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Register a new userRole of topology on the work distribution function of a quenched Haldane model of graphene
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Added by
Sourav Bhattacharjee
Publication date
2018
fields
Physics
and research's language is
English
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We investigate the effect of equilibrium topology on the statistics of non-equilibrium work performed during the subsequent unitary evolution, following a sudden quench of the Semenoff mass of the Haldane model. We show that the resulting work distribution function for quenches performed on the Haldane Hamiltonian with broken time reversal symmetry (TRS) exhibits richer universal characteristics as compared to those performed on the time-reversal symmetric massive graphene limit whose work distribution function we have also evaluated for comparison. Importantly, our results show that the work distribution function exhibits different universal behaviors following the non-equilibrium dynamics of the system for small $phi$ (argument of complex next nearest neighbor hopping) and large $phi$ limits, although the two limits belong to the same equilibrium universality class.
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The local quench of a Fermi gas, giving rise to the Fermi edge singularity and the Anderson orthogonality catastrophe, is a rare example of an analytically tractable out of equilibrium problem in condensed matter. It describes the universal physics which occurs when a localized scattering potential is suddenly introduced in a Fermi sea leading to a brutal disturbance of the quantum state. It has recently been proposed that the effect could be efficiently simulated in a controlled manner using the tunability of ultra-cold atoms. In this work, we analyze the quench problem in a gas of trapped ultra-cold fermions from a thermodynamic perspective using the full statistics of the so called work distribution. The statistics of work are shown to provide an accurate insight into the fundamental physics of the process.
We propose an experimental setup to measure the work performed in a normal-metal/insulator/superconducting (NIS) junction, subjected to a voltage change and in contact with a thermal bath. We compute the performed work and argue that the associated heat release can be measured experimentally. Our results are based on an equivalence between the dynamics of the NIS junction and that of an assembly of two-level systems subjected to a circularly polarised field, for which we can determine the work-characteristic function exactly. The average work dissipated by the NIS junction, as well as its fluctuations, are determined. From the work characteristic function, we also compute the work probability-distribution and show that it does not have a Gaussian character. Our results allow for a direct experimental test of the Crooks-Tasaki fluctuation relation.
We derive a systematic, multiple time-scale perturbation expansion for the work distribution in isothermal quasi-static Langevin processes. To first order we find a Gaussian distribution reproducing the result of Speck and Seifert [Phys. Rev. E 70, 066112 (2004)]. Scrutinizing the applicability of perturbation theory we then show that, irrespective of time-scale separation, the expansion breaks down when applied to untypical work values from the tails of the distribution. We thus reconcile the result of Speck and Seifert with apparently conflicting exact expressions for the asymptotics of work distributions in special systems and with an intuitive argument building on the central limit theorem.
In a finite time quantum quench of the Haldane model, the Chern number determining the topology of the bulk remains invariant, as long as the dynamics is unitary. Nonetheless, the corresponding boundary attribute, the edge current, displays interesting dynamics. For the case of sudden and adiabatic quenches the post quench edge current is solely determined by the initial and the final Hamiltonians, respectively. However for a finite time ($tau$) linear quench in a Haldane nano ribbon, we show that the evolution of the edge current from the sudden to the adiabatic limit is not monotonic in $tau$, and has a turning point at a characteristic time scale $tau=tau_c$. For small $tau$, the excited states lead to a huge unidirectional surge in the edge current of both the edges. On the other hand, in the limit of large $tau$, the edge current saturates to its expected equilibrium ground state value. This competition between the two limits lead to the observed non-monotonic behavior. Interestingly, $tau_c$ seems to depend only on the Semenoff mass and the Haldane flux. A similar dynamics for the edge current is also expected in other systems with topological phases.
Work statistics characterizes important features of a non-equilibrium thermodynamic process. But the calculation of the work statistics in an arbitrary non-equilibrium process is usually a cumbersome task. In this work, we study the work statistics in quantum systems by employing Feynmans path-integral approach. We derive the analytical work distributions of two prototype quantum systems. The results are proved to be equivalent to the results obtained based on Schr{o}dingers formalism. We also calculate the work distributions in their classical counterparts by employing the path-integral approach. Our study demonstrates the effectiveness of the path-integral approach to the calculation of work statistics in both quantum and classical thermodynamics, and brings important insights to the understanding of the trajectory work in quantum systems.
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