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Nonequilibrium matter exchange
between finite quantum systems
Juyeon Yi (Pusan National University)
Euijin Jeon and Yong Woon Kim (KAIST)
Matter moves…
Oliver Lodge
For quantum mechanical systems, steady state can exist
even when they are isolated
Fermi’s golden rule
total transition probability
Transition rate is constant in time
Question
If two systems are large enough, can we expect
steady state (SS) in which constant matter current flows?
No !
If SS exists, we reach a unphysical situation
where current flows from an empty bucket
Grasp a picture through an example…
1D tight-binding fermions
Initial equilibrium
end-point coupling
System parameters
temperatures, chemical potentials, sizes, band widths, coupling strength
(energy band width)
Quasi-continuum
(level spacing)
(inter chain coupling)
Nearly half filling
(intra chain coupling)
Weak coupling
mass current vs normalized time
(current from high to low chemical potential system)
what are the normalization constants?
Landauer-Buettiker formula for
currents between infinite systems
Roundtrip time of a particle moving
with the Fermi velocity
size dependence
backflow
(current from high to low chemical potential system)
scattering picture
(from the right to the left)
(First stage )
Second stage
(wave number ) × (path length)
Interference effect
Roundtrip along the left system
is concurrent with the round trip
along the right system at 𝝉 = 𝟐𝝉𝑹
Onsager reciprocal relation (ORR)
Mass current
Heat current
Onsager reciprocal relation (ORR)
Landauer formula and Onsager relation
Transient fluctuation theorem
Jarzynski and Wojcik (2004 Phys. Rev. Lett. 92, 230602)
number exchange :
energy exchange :
Mass current
Heat current
total energy change :
If
1
Onsager symmetry exists !
Onsager reciprocal relation for strong coupling
More generally for
correlations
Correlations
Time reversal symmetry
Spontaneous matter flow
and
are also Onsager symmetric.
Onsager relation also holds
if heat and number change are strongly correlated with large values of W
Bennett weighting factor
Long time behaviors
Disorder effects