 20 PY - 2011 IS - 8 SP - 1765 EP - 1773 PG - 9 SN - 0218-3013 DO - 10.1142/S0218301311019660 UR - https://m2.mtmt.hu/api/publication/2680753 ID - 2680753 LA - English DB - MTMT ER - TY - JOUR AU - Csire, Gábor AU - Schumayer, D AU - Apagyi, Barnabás TI - Effect of scattering lengths on the dynamics of a two-component Bose-Einstein condensate JF - PHYSICAL REVIEW A J2 - PHYS REV A VL - 82 PY - 2010 IS - 6 SN - 2469-9926 DO - 10.1103/PhysRevA.82.063608 UR - https://m2.mtmt.hu/api/publication/2284192 ID - 2284192 AB - We examine the effect of the intra- and interspecies scattering lengths on the dynamics of a two-component Bose-Einstein condensate, particularly focusing on the existence and stability of solitonic excitations. For each type of possible soliton pairs, stability ranges are presented in tabulated form. We also compare the numerically established stability of bright-bright, bright-dark, and dark-dark solitons with our analytical prediction and with that of Painlevé analysis of the dynamical equation. We demonstrate that tuning the interspecies scattering length away from the predicted value (keeping the intraspecies coupling fixed) breaks the stability of the soliton pairs. © 2010 The American Physical Society. LA - English DB - MTMT ER - TY - JOUR AU - Hilk, D AU - Scheid, W AU - Pálmai, Tamás Vencel AU - Apagyi, Barnabás TI - Study of the Cox-Thompson inverse scattering method with a Coulomb potential JF - JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL J2 - J PHYS A-MATH THEOR VL - 43 PY - 2010 IS - 22 PG - 10 SN - 1751-8113 DO - 10.1088/1751-8113/43/22/225302 UR - https://m2.mtmt.hu/api/publication/2657274 ID - 2657274 AB - In order to learn more about the precision of the inversion by the Cox-Thompson method, we investigated the inversion of phase shifts of a singular potential, namely of a Coulomb potential. Using asymptotically Riccati-Bessel functions as reference functions, we could only approximately reproduce the singularity of the Coulomb potential at the origin. We also show uncertainties in the inverted potential due to different minima in the minimization solution of the nonlinear equations of the Cox-Thompson procedure. As a result, we conclude that one has to take much care with the inversion of experimental phase shifts suffering from measurement errors. LA - English DB - MTMT ER - TY - JOUR AU - Pálmai, Tamás Vencel AU - Apagyi, Barnabás AU - Scheid, W TI - Development of a Cox-Thompson inverse scattering method to charged particles JF - JOURNAL OF PHYSICS G-NUCLEAR AND PARTICLE PHYSICS J2 - J PHYS G NUCL PARTIC VL - 37 PY - 2010 IS - 2 SN - 0954-3899 DO - 10.1088/0954-3899/37/2/025101 UR - https://m2.mtmt.hu/api/publication/2657276 ID - 2657276 AB - A Cox-Thompson fixed-energy quantum inverse scattering method is developed further to treat long-range Coulomb interaction. Depending on the reference potentials chosen, two methods have been formulated which produce inverse potentials with singular or finite value at the origin. Based on the quality of reproduction of input experimental phase shifts, it is guessed that the p-a interaction possesses an interesting repulsive hard core. LA - English DB - MTMT ER - TY - JOUR AU - Pálmai, Tamás Vencel AU - Apagyi, Barnabás TI - On nonsingular potentials of Cox-Thompson inversion scheme JF - JOURNAL OF MATHEMATICAL PHYSICS J2 - J MATH PHYS VL - 51 PY - 2010 IS - 2 SN - 0022-2488 DO - 10.1063/1.3282849 UR - https://m2.mtmt.hu/api/publication/2657275 ID - 2657275 AB - We establish a condition for obtaining nonsingular potentials using the Cox-Thompson inverse scattering method with one phase shift. The anomalous singularities of the potentials are avoided by maintaining unique solutions of the underlying Regge-Newton integral equation for the transformation kernel. As a by-product, new inequality sequences of zeros of Bessel functions are discovered. (C) 2010 American Institute of Physics. [doi: 10.1063/1.3282849] LA - English DB - MTMT ER - TY - JOUR AU - Apagyi, Barnabás AU - Scheid, W TI - QUANTUM INVERSE SCATTERING PROBLEM FOR COUPLED CHANNELS JF - MODERN PHYSICS LETTERS B J2 - MOD PHYS LETT B VL - 22 PY - 2008 IS - 23 SP - 2241 EP - 2256 PG - 16 SN - 0217-9849 DO - 10.1142/S021798490801700X UR - https://m2.mtmt.hu/api/publication/2657280 ID - 2657280 AB - The article gives a concise review on methods for solving the inverse scattering problem of coupled reaction channels in quantum mechanics at fixed energy and presents specific applications to nuclear reactions. Two methods are considered, namely the Newton Sabatier method and an approximate method based on the first Born approximation. Examples with artificial coupling potentials are shown to provide successful tests of both the methods. Further developments of the coupled channel inverse problem at fixed energy are needed for manifold applications in various fields of physics. LA - English DB - MTMT ER - TY - JOUR AU - Apagyi, Barnabás AU - Horváth, Miklós TI - Proceedings of the International Conference on Inverse Quantum Scattering Theory, 27-31 August 2007, Siofok, Hungary PREFACE JF - MODERN PHYSICS LETTERS B J2 - MOD PHYS LETT B VL - 22 PY - 