transport through ballistic chaotic cavities in the classical limit piet brouwer laboratory of...
Post on 21-Dec-2015
213 views
TRANSCRIPT
- 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