Beyond Hermiticity: open quantum systems  Page description

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Details of project

 
Identifier
112962
Type K
Principal investigator Lévai, Géza
Title in Hungarian Túl a hermiticitáson: nyitott kvantumrendszerek
Title in English Beyond Hermiticity: open quantum systems
Keywords in Hungarian kvantummechanika, nem-hermitikus modellek, S-mátrix, bomló állapotok, rezonanciák, szóráselmélet, határfeltételek, néhánytest-rendszerek
Keywords in English quantum mechanics, non-Hermitian models, S-matrix, decaying states, resonances, scattering theory, boundary conditions, few-body systems
Discipline
Physics (Council of Physical Sciences)100 %
Ortelius classification: Quantum field theory
Panel Physics
Department or equivalent Laboratory of Theoretical Physics (Institute for Nuclear Research, Hungarian Academy of Sciences)
Participants Cseh, József
Hornyák, István
Kovács, József
Kruppa, András Tibor
Salamon, József Péter
Vajday, László Péter
Vertse, Tamás
Starting date 2014-09-01
Closing date 2019-08-31
Funding (in million HUF) 21.740
FTE (full time equivalent) 17.08
state running project





 

Final report

 
Results in Hungarian
A projekt során a résztvevők egymást kiegészítő tapasztalatát hasznosítottuk nyitott kvantumrendszerek és nem-Hermitikus modellek tanulmányozásához. Vizsgáltuk a kötött, szórási és rezonanciaállapotok leírására alkalmazott fenomenologikus magfizikai potenciálok pólusszerkezetét. Numerikus alkalmazásokhoz kifejlesztettünk egy programot, míg az analitikus és numerikus módszerek kombinálásával realisztikusabb potenciálalakokat dolgoztunk ki. Mikroszkopikus néhánytest-modelleket alkalmaztunk lazán kötött atommagfizikai és atomfizikai rendszerek leírására. A 17O(p,γ)18F reakció adatainak elméleti analízisével hozzásegítettük az Atomki Nukleáris Asztrofizikai Csoportját ahhoz, hogy az asztrofizikai S-faktort pontosabban tudják extrapolálni. Egyes szimmetriaelveket és algebrai módszereket alkalmazva kiterjesztettük az atommagok szerkezetét és reakcióit célzó vizsgálatainkat a mikroszkopikus modellekkel elérhetetlen tömegtartományra. A multikonfigurációs dinamikai szimmetria alkalmazásával különbözö konfigurációkhoz és energiatartományokhoz tartozó atommagspektrumok egységes leírását adtuk, megfogalmazva olyan jóslatokat, amelyeket a kísérletek igazoltak. A kvantummechanika terén egzaktul megoldható potenciálok széles körének (pl. a Natanzon-soztálynak) vezettük be a PT-szimmetrikus változatát. Emellett tárgyaltuk az operátorok szinguláris potenciálokhoz köthető önadjungált kiterjesztését, illetve vizsgáltuk a Natanzon osztályon kívül eső potenciálok megoldásait is.
Results in English
We utilized the complementary experience of the research team in studying open quantum systems and non-Hermitian models. We studied the pole structure of phenomenological potentials used in nuclear physics to describe bound, scattering and resonace states. An advanced computer code was written for numerical studies, while in combined analytical and numerical calculations we focused on developing more realistic potential shapes. We applied microscopic few-body models to describe loosely bound nuclear and atomic physical systems. Our theoretical analysis of the data on the the 17O(p,γ)18F reaction helped the Nuclear Astrophysical Group of Atomki in obtaining more reliable extrapolation of the astrophysical S factor. With the use of symmetry principles and algebraic methods we extended the study of the structural and reaction aspects of nuclei to a mass range, which is prohibitively difficult for most microscopic models. Using the multi-configurational dynamical symmetry, we gave unified description of detailed spectra of different configuration in different energy windows with a prediction that was supported by experiments. In quantum mechanics we described the complex PT-symmetric version of a number of exactly solvable potentials, including the rather wide Natanzon potential class. In addition, we discussed the self-adjoint extension of operators relevant to singular potentials, and studied the solutions of certain potentials beyond the Natanzon class.
Full text https://www.otka-palyazat.hu/download.php?type=zarobeszamolo&projektid=112962
Decision
Yes





 

