Hisao Hayakawa (YITP, Kyoto University) based on collaboration with T. Yuge, T. Sagawa, and A. Sugita 1/24 44 Symposium on Mathematical Physics "New Developments in the Theory of Open Quantum Systems" Toruń, June 20-24, 2012 (June 24)
Tetsuro Yuge (YITP->Osaka Univ.) Ayumu Sugita (Osaka City Univ.) Takahiro Sagawa (YITP) & Ryosuke Yoshii (YITP) I would like to thank all these collaborators on this problem. 2/24
Introduction Geometric Pump for Fermion Transport ◦ Setup ◦ Main Results ◦ Special Cases & Example Application to Entropy Production Discussion Conclusion 3/24
Introduction Geometric Pump for Fermion Transport ◦ Setup ◦ Main Results ◦ Special Cases & Example Application to Entropy Production DIscussion Conclusion 4/24
In mesoscopic systems, a current can exist even at zero bias. This effect is called the quantum pumping. 5/24 Nano-machine to extract work
Adiabatic quantum pump ◦ Geometric effect is important (P. W. Brower, PRB58, (1998)). ◦ Control of system parameters Can we get the pump effect by controlling reservoir parameters? 6/24
Introduction Geometric Pump for Fermion Transport ◦ Setup ◦ Main Results ◦ Special Cases & Example Application to Entropy Production Discussion Conclusion 7/24
Projection measurement Counting: ◦ Number of spinless electrons transfer from L to R Statistics & cumulant generating function 8/24
We assume that the total Hamilitonian satisfies von-Neumann equation. We calculate the modified von-Neumann equation via the counting field: Ref. 9/24
10/24 χ
Control parameters 11/24
where 12/24
Based on FCS Born-Markov approximation + rotational wave approximation (RWA), we obtain 13/24
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Introduction Geometric Pump for Fermion Transport ◦ Setup ◦ Main Results ◦ Special Cases & Example Application to Entropy Production Discussion Conclusion 17/24
The method we adopted can be used for the calculation of any other quantities. We can discuss the path dependence of the nonequilibrium entropy production. Namely, the entropy is a geometric quantity under a nonequilibrium situation. Note that the entropy production is a non- conserved quantity. See Sagawa and HH, PRE 84, (2011). 18/24 heat
Path-dependence quasi-static process parameters space 19/24
Introduction Geometric Pump for Fermion Transport ◦ Setup ◦ Main Results ◦ Special Cases & Example Application to Entropy Production Discussion Conclusion 20/24
Effects of spins and many-body interactions ◦ We have already calculated Kondo problem (R. Yoshii and HH, in preparation). ◦ The many-body effect can be absorbed via Schrieffer-Wolff transform. Without the potential scattering term, the result is unchanged. If we introduce the term, the symmetry of evolution matrix is changed. So there is possibility to have the geometric effect. 21/24
So far, we assume that particles are Fermions. However, our analysis is based on RWA (quasi-classical) and the result contains only distribution function of reservoirs. We expect that the geometric effect can appear for Bosons. See Jie Ren et al., PRL 104, (2010). 22/24
Introduction Geometric Pump for Fermion Transport ◦ Setup ◦ Main Results ◦ Special Cases & Example Application to Entropy Production Discussion Conclusion 23/24
We have analyzed a quantum pump effect on Fermion transport. We have found that spinless Fermions without interactions do not have any geometric effect if we control reservoir parameters. We confirm that there exist geometric effects for the control of system parameters. Such an idea can be used for entropy production. ◦ Geometric effects are important. We are now calculating the Kondo problem. 24/24