Emergent Phenomena in mesoscopic systems

1. Emergent Phenomena in mesoscopic systems S. Frauendorf Department of Physics University of Notre Dame

2. Emergent structures and properties in nature An emergent behaviour or emergent property can appear when a number of simple entities (agents) operate in an environment, forming more complex behaviours as a collective Emergent structures are patterns not created by a single event or rule. There is nothing that commands the system to form a pattern, but instead the interactions of each part to its immediate surroundings causes a complex process which leads to order The complex behaviour or properties are not a property of any single such entity, nor can they easily be predicted or deduced from behaviour in the lower-level entities: they are irreducible. 1

3. Living systems-ant colony A more detailed biological example is an ant colony. The queen does not give direct orders and does not tell the ants what to do. Instead, each ant reacts to stimuli in the form of chemical scent from larvae, other ants, intruders, food and build up of waste, and leaves behind a chemical trail, which, in turn, provides a stimulus to other ants. Here each ant is an autonomous unit that reacts depending only on its local environment and the genetically encoded rules for its variety of ant. Despite the lack of centralized decision making, ant colonies exhibit complex behavior and have even been able to demonstrate the ability to solve geometric problems. For example, colonies routinely find the maximum distance from all colony entrances to dispose of dead bodies. A termite "cathedral" mound produced by a termite colony: a classic example of emergence in nature. 2

4. Physics Emergence means complex organizational structure growing out of simple rule. (p. 200) Protection generates exactness and reliability,… The universal properties of ordering of rigid bodies, the flow of superfluids, and even the emptiness of space are among the many concrete, well documented examples of this effect. (p. 144) Macroscopic emergence, like rigidity, becomes increasingly exact in the limit of large sample size, hence the idea of emerging. There is nothing preventing organizational phenomena from developing at small scale,…. (p. 170) 3

5. Emergent phenomena • Liquid-Gas Phase boundary • Rigid Phase – Lattice • Superconductivity (Meissner effect, vortices) • Laws of Hydrodynamics • Laws of Thermodynamics • Quantum sound • Quantum Hall resistance • Fermi and Bose Statistics of composite particles • … • … 4

6. Mesoscopic systems Emergence of a macroscopic phenomena with N. Appearance of “finite size corrections” to familiar macroscopic phenomena in very small probes (quantum dots, quantum wells, quantum junctions, quantum wires).

7. Emergence of cubic crystal structure in salt clusters Abundance in the cluster beam T. P.Martin Physics Reports 273 (1966) 199-241 5

8. Ca clusters: the transition to the bulk is not smooth fcc lattice: Close packing with translational symmetry Icosahedra: Close packing with small surface Abundance in the cluster beam bulk 6 T. P.Martin Physics Reports 273 (1966) 199-241

9. Water - dramatic example 7

10. 8

11. Emergent phenomena - nuclei • The nucleon liquid • Superfluidity, superconductivity • Shell structure • Spatial orientation • Temperature • Phases and phase transitions Extrapolation to bulk Finite nuclei 9

12. Neutron stars Suprafluid, superconducting nuclear matter and more. Studying the scaling of clusters properties seems instructive, because these properties are well known for the bulk. SGR 1806-20 7

13. Astrophysics: What is the equation of state for nuclear matter? Nuclei are only stable for A<300. Clusters can be made for any N. Liquid drop model: Volume + Surface energy

14. Transition to the bulk liquid The liquid drop model scaling law seems reliable. Binding energy of K clusters Coulomb energy Neutral –one component 8

15. Ionization energy of Na clusters Other quantities scale in the same way. 9

16. Strong correlation Nuclei: charged two-component liquid How good is it? Symmetry energy ???? Is there a term ? Clusters may provide examples for scaling. What is the bulk equation of state? For example: compressibility 10

17. clusters probably exist only for N>50 produced for all N. He droplets – getting really close to nuclei clusters are most similar to nuclei. Liquid at zero temperature Electrical neutral: Limit N-> easily achieved. Strong zero point motion. Weakly bound nuclei Very hard to experiment with, because of small energy scale. 11

18. Experiment? Study of : theory 12

19. Superconductivity/Superfluidity Described by the Landau – Ginzburg equations for the order parameter Density of Cooper pairs Controlled by ( inside the superconductor) coherence length (size of Cooper pair) penetration depth of magnetic field G, , Fermi energy , and critical Temperature related by BCS theory. 13

20. normal H super T Phase diagram of a macroscopic type-I superconductor Meissner effect 32

21. Type II superconductor 14

22. Solid state, liquid He: Calculation of very problematic – well protected. Take from experiment. local BCS very good Nuclei: Calculation of not possible so far. Adjusted to even-odd mass differences. highly non-local BCS poor 16 How to extrapolate to stars? Vortices, pinning of magnetic field?

