Geometric energy transport and refrigeration with driven quantum dots

Solution of master equations by fermionic-duality: Time-dependent charge and heat currents through an interacting quantum dot proximized by a superconductor

“…As in prior work we find that the relevant stationary values are not only those of the actual system but also those of the dual system. This remarkable insight has significantly advanced the analysis of the parameter dependence of the transient state evolution [9,16,19,54]. Our result extends this to interacting systems proximized by a superconductor but additionally points out two important refinements.…”

“…( 9) can be written where the energy current I E (t) is given by setting µ = 0 in the expression for I Q (t). This solution applies to any initial state |ρ 0 ) that is diagonal in the energy basis, specified by the initial expectation values of the polarization 〈A 0 〉 ρ 0 and parity 〈p〉 ρ 0 subject to the constraint (54),…”

“…The first factor quantifies the ability of quantity x to "probe" the y-part of the state evolution, the second one captures the initial-state dependence of the latter, see also Ref. [54]. For example, the charge current (70) does not probe the parity decay, (I N |p) = 0, and thus -by duality-depends on the physical parameters only through the stationary state of the actual system, in particular, through the value of the polarization observable 〈A〉 z in (c ′ |ρ 0 ) [Eq.…”

“…gives two solutions: γ c = γ p /2 and |γ s | = γ c . For the latter case the physical bound |γ s | ≤ γ p − γ c [Eq (54)…”

Inverse current induced thermoelectric conversion in a parallel-coupled double quantum dot system

“…Conventional thermoelectric conversion is based on the Seebeck effect, where a temperature gradient drives a particle current to overcome a voltage bias to do work, known as a thermoelectric heat engine, or based on the Peltier effect, where a voltage bias drives a heat current from a low-temperature reservoir to a high-temperature reservoir, known as a thermoelectric refrigerator [1,2]. In recent years, thermoelectric conversion has been widely studied, both theoretically [3][4][5][6] and experimentally [7][8][9][10]. In particular, the relevant research has been expanded from two-terminal structures [11][12][13][14] to three-terminal [15][16][17][18][19][20] or even multi-terminal structures [21][22][23][24], from linear regime [25][26][27] to nonlinear regime [28][29][30][31][32], and from semiconductor systems [1,[33][34][35] to quantum systems [2-4, 6-10, 15-17, 36-39].…”