B.Spivak University of Washington

1. Magnetic field dependence of chemical reactions B.Spivak University of Washington

2. Magnetic field dependence of chemical reactions at room temperature Turro N.1983 Salikhov K, Molin Yu, Sagdeev R. , Buchachenko S. 1984 Steiner U., Ulrich T. 1989 B. Spivak, Fei Zhou 1994 Hypothetic magnetic sense of animals. See for reviews Able 1984, Wiltchenko 2005, Johnsen 2005 Orientation of migratory birds is light dependent W. Witchenko 1981 Resonance effects (EPR) in avian navigation T. Ritz at all 2004 Critic: K.V. Kavokin, Bioelectromagnetics 30, 402, 2009 Magnetic field dependence of luminescence in light emitting organic diodes

3. can chemical reaction rates depend on magnetic field at room temperature ? A model: particles with spin ½ are created randomly in space and time with an average intensity <I>. They diffuse, and recombine into a singlet state

4. mean field equation for the particle concentration 0 In this approximation there is no magnetic field dependence of n(t)! If the particles are created uniformly in space, there is also no dependence of on the diffusion coefficient D.

5. Fluctuation “corrections” to the mean field results Qualitative picture, stationary case, and 1/ts=0 a. the fluctuation corrections are determined by particle diffusion. b. in d=2 (marginal case) there is no stationary solution, and the concentration diverges logarithmically as a function of time.

6. Fluctuational correction to the recombination rate. Langevin approach.

7. the role of dimensionality of space l is the mean free path

8. in 3d case the magnetic field dependence of the rate requires a special analysis

9. a) the recombination rate is strongly H-dependent b) the expression for the correction to the recombination rate is similar to the weak localization correction to conductivity Do an entanglement between spins and spin coherence play any role? At room temperatures the diffusion is classical and incoherent. However, spins are quantum on the time scale smaller than the spin relaxation time ts

10. Is it possible that n(t,H) depends on the direction of the magnetic field at high temperature? An example: a particle has spin 1 in the ground state and spin zero in an exited state. There is an unplolarized light beam in z-direction 0 ? Sz = 1 0 -1 In the absence of spin relaxation and magnetic field spins are aligned (Sz =0), and there is no light absorption. In a stationary situation the excited level is populated only because of mixing of Sz =0 level with Sz =1,-1 levels. Only the component of the magnetic field, Hz parallel to the beam contributes to the mixing.

11. Non-stationary case. Zeldovich approach In the mean field approximation there is no H-dependence of the particle concentration The role of fluctuations: t=L2 /D L

12. Conclusion: chemical reaction rates can depend on the magnitude of the magnetic field at room temperature in the presence of unpolarized light it is relatively easy to construct a model where the rate depends on the direction of the magnetic field as (sin q)2 , where q is the angle between the magnetic field and the light beam direction to get this dependence proportional to (sin q) (avian navigation) one has to have circularly polarized light is it possible that the avian navigation involves nuclear spin polarization ?