2008 IS - 23 SP - V EP - V SN - 0217-9849 UR - https://m2.mtmt.hu/api/publication/2657277 ID - 2657277 LA - English DB - MTMT ER - TY - BOOK ED - Apagyi, Barnabás ED - Horváth, Miklós TI - Proceedings of the International Conference on Inverse Quantum Scattering Theory T3 - Modern Physics Letters B, ISSN 0217-9849 ; 22, No. 23. ET - 0 PB - World Scientific C1 - Singapore PY - 2008 UR - https://m2.mtmt.hu/api/publication/2664372 ID - 2664372 LA - English DB - MTMT ER - TY - JOUR AU - Horváth, Miklós AU - Apagyi, Barnabás TI - Solution of the inverse scattering problem at fixed energy for potentials being zero beyond a fixed radius JF - MODERN PHYSICS LETTERS B J2 - MOD PHYS LETT B VL - 22 PY - 2008 IS - 23 SP - 2137 EP - 2149 PG - 13 SN - 0217-9849 DO - 10.1142/S0217984908016923 UR - https://m2.mtmt.hu/api/publication/2657278 ID - 2657278 AB - Based on the relation between the m-function and the spectral function we construct an inverse quantum scattering procedure at fixed energy which can be applied to spherical radial potentials vanishing beyond a fixed radius alpha. To solve the Gelfand-Levitan-Marchenko integral equation for the transformation kernel, we determine the input symmetrical kernel by using a minimum norm method with moments defined by the input set of scattering phase shifts. The method applied to the box and Gauss potentials needs further practical developments regarding the treatment of bound states. LA - English DB - MTMT ER - TY - JOUR AU - Pálmai, Tamás Vencel AU - Horváth, Miklós AU - Apagyi, Barnabás TI - Simplified solutions of the Cox-Thompson inverse scattering method at fixed energy JF - JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL J2 - J PHYS A-MATH THEOR VL - 41 PY - 2008 IS - 23 SN - 1751-8113 DO - 10.1088/1751-8113/41/23/235305 UR - https://m2.mtmt.hu/api/publication/2657282 ID - 2657282 AB - Simplified solutions of the Cox-Thompson inverse quantum scattering method at fixed energy are derived if a finite number of partial waves with only even or odd angular momenta contribute to the scattering process. Based on new formulae various approximate methods are introduced which also prove applicable to the generic scattering events. LA - English DB - MTMT ER - TY - JOUR AU - Pálmai, Tamás Vencel AU - Horváth, Miklós AU - Apagyi, Barnabás TI - SEMI-ANALYTIC EQUATIONS TO THE COX-THOMPSON INVERSE SCATTERING METHOD AT FIXED ENERGY FOR SPECIAL CASES JF - MODERN PHYSICS LETTERS B J2 - MOD PHYS LETT B VL - 22 PY - 2008 IS - 23 SP - 2191 EP - 2199 PG - 9 SN - 0217-9849 DO - 10.1142/S0217984908016972 UR - https://m2.mtmt.hu/api/publication/2657279 ID - 2657279 AB - Solution of the Cox-Thompson inverse scattering problem at fixed energy(1-3) is reformulated resulting in semi-analytic equations. The new set of equations for the normalization constants and the nonphysical (shifted) angular momenta are free of matrix inversion operations. This simplification is a result of treating only the input phase shifts of partial waves of a given parity. Therefore, the proposed method can be applied for identical particle scattering of the bosonic type (or for certain cases of identical fermionic scattering). The new formulae are expected to be numerically more efficient than the previous ones. Based on the semi-analytic equations an approximate method is proposed for the generic inverse scattering problem, when partial waves of arbitrary parity are considered. LA - English DB - MTMT ER - TY - JOUR AU - Schumayer, D AU - Melchert, O AU - Scheid, W AU - Apagyi, Barnabás TI - Effective Rb-Rb inter-atomic potential from ultracold Bose-gas collisions JF - JOURNAL OF PHYSICS B: ATOMIC MOLECULAR AND OPTICAL PHYSICS J2 - J PHYS B AT MOL OPT PH VL - 41 PY - 2008 IS - 3 SN - 0953-4075 DO - 10.1088/0953-4075/41/3/035302 UR - https://m2.mtmt.hu/api/publication/2657283 ID - 2657283 AB - Scattering phase shifts obtained from Rb-87 Bose-gas collision experiments are used to reconstruct effective potentials resulting, self-consistently, in the same scattering events observed in the experiments at a particular energy. We have found that the interaction strength close to the origin suddenly changes from repulsion to attraction when the collision energy crosses, from below, the l = 2 shape resonance position at E approximate to 275 mu K. This observation may be utilized in outlining future Bose-gas collision experiments. LA - English DB - MTMT ER - TY - JOUR AU - Varga, P AU - Apagyi, Barnabás TI - Phase estimation procedure to solve quantum-mechanical eigenvalue problems JF - PHYSICAL REVIEW A J2 - PHYS REV A VL - 78 PY - 2008 IS - 2 SN - 2469-9926 DO - 10.1103/PhysRevA.78.022337 UR - https://m2.mtmt.hu/api/publication/2657281 ID - 2657281 AB - A simple phase estimation procedure is outlined and applied to solve standard quantum-mechanical problems. The procedure needs only one qubit to read off the eigenenergy obtained by iterative measurements, while the system qubits provides the corresponding eigenstates. No a priori information is needed about the system states and energies, therefore, the procedure may be launched from a completely random initial state. LA - English DB - MTMT ER -