02.12. 14. In Search of Fundamental Symmetries

1. 02.12. 14. In Search of Fundamental Symmetries Broken symmetry in nonrelativistic physics and Theory of Polarons A.V.Tulub

2. Broken symmetry in non relativistic physics • 1. Electronic structure calculations • 2. Molecular structure. • 3. Translational invariance. • 4. Polaron theory.

3. Polarons Theory. Pekar broken symmetry solution arise from the wave function structure

4. Translational invariance 1.S.V. Tyablikov. An Adiabatic Form of perturbation Theory in the Problem of the interaction of a particle with a Quantum Field. JETP.21, P. 377,(1951). « Пекар пытался учесть трансляционное вырождение в задаче о поляроне, однако непоследовательный учет этого вырождения и полуклассическое рассмотрение кристалла требует весьма осторожного обращения с результатами Пекара» 2. Fröhlich, H.Pelzer, S. Zienau. Phil.Mag. 41,221,1951. «Электрон, несмотря на поляризацию, может свободно перемещаться по кристаллу» . Боголюбов Н.Н. 3. Translational invariance.The introduction of a classical field. Motion of a superfluid in a narrow canal and Josephson effect. JETP.V. 61,P.1986,1971 (with B.Lukin)

5. Сarge transfer in DNA. D.Porath et al, Nature, 403, (2000), 635

6. Holstein Hamiltonian

7. DNA-molecule in a practice Биочип

8. Literature • 1. S.I. Pekar. Theory of Polarons. JETP.19, P.796, (1949). • 2. S.V. Tyablikov. An Adiabatic Form of perturbation Theory in the Problem of the interaction of a particle with a Quantum Field. JETP.21, P. 377,(1951). 3. T.D. Lee, F. Low, D. Pines. The Motion of slow Electrons in a Polar Crystal. Phys.Rev.90,P.297, (1953). • 4.R.P. Feynmann. Slow electrons in a Polar Crystals. Phys.Rev.V.97, P.660, (1955). • 5. E.P.Gross. Phys.Rev.V.100,1671,(1955). • 6. A.V.Tulub. Phonon interactions of electrons in polar crystals.. JETP.V34,P.1641, (1958). • 7. A.V.Tulub. On the theory of cyclotron resonance in polar crystals. JETP.V38,№ 2,P.565., (1959). • 8. A.V.Tulub. Mean free path of an exiton in polar crystals. JETP.V39,№ 6,P.1859 (1959). • 9. A.V.Tulub. Recoil Effect in Quantum Field Theory. Vestnik Leningrad Uni.22,P.104,(1960). • 10. A.V.Tulub. Slow electrons in a Polar Crystals.JETP.V41,P.1828, (1961). • Present works • 1 . N. I. Kashirina.Application of Quantum Field Theory Methods to the Development • of the translation –invariant Polaron and Bipolaron Theory.Ukr.J.Phys.2014,V.59, №11, P.2071. • 2. V.D.Lakhno. Large –radius Holstein polaron and the problem of spontaneous • symmetry breaking. Progress in Theoretical and Experimental Physics.2014 ( Japan). • 3. N. I. Kashirina. V.D.Lakhno, A.V.Tulub. JETP.,141,924,(2012). • Kashirina • «Weak or intermediate coupling should be realized in real crystal»

9. 1 . N. I. Kashirina.Application of Quantum Field Theory Methods to the Development of the translation –invariant Polaron and Bipolaron Theory. Ukr.J.Phys.2014,V.59, P.2071. 2. V.D.Lakhno. Large –radius Holstein polaron and the problem of spontaneous symmetry breaking. Progress in Theoretical and Experimental Physics.2014 ( Japan).

10. Theory of Polarons. (1) Elimination of electron coordinates (2) Self interaction field. Were is the mass of a polaron?

11. Scattering. The mean free path The ground state wave function Scattering amplitude Resonance structure of the scattering amplitude depends on the value of the coupling constant. Max. value of the coupling constant.

