Welcome to the website supporting the virtual seminar series on Pseudo-Hermitian Hamiltonians in Quantum Physics.

This virtual seminar series is part of the regular real life seminar series on Pseudo-Hermitian Hamiltonians in Quantum Physics that was initiated by Miloslav Znojil in 2003. It is intended to bridge the gap, caused by the COVID-19 pandemic, between the real life XIXth meeting and the upcoming XXth meeting in Santa Fe in 2021. For past events see the PHHQP website. The subject matter of this series is the study of physical aspects of non-Hermitian systems from a theoretical and experimental point of view. Of special interest are systems that possess a PT-symmetry (a simultaneous reflection in space and time).

Proceedings: Journal of Physics: Conference Series Volume 2038


Upcoming : Géza Lévai, (Institute for Nuclear Research, Hungary), 03/02, 15:00 London time (=15:00 GMT)

Do similar potential shapes lead to similar physical results? A case study with two PT-symmetric potentials

Abstract: It is often possible to guess the main characteristics of quantum mechanical potentials without solving them exactly or numerically. For example, the shape of the potential gives a hint of where the maximum of the wave functions can be expected; its asymptotic behavior is a telling sign on whether the number of bound states is finite or infinite, etc. This intuitive approach works for most real potentials, however, the situation changes for complex potentials.

Here we discuss two such potentials that have similar shape: the PT-symmetric Rosen-Morse II and the finite PT-symmetric square well potentials. Their real compoment is the Pöschl-Teller hole [VR~ -sech2(x)] and the finite real square well, while their imaginary component is the tanh(x) function and the constant function outside the boundaries of the real square well. The question we address is whether the physical characteristics of the two potential show any similarity. The PT-symmetric Rosen-Morse II potential has the special feature that it supports exclusively real energy eigenvalues [2], no matter how large the coupling coefficient of its imaginary component is. Increasing it leds to rapidly increasing real eigenvalues, rather than to their complexification. This finding has been attributed to the asymptotically non-vanishing imaginary potential component. The finite PT-symmetric square well was discussed only recently [2], inspired by this unusual finding.

We present an analytical proof that the energy eigenvalues
of the PT-symmetric square well potential are also real. We
also derive the transmission and reflection coefficients,
demonstrate that they exhibit handedness and link them with
the bound states. Some important differences are also pointed out. As a consistency check, we also analyse the common limit of the two potentials: the potential with a Dirac-delta and the step function as its real, and imaginary component, respectively [3].

[1] G. Lévai and E. Magyari, J. Phys. A:Math. Theor. 42 (2009) 195302

[2] G. Lévai and J. Kovács,  J. Phys. A:Math. Theor. 52 (2019) 025302

[3] J. Kovács and G. Lévai, Acta Polytechnica 57 (2017) 412

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Upcoming seminars

Géza Lévai, 03/02, 15:00 London time (=15:00 GMT)

Do similar potential shapes lead to similar physical results?
A case study with two PT-symmetric potentials

Aurelia Chenu, 17/02, 15:00 London time (=15:00 GMT)

From hybrid polariton to dipolariton using non-Hermitian Hamiltonians to handle particle lifetimes

Adolfo del Campu, 03/03, 15:00 London time (=15:00 GMT)

Spectral Filtering Induced by Non-Hermitian Evolution with Balanced Gain and Loss: Enhancing Quantum Chaos

Carl Bender, 17/03, 15:00 London time (=15:00 GMT)


The Seminars 2021: Term II – XIX(opens in a new tab)

