Lunedì 24 - Mercoledì 26 giugno 2013, Università di Parma

programma di lunedì 24 giugno 2013
Giuliano Benenti - Università degli Studi dell'Insubria
Coupled particle and heat transport: a dynamical system's perspective image
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.

[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].
Paolo De Gregorio - INFN Padova
On the effect of heat fluxes on the vibrational energy of a solid image
Starting from operational concerns in Gravitational Waves detection attempts, the RareNoise collaboration has devised a few experiments to determine whether nonequilibrium should be expected to play a role in a large class of precision measurements. The most impacting result has been to demonstrate that temperature differences across a macroscopic oscillator cause a marked increase of the amplitude of the fluctuations of a few low-frequency resonant modes. If one were to make use of the concept of effective temperature, it would mean that to within room temperature, the equivalent energy stored in those modes is of the order of 400 and up to 900 K. From another perspective, this may be viewed as an explicit measurable violation of the energy equipartition principle induced by a heat flux. Numerical simulation results of a semi-open linear chain are in agreement with the experimental finding, which can be explained at the most basic level also theoretically. One assumes that heat fluxes go hand in hand with an increase of intermodal correlations, which can sometimes become measurable depending on the strength of the coupling.
10:50-11:20pausa caffè
Giuseppe Gonnella - Università degli Studi di Bari
Singular behaviour of heat fluctuations in a quenched ferromagnet image
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.
Pietro Coletti - Università di Roma "Roma Tre"
Dynamical metastability in the Potts model image

The Potts model is a generalization of the Ising model, with \(q\) different state available for every lattice site. For \(q>4\) the system undergoes a first order phase transition, whose control parameter is the temperature. The presence of multiple equilibrium phase can slow down the dynamics towards equilibrium.

We investigated the dynamical metastability of the Potts model on a square lattice after a quench just below the discontinuous transition temperature. By mean of the correlation function of the system we identified the metastable realization and we have studied their energy distribution and the dependence of the spinodal temperature with the system size, in order to assert whether or not metastability is a finite-size effect.

Matteo Marcuzzi - SISSA Trieste

Collective non-equilibrium dynamics in the presence of surfaces image

Symmetries can be regarded as non-trivial constraints limiting the freedom of a physical system. It has to be expected, therefore, that upon relieving some of those restriction will lead to the emergence of new phenomena. A fundamental example is provided by space- and time-translational invariance in statistical systems, which can be thought to eff ectively hold at a coarse-grained scale and can be broken by the introduction of boundaries, implemented by surfaces for the former (an unavoidable feature in any real sample) and, for the latter, by some initial condition for the dynamics which causes a non-equilibrium evolution. While the separate e ffects of these two boundaries are well understood, additional, unexpected features arise upon approaching the eff ective edge formed by their intersection. In order to investigate them we have focused on a classical semi-infinite Ising model evolving out of equilibrium after a temperature quench from the disordered phase to its critical point. Considering both critical and tricritical values of the coupling among surface spins, we have found numerical evidence of a scaling regime with universal features which emerges upon approaching the spatio-temporal edge and we have rationalised such findings within a field-theoretical approach.

Reference: M. Marcuzzi, A. Gambassi and M. Pleimling, EPL 100, 46004 (2012)
Federico Corberi - Università di Salerno
Con quale velocità si ordina un sistema disordinato ?image
Mentre la cinetica di ordinamento di fase è un processo relativamente ben compreso in sistemi puri, la nostra conoscenza di questo fenomeno in mezzi disordinati è assai più lacunosa. In particolare, per quanto riguarda la legge di crescita delle regioni ordinate, esistono risultati contrastanti a favore di leggi logaritmiche oppure algebriche. Discuterò qual è il meccanismo all'origine di questi diversi comportamenti.
13:00-14:30pausa pranzo
Arianna Montorsi - Politecnico di Torino
Hidden order beneath the gapped phases of low dimensional fermionic systems image

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


[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

Davide Valenti - Università di Palermo
Quantum particle in asymmetric bistable potential: transient dynamics and asymptotic behaviour image

We consider the transient dynamics and asymptotic behaviour of a dissipative multilevel quantum system, consisting of a particle in an asymmetric double well potential. The environment is the thermal bath described by the Caldeira-Leggett model with Ohmic spectral density. The time evolution of the system is studied through the populations, the diagonal elements of the reduced density matrix of the system, in the Discrete Variable Representation (i.e. in a spatially localized basis): they are the solution of a Markovian approximated master equation, derived, in the strong coupling regime, from a discretized double path integral with the Feynman-Vernon influence functional.

First we evaluate the populations by varying the damping constant i.e. the strength of the coupling with the environment. At higher damping we find a delayed dynamics, due to the quantum Zeno effect. In particular we observe that the population of the metastable state, located in the higher well, reaches its maximum value at later times as the the coupling strength is increased.

As a second step, we study the mean escape time (MET) from the metastable state, varying both the bath's temperature and coupling strength. We find that for weaker damping the MET exhibits, as a function of the temperature, a nonmonotonic behavior, which resembles the noise enhanced stability (NES) phenomenon observed in several nonlinear classical systems. Conversely, increasing the coupling strength, the MET becomes independent of the temperature (quantum Zeno effect).

We conclude our study considering the presence of an external periodical driving force. We study the time evolution of all populations as a function of the amplitude A and frequency \(\nu\) of the periodical signal, in different damping/temperature regimes. We also analyze the combined effect of the thermal noise and external driving on the long-time behaviour of the system. In particular, we find that both the energy and asymptotic population of the metastable state exhibit a nonmonotonic behaviour as functions of the frequency \(\nu\).
16.30-17.00pausa caffè
Fausto Borgonovi - Università Cattolica Brescia
A quantum biological switch image
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.
Andrea Carati - Università degli Studi di Milano
Metaequilibrium statistical thermodynamics image
Dal teorema di Fluttuazione Dissipazione si ottengono formule per i coefficienti delle forme differenziali \(\delta Q\) e \(\delta W\) del calore assorbito e del lavoro compiuto dal sistema di interesse. Qui dimostriamo che la forma differenziale \(\delta Q- \delta W\) e' chiusa. Sicché esiste una energia interna definita da \( dU= \delta Q- \delta W\).
Matteo Polettini - University of Luxembourg
The gauge symmetry of nonequilibrium thermodynamics image
Picking up a thread of discussion initiated at the 15th Pama Seminar, I will discuss how to reconcile non-invariance of the Gibbs-Shannon entropy under coodinate transformations with the required invariance of the laws of thermodynamics, a problem that mingles with that of the apparent subjectivity of the information-theoretic approach to Statistical Mechanics. In particular, I will show how to derive general features of thermodynamics from a gauge principle, I will discuss the gauge connection and its curvature, and I will give an application to the Minimum Entropy Production Priciple.