12. Numerical value. Polaron energy as the function of coupling constant. • Try function f of the coupling constant. • F = -NV exp(-k2/2a2) N. I. Kashirina.Application of Quantum Field Theory Methods to the Development of the translation –invariant Polaron and Bipolaron Theory.Ukr.J.Phys.2014,V.59, №11, P.2071.

13. Instead of an electron an atom. Symmetry breaking. Difference between left and right polarization in He-Ne laser. • 1. N.N. Rozanov, A.V. Tulub// Doklady USSR V. 165,№ 6, P.1280.(1965) • 2. N.N. Rozanov, A.V.Tulub // Doklady USSR V. 181,№ 4, P.830(1968) a) quantum field, 2) classical field. Nonlinear effectin a magnetic field A. V. Tulub. // New derivation of the of the formulas of nonlinear susceptibilities. Doklady USSR .V. 212, ,P. 584 1972.

14. Superconductivity. 1. G.M. Eliashberg. «Interaction between electrons and lattice vibrations in a superconductor» JETP.V.38,P.966,(1960).Frolich Hamiltonian. 2, Superconductivity arise primarily from a from magnetic coupling, induced attraction interaction. Inverse isotope effect. Journal Phys. Soc. Japan V.78,№ 9,P. 094718

15. Kamihara et al. // Superconductivity in Iron Compounds. (Journ. Amer.Chem. Soc. V.130,P,3296 (2008). Symmetry Braking in a molecular structure. Fe(2) molecule in a free space and in the embedding. Superconductivity arise primarily from a from magnetic coupling, involving the ground as well the excited states. Ground and excited spin states of the molecular cluster Fe(2)Si(18). CI –method.

16. Fe(2)Si(18). Ferromagnetic coupling. Ground state.Total spin S=4. • r(Fe1Si14)=3.027, r(Fe1Si17)=3.029,r(Fe1Si15)=2.578, r(Fe1Si18)=2.578,r(Fe1Si16)=2.591, r(Fe1Si19)=2.591,r(Fe1Si8)=2.906, r(Fe1Si5)=2.908,r(Fe1Si3)=2.951, r(Fe1Si6)=2.952,r(Fe1Si4)=2.934, r(Fe1Si7)=2.933,r(Fe1Fe2)=2.817,r(Fe2Si8)=3.535, r(Fe2Si5)=3.537,r(Fe2Si3)=2.833, r(Fe2Si6)=2.834,r(Fe2Si4)=2.829, r(Fe2Si7)=2.829,r(Fe2Si20)=2.768, r(Fe2Si11)=2.768,r(Fe2Si9)=2.647, r(Fe2Si12)=2.648,r(Fe2Si10)=2.646, r(Fe2Si13)=2.645 • q(Fe1)=1.749, q(Fe2)=0.889,q(Si14)=0.306, q(Si17)=0.308,q(Si15)=‑0.432, q(Si18)=‑0.433,q(Si16)=‑0.422, q(Si19)=‑0.420,q(Si8)=‑0.003, q(Si5)=‑0.002,q(Si3)=‑0.284, q(Si6)=‑0.282,q(Si4)=‑0.298, q(Si7)=‑0.300,q(Si20)=0.162, q(Si11)=0.163,q(Si9)=‑0.175, q(Si12)=‑0.176,q(Si10)=‑0.175, q(Si13)=‑0.174

17. Модель осциллятора пары Watson - Crick

18. Сarge transfer in DNA. D.Porath et al, Nature, 403, (2000), 635

19. ATP molecule in interaction with Mg[(H(2)O](6) cluster Grignard-type problem

20. Tubulin

21. Тубулиновые микротрубки

22. Crossing of the different singlet and triplet PES in the case Mg +ATP interaction. Coherence.

23. Grignard reaction. Singlet and triplet crossing.

24. Благодарю за вниманиеAcknowledgements