List of publications

 
Lévai G: PT symmetry in Natanzon-class potentials, International Journal of Theoretical Physics 54: 2724-36, 2015
Baran A, Noszály Cs, Salamon P, Vertse T: Calculating broad neutron resonances in a cut-off Woods-Saxon potential, European Physical Journal A Hadrons and Nuclei 51: 76, 2015
Hornyák I, Kruppa AT: An algorithm for the calculation of the partial wave expansion of the Coulomb-distorted plane wave, Computer Physics Communications (in press), 2015
Kruppa AT, Vajday L: Translates of exponential monomials on some two-point support hypergroups, Journal of Mathematical Analysis (in press), 2015
Cseh J, Riczu G: Quartet excitations and cluster spectra in light nuclei, Phys. Lett. B (submitted), 2015
Id Betan RM, Kruppa AT, Vertse T: Shadow poles in a coupled-channel problem calculated with Berggren basis, Phys. Rev. C (submitted), 2015
Baran A, Noszály Cs, Salamon P, Vertse T: Calculating broad neutron resonances in a cut-off Woods-Saxon potential, European Physical Journal A Hadrons and Nuclei 51: 76, 2015
Hornyák I, Kruppa AT: An algorithm for the calculation of the partial wave expansion of the Coulomb-distorted plane wave, Computer Physics Communications 197 291, 2015
Kruppa AT, Vajday L: Translates of exponential monomials on some two-point support hypergroups, Journal of Mathematical Analysis Vol. 6, Issue 3, Paper 2, 2015
Cseh J, Riczu G: Quartet excitations and cluster spectra in light nuclei, Phys. Lett. B 757 312, 2016
P. Salamon, Á. Baran, T. Vertse,: Distribution of the S-matrix poles in Woods-Saxon and cut-off Woods-Saxon potentials, Nucl. Phys. A 952 1, 2016
G. Lévai, Á. Baran, P. Salamon, T. Vertse: Analytical solutions for the radial Scarf II potential, submitted to J. Phys. A:Math. Theor., 2016
S. Shubhchintak, C. A. Bertulani, A. M. Mukhamedzhanov, A. T. Kruppa: Radiative nucleon capture with quasi-separable potentials, submitted to J. Phys. G:Nucl. Part. Phys., 2016
L. Székelyhidi, L. Vajday: Spectral Synthesis on Commutative Hypergroups, Annales Univ. Sci. Budapest., Sect. Comp., in press, 2016
G. Lévai: Exactly solvable PT-symmetric models, Imperial College Press, submitted, 2016
G. Lévai: Accidental crossing of energy eigenvalues in PT-symmetric Natanzon-class potentials, submitted to Annals of Physics (N. Y.), 2016
P. Adsley, D.G. Jenkins, J. Cseh, S.S. Dimitriova, J.W. Brummer, K. C. W. Li, D. J. Marin-Lambarri, K. Lukyanov, N.Y. Kheswa, R. Neveling, P. Papka, L. Pellegri, V. Pesudo, L.C. Pool, G. Riczu, F.D. Smit, J.J. van Zyl, E. Zemlyanaya: Alpha clustering in 28Si probed through the identification of high-lying 0+ states, arXiv 1609.00296 [nucl-ex], submitted to Phys. Rev. C, 2016
G. Lévai: Semimicroscopic algebraic description of alpha clustering in Ne isotopes, J. Phys. Conf. Ser., submitted, 2016
G. Lévai, Á. Baran, P. Salamon, T. Vertse: Analytical solutions for the radial Scarf II potential, Phys. Lett. A 381 1936, 2017
S. Shubhchintak, C. A. Bertulani, A. M. Mukhamedzhanov, A. T. Kruppa: Radiative nucleon capture with quasi-separable potentials, J. Phys. G:Nucl. Part. Phys. 43 125203, 2016
L. Székelyhidi, L. Vajday: Spectral Synthesis on Commutative Hypergroups, Annales Univ. Sci. Budapest., Sect. Comp. 45 111, 2016
G. Lévai: Exactly solvable PT-symmetric models, Imperial College Press, submitted, 2017
G. Lévai: Accidental crossing of energy eigenvalues in PT-symmetric Natanzon-class potentials, Annals of Physics (N. Y.) 380 1, 2017
P. Adsley, D.G. Jenkins, J. Cseh, S.S. Dimitriova, J.W. Brummer, K. C. W. Li, D. J. Marin-Lambarri, K. Lukyanov, N.Y. Kheswa, R. Neveling, P. Papka, L. Pellegri, V. Pesudo, L.C. Pool, G. Riczu, F.D. Smit, J.J. van Zyl, E. Zemlyanaya: Alpha clustering in 28Si probed through the identification of high-lying 0+ states, Phys. Rev. C 95 024319, 2017
G. Lévai: Semimicroscopic algebraic description of alpha clustering in Ne isotopes, J. Phys. Conf. Ser., 863 012017, 2017
Gy. Gyürky, A. Ornelas, Zs. Fülöp, Z. Halász, G.G. Kiss, T. Szücs, R. Huszánk, I. Hornyák, I. Rajta, and I. Vajda: Cross section measurement of the astrophysically important 17O(p,gamma)18F reaction in a wide energy range, Phys. Rev. C 95 035805, 2017
