Download presentation

Presentation is loading. Please wait.

Published byJohn Lewis Modified over 4 years ago

1
In quest of 4 He supersolid a work with J. Peter Toennies (MPI-DSO Göttingen), Franco Dalfovo (Uni Trento), Robert Grisenti & Manuel Käsz (Uni Frankfurt), Pablo Nieto (Automoma Madrid) History of a conjecture: BEC in a quantum solid ? Vacancy diffusivity and solid 4 He Poisson ratio The Geyser effect in solid 4 He vacuum expansion Bernoulli flow of a nominal 4 He solid Suppression of flow anomalies by 1% 3 He 4 He vacuum expansion from low -T sources Firenze 2005 - 1

2
History of a conjecture: BEC in a quantum solid? 1969 Andreev $ Lifshitz 1970 Chester Leggett 1977 Greywall 2004 Kim & Chan 2004 Ceperley & Bernu Firenze 2005 - 2

3
Kim & Chan 2004 measurements of non-classical rotational inertia Firenze 2005 - 3

4
no trend ? Kim & Chan Firenze 2005 - 4

5
Galli & Reatto 2001 (a) no ground state vacancies but only thermal vacancies (b-d) ground state + thermal vacancies (for different vacancy formation energies) what about injected (non-equilibrium) vacancies? Firenze 2005 - 5

6
Vacuum expansion of solid 4 He Firenze 2005 - 6

7
continuity Bernoulli Firenze 2005 - 7

8
4 He phase diagram Firenze 2005 - 8

9
The Geyser effect Firenze 2005 - 9

10
Period vs. T at constant pressure 40.7 bar 35.0 bar 32.0 bar Firenze 2005 - 10

11
Period versus P 0 at constant temperature Bernoulli Firenze 2005 - 11

12
P s/l information on dynamical processes inside solid 4 He P information on Poisson ratio of solid 4 He Firenze 2005 - 12

15
Poisson ratio of solid 4 He Firenze 2005 - 13

16
Plastic flow motion of dislocation motion of vacancies dominant in solid He (high diffusivity!) Polturak et al experiment (PRL 1998) vacancy injection at s/l interface + sweeping by pressure gradient Firenze 2005 - 14

17
Vacancy drift solid 4 He p-type SC Firenze 2005 - 15

18
V a = V* - V a V a = 35.15 Å 3 (atomic volume) V* 0.45V a (vacancy isobaric formation volume) A0A0 A s/l L Virtual volume to be filled by vacancies in the time L/u 0 u0u0 The vacancy mechanism Firenze 2005 - 16

19
accumulation of vacancies up to a critical concentration X c drift + diffusion diffusion Pressure distance from s/l interface 0L COLLAPSE! Geyser mechanism vacancy bleaching & resetting of initial conditions

20
Data on vacancy diffusivity and concentration in 4 He Firenze 2005 - 17

21
Transport theory Generation function surface generation velocity Firenze 2005 - 18

22
Solution for L Excess vacancies Current at the s/l interface (x = 0) due to excess vacancies = surface depletion layer thickness Firenze 2005 - 19

23
- the shape of the current depends on 2 parameters (, ) - the time scale implies another parameter ( v ) - the ratio of the oscillation amplitude to the constant background is measured by X 0 V a u v /u 0 and is of the order of a few percent (as seen in experiment) fitting reduced form: Firenze 2005 - 20

24
Theory vs. experiment D v = 1.3·10 -5 cm 2 /s v = 5.4·10 10 s/g u v = 2.0·10 -3 cm/s u s = 2u v s = 60 s v = 13 s * = 10.7 s 0 = 82 s P 0 = 31 bar T 0 = 1.74 K best fit with = 4 = 1.214 Firenze 2005 - 21

25
better fits are obtained with finite L (one more parameter) large means fast recombination Firenze 2005 - 22

26
Period 0 vs. diffusivity finite L approximate solution by Greens function method X c = critical concentration Firenze 2005 - 23

27
Firenze 2005 - 24

28
Anomalies below the point! Firenze 2005 - 25

29
a sharp transition in the flow regime at 1.58 K ! Firenze 2005 - 26

30
Effects of 3 He on the anomalies from R. Richardson et al Firenze 2005 - 27

31
3 He-vacancy binding energy Firenze 2005 - 28

32
normal behaviour induced by less than 1% 3 He ! Firenze 2005 - 29

33
CONCLUSIONS 1.The geyser effect indicates (via Bernoullis law) an oscillation of the s/l (quasi-)equilibrium pressure at a given T: vacancy concentration appears to be the only system variable which can give such effect. 2. Below the temperature flow anomalies are observed: (a) The most dramatic one is the occurrence of a Bernoulli flow corresponding to pressures > Pm, at which 4 He should be solid. (b) Below 1.58 K a sharp drop of the geyser period signals a dramatic change in the flow properties of solid 4 He. These anomalies, suggesting superflow conditions, are attributed to injected excess vacancies, and agree with Galli and Reatto predictions for a vacancy-induced (Andreev-Lifshitz) supersolid phase. 3.A 3 He concentration of 0.1% is shown to suppress the flow anomalies, suggesting a quantum nature of the superflow. Firenze 2005 - 30

34
2 I = flow (current), assumed approximately constant over a period A 0 = tube section A = average flow cross section in the s/l interface region (A is slightly < A 0 ) g 0 = conductivity far away from the s/l interface due to the equilibrium concentration of vacancies X 0 : g 0 = X 0 v where v is the vacancy mobility g = conductivity near the s/l interface: g = X v where X is the actual vacancy concentration near the s/l interface. Immediately after the collapse (brown and red lines in the figure) X << X 0 and g << g 0 whereas just before the collapse (green line) X >> X 0 and g >> g 0. When X = X 0 (purple line) the gradient is the same between 0 and L 0. The corresponding gradients are inversely proportional (see figure)! 1 Pressure gradients: 3 Length L of the gradient near the s/l interface (solve the above system for P L and L): where the term in parenthesis is constant. For A A 0 it appears that L grows with g/g 0 = X/X 0 as qualitatively shown in the figure. Thus the sensor during the period measures a pressure varying from P 0 to P s/l

Similar presentations

OK

Introduction to Feedback Systems / Önder YÜKSEL 03.05.2004Bode plots 1 Frequency response:

Introduction to Feedback Systems / Önder YÜKSEL 03.05.2004Bode plots 1 Frequency response:

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google