Transport through ballistic chaotic cavities in the classical limit Piet Brouwer Laboratory of...
Preview:
Citation preview
- Slide 1
- Transport through ballistic chaotic cavities in the classical
limit Piet Brouwer Laboratory of Atomic and Solid State Physics
Cornell University Support: NSF, Packard Foundation Humboldt
Foundation With: Saar Rahav Wesleyan October 26 th, 2008
- Slide 2
- Ballistic chaotic cavities: Energy levels level density mean
level density: depends on size Conjecture: Fluctuations of level
density are universal and described by random matrix theory
Bohigas, Giannoni, Schmit (1984) valid if L
- Slide 3
- Spectral correlations Correlation function Random matrix theory
in units of Altshuler and Shklovskii (1986) This expression for 1
only; Exact result for all is known. b: magnetic field
- Slide 4
- Ballistic chaotic cavities: transport level densityconductance
G
- Slide 5
- Ballistic chaotic cavities: transport level densityconductance
G G is random function of (Fermi) energy and magnetic field b
Marcus group
- Slide 6
- Ballistic chaotic cavities: transport level densityconductance
G Conjecture: Fluctuations of the conductance of an open ballistic
chaotic cavity are universal and described by random matrix theory
Blmel and Smilansky (1988)
- Slide 7
- Ballistic chaotic cavities: transport level densityconductance
G Conjecture: Fluctuations of the conductance of an open ballistic
chaotic cavity are universal and described by random matrix theory
Blmel and Smilansky (1988) Requirement for universality: Additional
time scale in open cavity: dwell time D ( )
- Slide 8
- 2 1 Conductance autocorrelation function Correlation function
Random matrix theory Jalabert, Baranger, Stone (1993) Efetov (1995)
Frahm (1995) in units of P j : probability to escape through
opening j L
- Slide 9
- This talk Semiclassical calculation of autocorrelation function
for ballistic cavity Role of the Ehrenfest time E Recover random
matrix theory if E > D (classical limit).
- Slide 10
- Semiclassics conductance = transmission = 1 reflection R j :
total reflection from opening j : classical trajectories A :
stability amplitude S : classical action Miller (1971) Blmel and
Smilansky (1988)
- Slide 11
- Semiclassics conductance = transmission = 1 reflection R j :
total reflection from opening j Miller (1971) Blmel and Smilansky
(1988) : classical trajectories A : stability amplitude S :
classical action
- Slide 12
- Conductance fluctuations Need to calculate fourfold sum over
classical trajectories. But: Trajectories 1, 1, 2, 2 contribute
only if total action difference S is of order h systematically
- Slide 13
- Conductance fluctuations 1 21 2 1 21 2 1 11 1 2 22 2 Need to
calculate fourfold sum over classical trajectories. But:
Trajectories 1, 1, 2, 2 contribute only if total action difference
S is of order h systematically Sieber and Richter (2001)
- Slide 14
- Conductance fluctuations 1 21 2 1 21 2 1 11 1 2 22 2 1 11 1 2
22 2 1 21 2
- Slide 15
- 1 21 2 1 21 2 1 11 1 2 22 2 1 11 1 2 22 2 1 21 2 This
contribution vanishes for chaotic cavity
- Slide 16
- Conductance fluctuations EE EE Duration of small angle
encounter with action difference S ~ h is Ehrenfest time E : :
Lyapunov exponent Aleiner and Larkin (1996)
- Slide 17
- Conductance fluctuations EE EE random matrix theory if E