P. Salamon, T. Vertse: Smoothed square well potential, Eur. Phys. J. A 53 152, 2017
J. Cseh, G. Riczu, J. Darai, T. Dytrych, E. Betak: Exotic shapes and exotic symmetries, Submitted to Physica Scrpita, 2017
G. Lévai, A. M. Ishkhanyan: Exact solutions of the sextic oscillator from the bi-confluent Heun equation, Submitted to J. Phys. A:Math. Theor., 2017
K. Drumev, A Georgieva, J. Cseh: Phases and phase pransitions in the algebraic microscopic pairing-plus-quadrupole model: Role of the single-sarticle term in the Hamiltonian, Nuclear Theory, 2016
E. Betak, J. Cseh: State density formalism of the Iwamoto-Harada model : A suitable tool to treat cluster emission from heavy-ion collisions with account for spin variables, Submitted to Proc. International Conference On Nuclear Data, Bruges, Belgium, 11-16 Sep 2016, 2017
Á. Baran, T. Vertse: Matching polynomial tails to the cut-off Woods-Saxon potential, Submitted to the International Journal of Modern Physics E, 2017
I. Hornyák and A.T. Kruppa: Hylleraas and Kinoshita wave functions with correct cusp conditions, Submitted to Phys. Rev. A, 2017
G. Lévai, J. Kovács: The finite PT-symmetric square well potential, Submitted to Phys. Lett. A, 2017
Id Betan RM, Kruppa AT, Vertse T: Shadow poles in a coupled-channel problem calculated with Berggren basis, Phys. Rev. C 97 (2018) 024307, 2018
G. Lévai: Exactly solvable PT-symmetric models, PT symmetry in quantum and classical physics, C. M. Bender et al., Worl Scientific, ISBN 978-1-78634-595-0, 2018
J. Cseh, G. Riczu, J. Darai, T. Dytrych, E. Betak: Shapes, quartets and clusters of atomic nuclei in a semimicrsocopic framework, Bulgarian Journal of Physics 44 (2017) 466., 2017
G. Lévai, A. M. Ishkhanyan: Exact solutions of the sextic oscillator from the bi-confluent Heun equation, Submitted to Mod. Phys. Lett. A, 2018
K. Drumev, A Georgieva, J. Cseh: Phases and phase pransitions in the algebraic microscopic pairing-plus-quadrupole model: Role of the single-sarticle term in the Hamiltonian, Nuclear Theory 35 (2016) 263, 2016
E. Betak, J. Cseh: State density formalism of the Iwamoto-Harada model : A suitable tool to treat cluster emission from heavy-ion collisions with account for spin variables, EPJ Web of Conferences 146 (2017) 12023., 2017
Á. Baran, T. Vertse: Matching polynomial tails to the cut-off Woods-Saxon potential, International Journal of Modern Physics E 26 (2017) 17500078, 2017
I. Hornyák and A.T. Kruppa: Hylleraas and Kinoshita wave functions with correct cusp conditions, Physical Review A 96 (2017) 052506(7), 2017
G. Lévai, J. Kovács: The finite PT-symmetric square well potential, Submitted to J. Phys. A, 2018
J. Cseh, R. Trencsényi: On the symmetries of the 12C nucleus, International Journal of Modern Physics E 27 (2018) 1850013., 2018
K. P. Drumev, A. I. Georgieva, J. Cseh: Phases in an algebraic shell model of atomic nuclei, Nuclear Theory, Vol. 36, eds. M. Gaidarov, N. Minkov Heron Press, Sofia (Bulgaria) 2017, p. 261., 2017
G. Lévai: PT symmetry in Natanzon-class potentials, International Journal of Theoretical Physics 54: 2724-36, 2015
Á. Baran, Cs. Noszály, P. Salamon, T. Vertse: Calculating broad neutron resonances in a cut-off Woods-Saxon potential, European Physical Journal A Hadrons and Nuclei 51: 76, 2015
I. Hornyák, A. T. Kruppa: An algorithm for the calculation of the partial wave expansion of the Coulomb-distorted plane wave, Computer Physics Communications 197 291, 2015
A. T. Kruppa, L. Vajday: Translates of exponential monomials on some two-point support hypergroups, Journal of Mathematical Analysis Vol. 6, Issue 3, Paper 2, 2015
J. Cseh, G. Riczu: Quartet excitations and cluster spectra in light nuclei, Phys. Lett. B 757 312, 2016
Id Betan RM, Kruppa AT, Vertse T: Shadow poles in a coupled-channel problem calculated with Berggren basis, Phys. Rev. C 97 (2018) 024307, 2018
P. Salamon, Á. Baran, T. Vertse,: Distribution of the S-matrix poles in Woods-Saxon and cut-off Woods-Saxon potentials, Nucl. Phys. A 952 1, 2016
