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Register a new userStatistics of work performed by optical tweezers with general time-variation of their stiffness
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We derive an exact expression for the probability density of work done on a particle that diffuses in a parabolic potential with a stiffness varying by an arbitrary piecewise constant protocol. Based on this result, the work distribution for time-continuous protocols of the stiffness can be determined up to any degree of accuracy. This is achieved by replacing the continuous driving by a piecewise constant one with a number $n$ of positive or negative steps of increasing or decreasing stiffness. With increasing $n$, the work distributions for the piecewise protocols approach that for the continuous protocol. The moment generating function of the work is given by the inverse square root of a polynomial of degree $n$, whose coefficients are efficiently calculated from a recurrence relation. The roots of the polynomials are real and positive (negative) steps of the protocol are associated with negative (positive) roots. Using these properties the inverse Laplace transform of the moment generating function is carried out explicitly. Fluctuation theorems are used to derive further properties of the polynomials and their roots.
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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 apply Pontryagins principle to drive rapidly a trapped overdamped Brownian particle in contact with a thermal bath between two equilibrium states corresponding to different trap stiffness $kappa$. We work out the optimal time dependence $kappa(t)$ by minimising the work performed on the particle under the non-holonomic constraint $0leqkappaleqkappa_{max}$, an experimentally relevant situation. Several important differences arise, as compared with the case of unbounded stiffness that has been analysed in the literature. First, two arbitrary equilibrium states may not always be connected. Second, depending on the operating time $t_{text{f}}$ and the desired compression ratio $kappa_{text{f}}/kappa_{text{i}}$, different types of solutions emerge. Finally, the differences in the minimum value of the work brought about by the bounds may become quite large, which may have a relevant impact on the optimisation of heat engines.
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.
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.
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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