The understanding of coupled particle and heat transport in complex systems is a fundamental problem, also of practical interest in connection with the challenging task of developing high-performance thermoelectric materials. We will discuss thermoelectric transport phenomena from the perspective of dynamical nonlinear systems [1], focusing on stylized classical and quantum models, including the disordered hard-point gas and asymmetric quantum-dot ring structures pierced by an Aharonov-Bohm flux. We will show that neither energy filtering nor the so-called strong coupling between particle and energy fluxes are necessary conditions for achieving the Carnot efficiency. In particular, we will propose a mechanism for increasing the thermoelectric figure of merit in interacting systems with a single relevant constant of motion, typically in momentum-conserving systems [2]. Such a general result will be illustrated by means of a diatomic chain of hard-point colliding particles and in a two-dimensional multiparticle collision dynamics model, where the total momentum is the only relevant conserved quantity [2-3]. We will then focus on systems with broken time-reversal symmetry [4-7], for which the maximum efficiency and the efficiency at maximum power are both determined by two parameters: a ``figure of merit'' and an asymmetry parameter. In contrast to the time-symmetric case, the figure of merit is bounded from above; nevertheless the Carnot efficiency can be reached at lower and lower values of the figure of merit and far from the strong coupling condition as the asymmetry parameter increases. Moreover, the Curzon-Ahlborn limit for efficiency at maximum power can be overcome within linear response. Finally, we will show that a weak magnetic field generally improves either the efficiency of thermoelectric power generation or of refrigeration, the efficiencies of the two processes being no longer equal when a magnetic field is added.

References:
[1] G. Benenti and G. Casati, Increasing thermoelectric efficiency: dynamical models unveil microscopic mechanisms, Phil. Trans. R. Soc. A 369, 466 (2011).
[2] G. Benenti, G. Casati and J. Wang, Conservation laws and thermodynamic efficiencies, Phys. Rev. Lett. 110, 070604 (2013).
[3] K. Saito, G. Benenti and G. Casati, A microscopic mechanism for increasing thermoelectric efficiency, Chem. Phys. 375, 508 (2010).
[4] G. Benenti, K. Saito and G. Casati, Thermodynamic bounds on efficiency for systems with broken time-reversal symmetry, Phys. Rev. Lett. 106, 230602 (2011).
[5] K. Saito, G. Benenti, G. Casati and T. Prosen, Thermopower with broken time-reversal symmetry, Phys. Rev. B 84, 201306(R) (2011). law in small molecular wires, Phys. Rev. B 86, 035433 (2012).
[6] M. Horvat, T. Prosen, G. Benenti and G. Casati, Railway switch transport model, Phys. Rev. E 86, 052102 (2012).
[7] V. Balachandran, G. Benenti and G. Casati, Efficiency of three-terminal thermoelectric transport under broken-time reversal symmetry, preprint arXiv:1301.1570 [cond-mat.mes-hall].

The off-equilibrium probability distribution of the heat exchanged by a ferromagnet in a time interval after a quench below the critical point is calculated analytically in the large-\(N\) limit. Here \(N\) is the number of components of the vectorial order parameter. The distribution shows a singular behavior with a critical threshold below which a macroscopic fraction of heat is released by the \(k=0\) Fourier mode of the order parameter. The mathematical structure producing this phenomenon is the same responsible of the order parameter condensation in the equilibrium low temperature phase. The heat exchanged by the individual Fourier modes follows a non trivial pattern, with the unstable modes at small wave vectors warming up the modes around a characteristic finite wave vector \(k_M\). Two internal temperatures, associated to the \(k=0\) and \(k=k_M\) modes, rule the heat currents through a fluctuation relation similar to the one for stationary systems in contact with two thermal reservoirs.

The parity order hidden in the Mott insulating phase of 1D bosonic gases was observed via high-resolution imaging in optical lattices [1]. In the fermionic case, it was shown in [2] that spin and charge parity orders characterize the two gapped phases of the 1D Hubbard model, suggesting also the possible detection of pairs of fermions with opposite spins on neighboring sites in the Luther Emery phase. The discoveries can be casted into a general result obtained in [3], stating that long-range order is present in every gapped phase of one dimensional fermionic systems. It is captured by two-point correlators of appropriate charge and/or spin operators of nonlocal type. At least one of them remains asymptotically finite in each gapped phase, vanishing at the transition.

We discuss the above findings and give some preliminary result about their generalization to the two-dimensional case.

In collaboration with M. Roncaglia

References

[1] M. Endres et al., Science 334 200 (2011)

[2] A. Montorsi, and M. Roncaglia, Phys. Rev. Lett. 109, 236404 (2012)

[3] L. Barbiero, A. Montorsi, and M. Roncaglia, "How hidden orders generate gaps in 1D fermionic systems", preprint arxiv:1302.6136

A linear chain of connected electron sites with two independent sinks, one attached to each end, is considered as a simple model for a quantum electron transfer in photosynthetic bio-complexes. Under the condition of a symmetric initial population in the middle of the chain, it is expected that the efficiency of the electron transfer from the middle of the chain to the sinks is dominated by the sink with the strongest coupling. However, we show that quantum effects can modify this intuitive ``classical'' mechanism so that electron transfer can occur through the weaker coupled sink with maximal efficiency. Using this capability we show how to make a quantum switch that can transfer an electron to the left or right branch of the chain, by changing the coupling to the sinks. The operational principles of this quantum device are given in term of superradiance transitions and subradiant states. When the realistic data are taken from the photosystem II reaction center, this quantum biological switch is shown to retain its reliability, even at room temperature.