Complete list of speakers

  1. Ali Mostafazadeh, (Koç University, Turkey) 07/05
  2. Nick Mavromatos, (King’s College, Uni. of London, UK) 14/05
  3. Phillip Mannheim, (University of Connecticut, US) 21/05
  4. Fabio Bagarello, (University of Palermo, Italy) 04/06
  5. Dorje Brody, (University of Surrey, UK) 18/06
  6. Savannah Garmon, (Osaka Prefecture University, Japan) 02/07
  7. Yogesh Joglekar, (Indiana Uni. Purdue University, US) 16/07
  8. Andrei Smilga, (University of Nantes, France) 23/07
  9. Eva-Maria Graefe, (Imperial College London, UK) 30/07
  10. Avadh Saxena, (Los Alamos National Laboratory, US) 13/08
  11. Li Ge, (City University of New York, US) 20/08
  12. Carl Bender, (Washington University in St. Louis, US) 27/08
  13. Vladimir Konotop, (Universidade de Lisboa, Portugal) 10/09
  14. Joshua Feinberg, (University of Haifa and Technion, Israel) 24/09
  15. Bhabani Prasad Mandal, (BHU, Varanasi, India) 08/10
  16. Stéphane Boris Tabeu, (University of Yaounde, Cameroon) 15/10
  17. Naomichi Hatano, (University of Tokyo, Japan) 22/10
  18. Stefan Rotter, (Vienna University of Technology, Austria) 05/11
  19. Maxim Chernodub, (Inst Denis Poisson, CNRS, France) 12/11
  20. Pijush Ghosh, (Siksha-Bhavana, Visva-Bharati, India) 19/11
  21. Mikhail Plyushchay, (Universidad de Santiago, Chile) 03/12
  22. Qing-hai Wang, (National Univ. of Singapore, Singapore) 17/12
  23. Gonzalo Muga, (University of the Basque Country, Spain) 14/01
  24. Stella Schindler, (Massachusetts Institute of Technology, US) 21/01
  25. Miloslav Znojil, (Nucl. Phys. Inst. of the AS, Czech Republic) 28/01
  26. Roman Riser, (University of Haifa, Israel) 11/02
  27. Duncan O’Dell, (McMaster University, Canada) 25/02
  28. Mustapha Maamache, (Ferhat Abbas University, Algeria) 11/03
  29. Andreas Ruschhaupt, (University College Cork, Ireland) 01/04
  30. Hamidreza Ramezani, (Univ. of Texas Rio Grande Valley, US) 08/04
  31. Andreas Fring, (City, University of London, UK) 22/04
  32. Andrew Harter, (University of Tokyo, Japan) 06/05
  33. Özlem Yeşiltaş, (Gazi University, Turkey) 20/05
  34. Iveta Semorádová, (Czech Techn. Univ. Prague, Czech Republic) 03/06
  35. Hugh Jones, (Imperial College London, UK) 17/06
  36. Marta Reboiro, (University of La Plata, Argentina) 01/07
  37. Ken Mochizuki, (Tohoku University, Japan) 15/07
  38. Daniel Dizdarevic, (Universität Stuttgart, Germany) 29/07
  39. Philip Mannheim, (University of Connecticut, US) 09/09
  40. Latevi Lawson, (African Inst. for Math. Sciences, Ghana) 23/09
  41. Jacob Muldoon, (Indiana University Purdue University, US) 30/09
  42. Ross Wakefield, (University of Bristol, UK) 30/09
  43. Abdelhafid Bounames, (University of Jijel, Algeria) 30/09
  44. Himadri Barman, (Zhejiang University, China) 30/09
  45. Andrei Smilga, (University of Nantes, France) 07/10
  46. Takanobu Taira (City, University of London, UK) 14/10
  47. Rebecca Tenney (City, University of London, UK) 14/10
  48. Akhil Kumar, (Indian Inst. of Science Educ. and Res., India) 14/10
  49. Kaustubh Argarwal, (Indiana University Purdue University, US) 14/10
  50. Federico Roccati, (Università degli Studi di Palermo, Italy) 21/10
  51. Ali Mostafazadeh, (Koç University, Turkey) 04/11
  52. Yogesh Joglekar, (Indiana Uni. Purdue University, US) 18/11
  53. Fabio Bagarello, (Università degli Studi di Palermo, Italy) 02/12
  54. Kohei Kawabata, (University of Tokyo, Japan) 09/12
  55. Tsuneya Yoshida, (University of Tsukuba, Japan) 16/12
  56. Kazuki Yokomizo, (RIKEN National Science Institute, Japan) 06/01
  57. Hamed Ghaemidizicheh, (Univ. Texas Rio Grande Valley, US) 20/01
  58. Géza Lévai, (Institute for Nuclear Research, Hungary) 03/02
  59. Aurelia Chenu, (University of Luxembourg, Luxembourg) 17/02
  60. Adolfo del Campo, (University of Luxembourg, Luxembourg) 03/03
  61. Carl Bender, (Washington University in St. Louis, US) 17/03
  62. Micheline Soley, (Yale Quantum Institute, US) 31/03
  63. Michael Lubasch, (Quantinuum Ltd, UK) 14/04