Problems of inverse scattering theory  Page description

Help  Print 
Back »
 

Details of project

  
Identifier
47035
Type K
Principal investigator Apagyi, Barnabás
Title in Hungarian Inverz szóráselméleti kutatások
Title in English Problems of inverse scattering theory
Panel Physics 1
Department or equivalent Department of Theoretical Physics (Budapest University of Technology and Economics)
Participants Horváth, Miklós
Lévay, Péter Pál
Schumayer, Dániel
Szilágyi, András
Starting date 2004-01-01
Closing date 2008-12-31
Funding (in million HUF) 4.181
FTE (full time equivalent) 0.00
state closed project





 

Final report

  
Results in Hungarian
Kifejlesztettünk egy új fix-energiás inverz kvantum szórás módszert. Szórási adatok invertálására alkalmassá tettük a Cox-Thompson inverz kvantum szórás eljárást. Bose-kondenzátumok ütközéséből származó fázistolás adatokból határoztunk meg effektív Rb-Rb atomi potenciálokat. Kétkomponensű Bose-Einstein kondenzátumok stabilitását vizsgáltuk. Megbecsültük a különző specimenek közti szóráshosszak azon tartományát, amely esetében szoliton gerjesztések létrejöhetnek a kondenzátumban. Kifejelesztettünk és numerikusan teszteltünk egy csatolt Gross-Pitaevskii egyenlet megoldó programot. A kutatási munkatervben vállalt 7 publikáció és 4 konferencia előadást jelentősen túl teljestettük, amennyiben 3 disszertáció, 3 konferenciakiadvány és 25 publiáció született az egy évvel meghosszabbított, 5 éves 4 résztvevős kutatás alatt. Ezen kívül egy nemzetközi inverz kvantum szórás konferenciát is rendeztünk (www.math.bme.hu/~hirvath/iqs).
Results in English
New fix-energy inverse quantum scattering method has been developed. The Cox-Thompson inverse quantum scattering procedure has been made appropriate to invert scattering data. We have determined Rb-Rb atomic scattering potential from data extracted from Bose condensate collisions. Stability of two-component Bose-Einstein condensates has been inversigated. Assessments have been given to values of interspecies scattering length at which soliton excitations are to be expected to exist inside the condensate. We have developed and numerically tested an evolution code which simulate the time evolution of a two-component Bose-Einstein condensate accoring to the Gross-Pitaevskii equation. The original undertaking has been well overcompleted in that 3 theses (1 Phd and 2 DSc), 3 conference contribution and 25 publications in journals of high international reputation have been delivered ba the 4 participants during the 5 years research. Besides also an international inverse quantum scattering conference has been held (www.math.bme.hu/~hirvath/iqs).
Full text http://real.mtak.hu/1673/
Decision
Yes





 