23. Mesoscopic regime 17

24. Intermediate state of Reduced viscosity Superfluidity Atttractive interaction between Fermions generates Cooper pairs -> Superfluid

25. Moments of inertia at low spin are well reproduced by cranking calculations including pair correlations. rigid irrotational Non-local superfluidity: size of the Cooper pairs larger than size of the nucleus. 18

26. is superfluid at this T. is not superfluid at this T. 19

27. behave like a superfluid! Rotational spectrum of in a droplet Rotational spectrum of in a droplet free Density of “normal” atoms Moment of inertia larger

28. Shell structure 21

29. Fermions in spherical Potential Nuclei: magnitude OK, damping with N and T OK. 22 Clusters: More washed out. Dies out quicker. Not quantitatively understood. Frauendorf, Pashkevich

30. Clusters allow us to study shell structure over a much larger range than nuclei. Explains the gross shell structure 23

31. Supershell structure of Na clusters N-dependent factor multiplied for compensating the too rapid damping with N! 24 Emergence of resistivity?

32. Imax>20 Currents caused by nucleons on periodic orbits Nuclear moments of inertia at high spin Pair correlations are quenched. M. Deleplanque, S.F. et al. Phys. Rev. C 69 044309 (2004) 25

33. Larmor: System in Magnetic field behaves like in rotating system (in linear order). 26

34. Emergence of thermodynamics Region of high level density: important for astrophysics, nuclear applications, … Limits to predictability of quantal states: uncertainties in the Hamiltonian deterministic chaos Give up individual quantal states: 28

35. Crossover phenomena Phase transitions T=0 transitions between different symmetries in nuclei. Spherical deformed IBA symmetries solid-liquid superfluid-normal liquid-gas Artificial limit by mean field approximation 29

36. The Casten Triangle of IBM 30

37. normal H super T Super-normal phase transition 32

38. Grand canonical Canonical Microcanonical 31

39. Canonical ensemble Grandcanonical ensemble 33

40. Melting of Na clusters 34

41. Microcanonical q latent heat 35 M. Schmitd et al.

42. Transition from electronic to geometric shells In Na clusters 36

43. Similar emergent phenomena in nuclear and non-nuclear mesoscopic systems. 37 Emerge with increasing particle number, while calculating them microscopically becomes increasingly difficult. New principles of organization (+ parameters) – to be found. Region where micro and makro calculations are possible. Comparing different types mesoscopic systems is instructive. Studies are complementary: bulk limit accessible or not, energy scale, external heat bath, …. More contact between the communities! More can be found in: S. Frauendorf, C. Guet, Ann. Rev. Nucl. Part. Sci. 51, 219 (2001)

44. Quantization of magnetic flux in type II superconductors Magneto-optical images of vortices in a NbSe2 superconducting crystal at 4.3 K after cooling in magnetic field of 3 and 7 Oe. 15

45. Emergence of orientation Example for spontaneous symmetry breaking: Weinberg’s chair Hamiltonian rotational invariant Why do we see the chair shape? Tiniest perturbation mixes |IM> states to a stable-oriented wave packet: the symmetry broken state. 17

46. 3 2 1 Mesoscopic variant I: Molecules Can be kicked and turned like a chair. Quantal states |IM> can be measured: Rotational bands Classical moments of inertia of arrangement of point masses. 18 16

47. HCl Microwave absorption spectrum

48. Well deformed Mesoscopic variant II: Nuclei Symmetry broken state described by the mean field. How is orientation generated? Deformed potential aligns the partially filled orbitals Riley Partially filled orbitals are highly tropic Nucleus is oriented – rotational band 19

49. E2 radiation M1 radiation