02.12. 14. In Search of Fundamental Symmetries

Broken symmetry in nonrelativistic physics and Theory of Polarons

A.V.Tulub

Broken symmetry in non relativistic physics

• 1. Electronic structure calculations • 2. Molecular structure. • 3. Translational invariance. • 4. Polaron theory.

Polarons Theory.

krkr iaiaVgH kkk

k expexp2

1 2

rkP

kkk aaiS exp

Pekar broken symmetry solution arise from the wave function structure

,...,,..,, 2121 qqФrqqr

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.

•

rkP

kkk aaiS exp

kkk faUaU 1

Motion of a superfluid in a narrow canal and Josephson effect. JETP.V. 61,P.1986,1971 (with B.Lukin)

Сarge transfer in DNA.

D.Porath et al, Nature, 403, (2000), 635

Holstein Hamiltonian

jiiiHN

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,

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iii

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22

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DNA-molecule in a practice

Биочип

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» •

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).

Theory of Polarons.

(1)

Elimination of electron coordinates

(2)

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,

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Were is the mass of a polaron? Self interaction field.

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11

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022

n

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Scattering. The mean free path

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Resonance structure of the scattering amplitude depends on the value of the coupling constant. Max. value of the coupling constant.

The ground state wave function

Scattering amplitude

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.

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)

22

3112

42112

511

22112

311111 EEEEEEEEEE

21

3221

44221

522

22121

3122122 EEEEEEEEEE

a) quantum field, 2) classical field.

Nonlinear effect in a magnetic field

A. V. Tulub. // New derivation of the of the formulas of nonlinear susceptibilities. Doklady USSR .V. 212, ,P. 584 1972.

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

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.

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

Модель осциллятора пары Watson - Crick

Сarge transfer in DNA.

D.Porath et al, Nature, 403, (2000), 635

ATP molecule in interaction with Mg[(H(2)O](6) cluster

Grignard-type problem

Tubulin

Тубулиновые микротрубки

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

Grignard reaction. Singlet and triplet crossing.

Благодарю за вниманиеAcknowledgements