January 12, 2006Physics Institute, Prague1 PT-symetrické modely v kvantové fyzice: novinky z konference (Stellenbosch, listopad 2005)

Prezentace na téma: "January 12, 2006Physics Institute, Prague1 PT-symetrické modely v kvantové fyzice: novinky z konference (Stellenbosch, listopad 2005)"— Transkript prezentace:

1 January 12, 2006Physics Institute, Prague1 PT-symetrické modely v kvantové fyzice: novinky z konference (Stellenbosch, listopad 2005)

2 January 12, 2006Physics Institute, Prague2 Otázka první: No jo, novinky, ale v jaké oblasti fyziky? Odpověď (v uspořádání podle řečníků): Scholz, Geyer, Heiss: jaderná fyzika Mostafazadeh: relativistická QM Bender: teorie pole a kosmologie Berry: optika Günther: magnetohydrodynamika a další: statistika,nelin.f.,SUSY,atom.f.

3 January 12, 2006Physics Institute, Prague3 Otázka druhá: jestliže novinky, pak napřed to nejzajímavější Uspořádání vyjde skoro stejně: Scholz, Geyer: o jednoznačnosti Θ Mostafazadeh: klasická limita PTSQM Bender: usnadnění regularizace Feyn.d. Berry, Ahmed: singularity, wedge-edge Günther, Kirillov: okolí EP, klasifikace Jones: Thirring, sine-Gordon (+rand.m.)

4 January 12, 2006Physics Institute, Prague4 Napřed ale krátká rekapitulace PTT: nehermitovské H – levé a pravé stavy matem.: nutnost dokázat realitu spektra modif. Dir. značení: biorthogonalita, bi-úplnost, spektr.repr. cíl: fyzika. Potřeba vybrat metriku Ө a inovovat principy korespondence; v tomto smyslu je PT pouhá technikalita

5 January 12, 2006Physics Institute, Prague5 No a teď k prvnímu tématu: připomínám: jedná se o starý problém nejednoznačnosti Θ s jadernou motivací v Dysonově IBM trfci herm. -> neherm. hlavní výhoda: zjednodušení výpočtů hlavní pokrok: Scholz (anglicky: PTO)

6 January 12, 2006Physics Institute, Prague6 1.Important results on the ambiguity of physical metrics Scholz (and Kriel): a transfer of ambiguity to PDE boundary conditions (inspired by Moyal, using Weber’s flow equations) added by A. M.: the disappearance of the ambiguity in the classical limit added by H.G. and H. J.: illustration in the Swanson's creation/annihilation model

7 January 12, 2006Physics Institute, Prague7 a.A transfer of ambiguity to PDE boundary conditions Frederik Scholtz Metrics and more from Moyal products [idea and ix^3 illustration] Johannes N Kriel Solving non-perturbative flow equations [Poster, some details of the method]

8 January 12, 2006Physics Institute, Prague8 b. Ambiguities and their disappearance in classical limit Ali Mostafazadeh (Koc/Istanbul, Turkey) Dynamically Equivalent but Kinematically Distinct Pseudo-Hermitian Quantum Systems [example: ix^3]

9 January 12, 2006Physics Institute, Prague9 c. Ambiguities in the Swanson's creation/annihilation model Hendrik Geyer Choice of physical operators and uniqueness of the metric [three different closed formulae for the metric in Hilbert space]

10 January 12, 2006Physics Institute, Prague10 Přišel čas na druhé téma: připomínám: očekává se vybudování klasické mechaniky s komplexním x či p hlavní nevýhoda: třista let to nikoho nenapadlo hlavní pokrok: Ali M. (anglicky: PTO)

11 January 12, 2006Physics Institute, Prague11 2. PT-symmetric-like systems in classical kinematical regime Bender: HO phase-space trajectories Berry: numerical experiments in optics Uwe G.: α-dynamos

12 January 12, 2006Physics Institute, Prague12 a. HO phase-space trajectories from complex initial bc's Carl M Bender (St Louis, USA) Some new results on PT-symmetric classical and quantum mechanics [N-tuple winding phenomenon – chaos?]

