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Abstract We study the universality of work statistics of a system quenched through a quantum critical surface. By using the adiabatic perturbation theory, we obtain the general scaling behavior for all cumulants of work. These results extend the studies of KZM scaling of work statistics from an isolated quantum critical point to a critical surface. As an example, we study the scaling behavior of work statistics in the 2D Kitaev honeycomb model featured with a critical line. By utilizing the trace formula for quadratic fermionic Hamiltonian, we obtain the exact characteristic function of work of the 2D Kitaev model at zero temperature. The results confirm our prediction.
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We derive analogues of the Jarzynski equality and Crooks relation to characterise the nonequilibrium work associated with changes in the spring constant of an overdamped oscillator in a quadratically varying spatial temperature profile. The stationary state of such an oscillator is described by Tsallis statistics, and the work relations for certain processes may be expressed in terms of q-exponentials. We suggest that these identities might be a feature of nonequilibrium processes in circumstances where Tsallis distributions are found.
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.
Motivated by experiments on splitting one-dimensional quasi-condensates, we study the statistics of the work done by a quantum quench in a bosonic system. We discuss the general features of the probability distribution of the work and focus on its behaviour at the lowest energy threshold, which develops an edge singularity. A formal connection between this probability distribution and the critical Casimir effect in thin classical films shows that certain features of the edge singularity are universal as the post-quench gap tends to zero. Our results are quantitatively illustrated by an exact calculation for non-interacting bosonic systems. The effects of finite system size, dimensionality, and non-zero initial temperature are discussed in detail.
We derive universal bounds for the finite-time survival probability of the stochastic work extracted in steady-state heat engines. We also find estimates for the time-dependent thresholds that the stochastic work does not surpass with a prescribed probability. At long times, the tightest thresholds are proportional to the large deviation functions of stochastic entropy production. Our results, which entail an extension of martingale theory for entropy production, are tested with numerical simulations of a stochastic photoelectic device.
We consider semi-infinite two-dimensional layered Ising models in the extreme anisotropic limit with an aperiodic modulation of the couplings. Using substitution rules to generate the aperiodic sequences, we derive functional equations for the surface magnetization. These equations are solved by iteration and the surface magnetic exponent can be determined exactly. The method is applied to three specific aperiodic sequences, which represent different types of perturbation, according to a relevance-irrelevance criterion. On the Thue-Morse lattice, for which the modulation is an irrelevant perturbation, the surface magnetization vanishes with a square root singularity, like in the homogeneous lattice. For the period-doubling sequence, the perturbation is marginal and the surface magnetic exponent varies continuously with the modulation amplitude. Finally, the Rudin-Shapiro sequence, which corresponds to the relevant case, displays an anomalous surface critical behavior which is analyzed via scaling considerations: Depending on the value of the modulation, the surface magnetization either vanishes with an essential singularity or remains finite at the bulk critical point, i.e., the surface phase transition is of first order.
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