G. Lévai, Á. Baran, P. Salamon, T. Vertse: Analytical solutions for the radial Scarf II potential, Phys. Lett. A 381 1936, 2017
S. Shubhchintak, C. A. Bertulani, A. M. Mukhamedzhanov, A. T. Kruppa: Radiative nucleon capture with quasi-separable potentials, J. Phys. G:Nucl. Part. Phys. 43 125203, 2016
L. Székelyhidi, L. Vajday: Spectral Synthesis on Commutative Hypergroups, Annales Univ. Sci. Budapest., Sect. Comp. 45 111, 2016
G. Lévai: Exactly solvable PT-symmetric models, PT symmetry in quantum and classical physics, C. M. Bender et al., Worl Scientific, ISBN 978-1-78634-595-0, 2018
G. Lévai: Accidental crossing of energy eigenvalues in PT-symmetric Natanzon-class potentials, Annals of Physics (N. Y.) 380 1, 2017
P. Adsley, D.G. Jenkins, J. Cseh, S.S. Dimitriova, J.W. Brummer, K. C. W. Li, D. J. Marin-Lambarri, K. Lukyanov, N.Y. Kheswa, R. Neveling, P. Papka, L. Pellegri, V. Pesudo, L.C. Pool, G. Riczu, F.D. Smit, J.J. van Zyl, E. Zemlyanaya: Alpha clustering in 28Si probed through the identification of high-lying 0+ states, Phys. Rev. C 95 024319, 2017
G. Lévai: Semimicroscopic algebraic description of alpha clustering in Ne isotopes, J. Phys. Conf. Ser., 863 012017, 2017
Gy. Gyürky, A. Ornelas, Zs. Fülöp, Z. Halász, G.G. Kiss, T. Szücs, R. Huszánk, I. Hornyák, I. Rajta, and I. Vajda: Cross section measurement of the astrophysically important 17O(p,gamma)18F reaction in a wide energy range, Phys. Rev. C 95 035805, 2017
P. Salamon, T. Vertse: Smoothed square well potential, Eur. Phys. J. A 53 152, 2017
J. Cseh, G. Riczu, J. Darai, T. Dytrych, E. Betak: Shapes, quartets and clusters of atomic nuclei in a semimicrsocopic framework, Bulgarian Journal of Physics 44 (2017) 466., 2017
G. Lévai, A. M. Ishkhanyan: Exact solutions of the sextic oscillator from the bi-confluent Heun equation, Mod. Phys. Lett. A 34 1950134, 2019, 2019
K. Drumev, A Georgieva, J. Cseh: Phases and phase pransitions in the algebraic microscopic pairing-plus-quadrupole model: Role of the single-sarticle term in the Hamiltonian, Nuclear Theory 35 (2016) 263, 2016
E. Betak, J. Cseh: State density formalism of the Iwamoto-Harada model : A suitable tool to treat cluster emission from heavy-ion collisions with account for spin variables, EPJ Web of Conferences 146 (2017) 12023., 2017
Á. Baran, T. Vertse: Matching polynomial tails to the cut-off Woods-Saxon potential, International Journal of Modern Physics E 26 (2017) 17500078, 2017
I. Hornyák and A.T. Kruppa: Hylleraas and Kinoshita wave functions with correct cusp conditions, Physical Review A 96 (2017) 052506(7), 2017
G. Lévai, J. Kovács: The finite PT-symmetric square well potential, J. Phys. A 52 025302, 2019, 2019
J. Cseh, R. Trencsényi: On the symmetries of the 12C nucleus, International Journal of Modern Physics E 27 (2018) 1850013., 2018
J. Hong, C. A. Bertulani, A. T. Kruppa: Neutron removal from the deformed halo nucleus 31Ne, Phys. Rev. C 96 064603, 2017, 2017
J. Kovács, G. Lévai: On the common limit of the PT-symmetric Rosen-Morse II and finite square well potentials, Acta Polytechnica 57 412, 2017, 2017
Á. Baran, Cs. Noszaly, T. Vertse: JOZSO, a computer code for calculating broad neutron resonances, Computer Physics Communications 228 185, 2018, 2018
A. T. Kruppa, J. Kovács, I. Hornyák: Description of two-electron atoms with correct cusp conditions, J. Phys. B , in press, 2019
A. M. Ishkhanyan, G. Lévai: Hermite function solutions of the Schrödinger equation for the sextic oscillator, Journal of Mathematical Physics, submitted, 2019
Á. Baran, T. Vertse: Dumping the tail of the Woods-Saxon potential, Nucl. Phys. A, submitted, 2019
G. Lévai, T. Soltész: Unified supersymmetric transformations for the harmonic oscillator and its rational extensions, European Journal of Physics, submitted, 2019
G. Lévai, J. M. Arias: Extending the exact solutions of the sextic oscillator, In preparation; to be submitted in October 2019, 2019





 

Events of the project

 
2019-06-25 12:20:45
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