13 January 12, 2006Physics Institute, Prague13 b. Numerical experiments in optics Michael V Berry (Bristol, UK) The optical singularities of bianisotropic crystals (-> D. Heiss: two-by-two model)

14 January 12, 2006Physics Institute, Prague14 c. Fourth-order spectral branch points in MHD dynamos Uwe Günther Bundle stratification of PT-symmetric 4x4 matrix systems [exceptional points - cf. also K. and M.]

15 January 12, 2006Physics Institute, Prague15 Třetí okruh otázek a odpovědí věnován bohapustějším spekulacím a proto nejzajímavější pro lidi jako já; ale přejděme raději zase do angličtiny:

16 January 12, 2006Physics Institute, Prague16 3. Key innovations within quasihermitian QM itself reflectionless models for cosmology [edge-of-the-wedge bc’s, ABB] Kleefeld: De-Broglie-Bohm quantization M. Z.: coupled-channel models and the concept of RT symmetry (details later)

17 January 12, 2006Physics Institute, Prague17 a. Edge-of-the-wedge bc's Zafar Ahmed (Bhabha Atomic Research Centre, Mumbai, India) [with Bender and Berry – both see elsewhere]

18 January 12, 2006Physics Institute, Prague18 b. De-Broglie-Bohm-like approach to PT quantization Frieder Kleefeld Non-Hermitian Quantum Theory and the Correspondence Principle [remember Prague]

19 January 12, 2006Physics Institute, Prague19 c. The concept of RT symmetry Miloslav Znojil (CAS, Prague) Coupling of channels in PT-symmetric models [Rotation R need not be Hermitian] Lecture on the web: [.pdf] - 131kb

20 January 12, 2006Physics Institute, Prague20 Dříve než dodám podrobnosti, o svém díle, vraťme se ještě v rychlosti k nelineárním modelům, k relativistickým modelům, k některým vzrušujícím leč čistě matematickým studiím, a konečně i k seznamu témat o nichž se nezmíním vrátane „satelitního” tématu „RMT”.

21 January 12, 2006Physics Institute, Prague21 4. Nonlinear physical models Hugh Jones: Sine-Gordon and massive Thirring E-M. Graefe: Finite-dimensional matrix nonlinear Schroedinger equation

22 January 12, 2006Physics Institute, Prague22 a. Sine-Gordon and massive Thirring models Hugh Jones Equivalent Hamiltonians for PT-symmetric versions of dual 2-dimensional field theories [form invariance]

23 January 12, 2006Physics Institute, Prague23 5. Relativistic physical models Ali Mostafazadeh: First-quantized Klein Gordon systems C. Berkdemir: Dirac equation – solvable cases

24 January 12, 2006Physics Institute, Prague24 a. First-quantized Klein Gordon system Ali Mostafazadeh (Koc/Istanbul, Turkey) Dynamically Equivalent but Kinematically Distinct Pseudo-Hermitian Systems [freedom and limitations]

25 January 12, 2006Physics Institute, Prague25 6. New mathematical methods Rigorous proofs of the reality of energies Perturbation theory Zeros of polynomials

26 January 12, 2006Physics Institute, Prague26 a. Rigorous proofs using the method of TQ equation Patrick Dorey On the reality (and unreality) of PT-symmetric quantum mechanics [see Shizuoka]

27 January 12, 2006Physics Institute, Prague27 b. Perturbation theory Oleg Kirillov Perturbation theory for non-self-adjoint operator matrices and its application to the MHD a^2 -dynamo

28 January 12, 2006Physics Institute, Prague28 c. Zeros of polynomials Stefan Weigert Detecting “Broken” PT-Symmetry [19th century mathematics]

29 January 12, 2006Physics Institute, Prague29 7. and miscellanea delta pot.: Uncu, num.: Weideman stability of perturbations: Caliceti collective Field Theory (Feinberg) Lipkin model (Heiss) pseudo-norms (Lévai) exceptional points (Mailybaev) unbound states (Mondragon)

30 January 12, 2006Physics Institute, Prague30 Satellite section: Non-Hermitian random-matrix models Hatano-Nelson, QCD with chem. pot. Jacobus Verbaarschot (Stony Brook, USA) Statistical physics structures Joshua Feinberg (Haifa, Israel) Unexpected links Maciej Nowak (Krakow, Poland)

31 January 12, 2006Physics Institute, Prague31 No a dočkali jsme se: teď moje vlastní nejnovější výsledky