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

2. An emergent behaviour or emergent property can appear when a number of simple entities (agents) operate in an environment,entities 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 Emergent structures and properties in nature 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 termite "cathedral" mound produced by a termite colony:termite a classic example of emergence in nature. 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.ant colony 2

4. Emergence means complex organizational structure growing out of simple rule. (p. 200) 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) 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) 3 Physics

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

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

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

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

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

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

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

18. Study of : theory 12 Experiment?

19. Superconductivity/Superfluidity Described by the Landau – Ginzburg equations for the order parameter 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 Density of Cooper pairs

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

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 How to extrapolate to stars?Vortices, pinning of magnetic field? 16

23. Mesoscopic regime 17

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

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

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

27. Rotational spectrum of in a droplet free behave like a superfluid! Rotational spectrum of in a droplet Density of “normal” atoms Moment of inertia larger Title: SUPERFLUID HELIUM DROPLETS: AN ULTRACOLD NANOLABORATORY, By: Toennies, J. Peter, Vilesov, Andrej F., Whaley, K. Birgitta, Physics Today, 0031-9228, February 1, 2001, Vol. 54, Issue 2

28. Shell structure 21

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

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

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

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

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

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 Artificial limit by mean field approximation solid-liquid superfluid-normal liquid-gas 29

36. The Casten Triangle of IBM 30

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

38. Grand canonical Canonical Microcanonical 31

39. Grandcanonical ensemble Canonical ensemble 33

40. Melting of Na clusters 34

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

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

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

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. Mesoscopic variant I: Molecules 1 2 3 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. 16 18

47. HCl Microwave absorption spectrum

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

49. E2 radiation M1 radiation

51. Spontaneous symmetry breaking Emergence Finite N: Localization Shell structure, center of mass motion Orientation rotational alignment, … rotational bands Symmetry breaking Periodic crystal structure rigidity, transverse sound

52. B 27