Mesoscopic Physics Yoseph Imry, WIS

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Mesoscopic PhysicsYoseph Imry, WIS

• Borderline between
• micro macro
• (Q.M -- statistical)
• regimes

macro
micro
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OUTLINE OF TALK

• DEPHASING
• Inelasticity - change of state of environment.
• Disordered conductors -- especially low
  dimensions.
• Nonequilibrium dephasing by quantum detector.
• Low-temperature limit ???

• GENERAL
• Conductance quantization.
• Equilibrium A-B effect, persistent currents.
• A-B resistance oscillations mesoscopic
  fluctuations.
• Elastic impurity scattering does NOT kill
  coherence!

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sxy is quantized in units of e2 / h in
2D Discovered by von Klitzing, Pepper and Dorda,
(1980)
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A-B Flux in an isolated ring

• A-B flux equivalent to boundary condition.
• Physics periodic in flux, period h/e
  (Byers-Yang).
• Persistent currentsexist due to flux.
• They do not decay by impurity scattering (BIL).

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Aharonov Bohm Oscillation
0.110
(a.u.)
C
I
0.105
Collector Current,
0.100
-10
-5
0
5
10
Magnetic Field,
B
mT
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Decoherence, by environment(via cplg to all
other degrees of freedom)

• What spoils the 2Re(?1 ?2 ) interference?
• Leaving a ("which path") trace in the environment
  ltenv1env2gt
  0
• Inducing uncertainty in the relative phase,
• arg(?1 ?2 )

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Electromagnetic Coupling to other degrees of
freedom
This is what charged Particles always do!!!
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These two statements are exactly equivalent
(SAI, 89)

• ??2O(1) ? ltenv1env2gt0
• FLUCTUATION-DISSIPATION
• THEOREM (FDT)

• Proof by considering the
• time evolution operator,
• U T exp-(1/h)?t HI(t) dt
• U induces changes in the environment state
• and creates an uncertainty in the phase,
  ?arg(?1 ?2)
• determined by the dynamic correlators of HI(t).

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Physical Remarks

• Reabsorbing the excitation restores the phase.
• But After interaction is
• switched off, envt
• becomes irrelevant.
• Special effects Retrieval
• of interference by measurements on envt.
• (epr, Stern, Hackenbroich Weidenmuller)

• No dephasing if identical excitation is produced
  by 2 paths.
• How much energy transferred
• is irrelevant!
• Excitation should resolve
• the 2 paths
• k (x1 x2) ? ?

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1/?? rate for particle to excite environment
(and lose phase!)

• Probability to excite the
• environment till time t,
• for a particle moving in
• medium, can be calculated
• via the
• Fermi Golden Rule
• Results produce all known
• cases (dirty metals, any d)
•  
•  
•  

• ? 1/?? ?dq ?d? Vq2
• Sp(-q, -?) Ss(q, ?).
• ? ?
• particle env.
• S (q, ?)dynamic structure facto
• F.T density-density corr. Fcn
• Measures the corr. of space-time density
  fluctuations ? much physical info. Known for
  models.
• (see later)

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Agreement (of AAK results ) with experiments

• Narrow wire (quasi 1D)
• 1/?? T2/3
• Very nontrivial (FLT???)
• What does exp say?

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LOW-TEMP SATURATION OF tf ? Mohanty, Jariwala
and Webb (1997) and many others.

• Must rule out EXTERNAL NOISE, MAGNETIC
  IMPURITIES...
• DISAGREES WITH USUAL THEORY!
• Debye-Waller-type phenomenon?
• Unexpected low-energy excitations?

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No Dephasing as T? 0 !

• Starting from our expression
• 1/?? ?dq ?d? Vq2
• SP(-q, -?) Ss(q, ?),
• we see that supports of two Ss
• DO NOT OVERLAP?? 0.
• Unless ?g.s. degeneracy (spins).
• T?0 deph ruled out
• by laws of thermodynamics!

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Experiment T? 0 deph is an artifact
? Pierre et al, 2003 Ovadyahu, 2001 ?
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Dephasing by nonequilibrium detector

• Lacking knowledge out of equilibrium FDT?...
• Purely Quantum-Mechanical Detector
• NO CLASSICAL OBSERVERS
• Buks et al Aleiner, Meir Wingreen, Levinson

Principle of exp
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Aharonov Bohm Oscillation
0.110
(a.u.)
C
I
0.105
Collector Current,
0.100
-10
-5
0
5
10
Magnetic Field,
B
mT
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Calc of tf (for dephasing tf dwell time)

• Obtained from
• Orthogonality induced in detector state (Buks et
  al).
• Real transitions induced in the detector (Aleiner
  et al).
• Noise induced by detector on electron in dot
  (Levinson).

• tf is the time through
• which the shot-noise of
• the detector current is
• its mean change via ?T
• due to electron in dot

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Buks et al, controlled dephasing results
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CONCLUSIONS

• Mesoscopic Physics helps us to undestand fully
  the issue of coherence (limiting the quantum
  behavior), which happens around tf, the
  (de)coherence time.
• Can, in some cases, control decoherence!!!
• A larger body decoheres faster. How can we avoid
  that? LRO???