List of publications

  
Horváth Miklós: Inverse scattering with fixed energy and an inverse eigenvalue problemon the half-line, Transactions of the Amer. Math. Soc. 358 (11) (2006) 5161-5177, 2006
Horváth Miklós and Kiss Márton: A bound for ratios of eigenvalues of Schrodinger operators with single-well potentials, Proceedings of the Amer. Math. Soc. 134 (2006) 1425-1434, 2006
Horváth Miklós and Kiss Márton: A bound for ratios of eigenvalues of Schrodinger operators on the real line, Discrete and Continuous Dynamical Systems, Supplement (2005) 403-409, 2005
P. Lévay:: Geometry of three-qubit entanglement, Phys. Rev. A71, 012334, 2005
P. Lévay: On the geometry of a class of N-qubit entanglement monotones, J. Phys. A38 (2005) 9075-9085, 2005
P. Lévay, Sz. Nagy and J. Pipek:: Elementary formula for entanglement entropies of fermionic systems, Phys. Rev. A72, 022302 (2005), 2005
P. Lévay: Geometric Phases, quant-ph/0509064, 2005
P. Lévay: Stringy black holes and the geometry of entanglement,, Phys. Rev. D74, 024030, 2006
P. Lévay: On the geometry of four qubit invariants:, J. Phys. A39 (2006) 9533-9545, 2006
P. Lévay: Strings, black holes, the tripartite entanglement of seven qubits, and the Fano plane, Phys. Rev. D 75, 024024 (2007), 2007
P. Lévay: ''Twistor methods and the geometry of entanglement'', ''Quantum Entanglement and Geometry'', Torun June 4-7, 2006
Schumayer Dániel: Interatomic-potencial inversion from ultracold Bose-gas collision, Few-Body Problems in Physics, FB18, Santos, Sao Paulo, Brasil, Aug. 21-26, 2006
M. Horváth: ''Some properties of the eigenvalues of Sturm-Liouville operators'', International Congress of Mathematicians, August 22-30, 2006, Madrid, 2006
Apagyi Barnabás: Kvantummechanikai potenciálok vizsgálata szóráselméleti módszerekkel, BME Elm. Fiz. Tsz. (2006), http://www.phy.bme.hu/~apagyi/pub2.html, 2006
P. Lévay: Three fermions with six single particle states can be entangled in two inequivalent ways, Phys. Rev. A 78 (2008) 022329, 2008
Schumayer Dániel: Theoretical study od solitonic excitation in Bose-Einstein condensates, BUTE, 2004, http://newton.phy.bme.hu/~schumayer, 2004
P. Lévay: Three-qubit interpretation of BPS and non-BPS STU black holes, Phys. Rev. D76, 106011, 2007
T. Pálmai, M. Horváth and B. Apagyi: Semi-analytic equations to the Cox-Thompson inverse scattering method at fixed energy for special cases, Modern Physics Letters B vol 22, No 23, 2191-2199, 2008
M. Horváth: Inverse problems for linear differential operators, http://www.math.bme.hu/~horvath, 2007
M. Horváth: Notes on the distribution of phase shifts, Modern Physics Letters B vol 22, No 23, 2163-2176, 2008
M. Horváth and M. Kiss: On the stability of inverse scattering with fixed energy, Inverse Problems 25(2009), 015011, 2009
P. Lévay: Three fermions with six single particle states can be entangled in two inequivalent ways, Phys. Rev. A78 (2008) 022329, 2008
Péter Varga and Barnabás Apagyi: Phase estimation procedure to solve quantum-mechanical eigenvalue problems, Phys. Rev. A78 (2008) 022337, 2008
I. Nagy and B. Apagyi: Stopping power of an electron gas for heavy unit charges: models in the kinetic approximation, ADVANCES IN QUANTUM CHEMISTRY, 46 (2004), 2004
Schumayer D and Apagyi B: Stability of static solitonic excitations of two-component Bose-Einstein condensates in finite range of interspecies scattering length $a_{12}$,, Phys. Rev. A, 69 (2004) 043620-1--8., 2004
Horváth Miklós: Inverse spectral problems and closed exponential systems, Annals of Mathematics, 162 (2005) 885-918, 2005
Apagyi B and Schumayer D:: Assessment of interspecies length $a_{12}$ from stability of static solitonic excitations of two-component Bose-Einstein condensates, Eur. Phys. J. B45 (2005) 55-61, 2005
O. Melchert, W. Scheid and B. Apagyi:: Inversion of real and complex phase shifts to potentials by the generalized Cox-Thompson inverse scattering method at fixed energy, J. Phys. G: Nucl. Part. Phys. 32 No 6 (2006) 849-858, 2006
Barnabás Apagyi, Werner Scheid, Oliver Melchert and Dániel Schumayer: Interatomic-potential inversion from ultracold Bose-gas collision, Nuclear Physics A 790 (2007) 767-770, 2007
D. Schumayer, O. Melchert, W. Scheid and B. Apagyi: Effective Rb-Rb inter-atomic potential from ultracold Bose-gas collision, J. Phys. B: At. Mol. Opt. Phys. 41 (2008) 035302, 2008
T. Pálmai, M. Horváth and B. Apagyi: Simplified solutions of the Cox-Thompson inverse scattering method at fixed energy, J. Phys. A 41(23)(2008), 235305, 2008
M. Horváth and B. Apagyi: Solution of the inverse scattering problem at fixed energy for potentials being zero beyond a fixed radius, Modern Physics Letters B vol 22, No 23, 2137-2150, 2008
B. Apagyi and W. Scheid: Quantum inverse scattering problem for coupled channels, Modern Physics Letters B 22 (2008) 2241-2256, 2008



Back »