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).
• ????? ??????? ?????? ?????????????? ??????????
  ? ?????? ? ????????, ?????? ??????????????????
  ???? ????? ?????????? ? ????????????????
  ???????????? ????????? ??????? ?????? ???????????
  ????????? ? ???????????? ??????
• 2. Fröhlich, H.Pelzer, S. Zienau. Phil.Mag.
  41,221,1951.
• ????????, ???????? ?? ???????????, ?????
  ???????? ???????????? ?? ?????????
• .
• ????????? ?.?.
• 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
?arge transfer in DNA.
D.Porath et al, Nature, 403, (2000), 635
6
Holstein Hamiltonian
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DNA-molecule in a practice
??????
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).
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Theory of Polarons.
 

• 
  (1)
• 
  Elimination of electron coordinates
• 
  (2)
• 
  

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

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Fe(2)Si(18). Ferromagnetic coupling. Ground
state.Total spin S4.

• r(Fe1Si14)3.027, r(Fe1Si17)3.029,r(Fe1Si15)2.5
  78, 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(S
  i16)-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(Si
  10)-0.175, q(Si13)-0.174

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?????? ??????????? ???? Watson - Crick
18
?arge transfer in DNA.
D.Porath et al, Nature, 403, (2000), 635
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ATP molecule in interaction with Mg(H(2)O(6)
cluster
Grignard-type problem
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Tubulin
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??????????? ???????????
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Crossing of the different singlet and triplet PES
in the case Mg ATP interaction. Coherence.
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Grignard reaction. Singlet and triplet crossing.
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????????? ?? ????????Acknowledgements