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Fluctuations of work in realistic equilibrium states of quantum systems with conserved quantities
by J. MurPetit, A. Relaño, R. A. Molina and D. Jaksch
 Published as SciPost Phys. Proc. 3, 024 (2020)
Submission summary
As Contributors:  Rafael Molina · Jordi MurPetit 
Preprint link:  scipost_201910_00032v3 
Date accepted:  20191213 
Date submitted:  20191211 01:00 
Submitted by:  MurPetit, Jordi 
Submitted to:  SciPost Physics Proceedings 
Proceedings issue:  24th European Few Body Conference (University of Surrey, U.K.) 
Academic field:  Physics 
Specialties: 

Approaches:  Theoretical, Computational 
Abstract
The outofequilibrium dynamics of quantum systems is one of the most fascinating problems in physics, with outstanding open questions on issues such as relaxation to equilibrium. An area of particular interest concerns fewbody systems, where quantum and thermal fluctuations are expected to be especially relevant. In this contribution, we present numerical results demonstrating the impact of conserved quantities (or ‘charges’) in the outcomes of outofequilibrium measurements starting from realistic equilibrium states on a fewbody system implementing the Dicke model.
Published as SciPost Phys. Proc. 3, 024 (2020)
Author comments upon resubmission
We very much appreciate the Referee’s positive outlook on our paper, and have modified our manuscript in line with his comments. The changes are listed below. Let us here just briefly comment on two points:

With regards to point 2 by the Referee, he is right in pointing that the eigenstates should generally be associated with a series of quantum numbers, one for each charge (Hamiltonian and other conserved charges). With this in mind, we have replaced n> with  n, i_1, ... i_{N_cons} >, and indicate explicitly “n stands for the quantum number that identifies the energy eigenvalue, E_n, while i_k is the quantum number labelling the eigenvalues, M_{k, i_k }, of the charge operator \hat{M}_k.”, and similarly for the final states m’> (lines 104108).

On the Referee's comment #3: Our generalised quantum fluctuation relations (as is generally the case with these kind of equalities) are valid for any time dependence in H(t). This generality includes processes where H(t) is parameterised by a continuous parameter, say H = H(lambda(t)) with lambda(t) a continuous function of t. But the QFRs can be also applied to quantum quenches, i.e., sudden changes of the parameters of the Hamiltonian. This is the case we have analysed in our simulations where the parameters (alpha, g) are changed in a stepwise manner. We now provide explicit details on this point when describing our numerical protocol in Section 3.2, and have added a more general statement in Sec. 2 (step 2 of the generalised TPM protocol).
We hope that, with these changes, our manuscript will be accepted for publication in SciPost Physics Proceedings.
List of changes
1. We have added Refs. [14] to address the Referee’s comment #1.
2.In reply to the Referee’s comment #2: We have clarified the notation of the initial and final eigenstates, to account for the various conserved charges at each stage of the protocol.
3. In reply to the Referee’s comment #3: We provide a more detailed description of the time dependence of our Hamiltonian, with a new sentence in Section 2 (step 2 of the generalised TPM protocol), and a new short paragraph including a new equation specifying the functions {alpha(t), g(t)} we used in Section 3 (step 2 of the numerical protocol).
4. We corrected the text as requested by the Referee’s comment #4. The set of references [22, 3436, 38] at the end of that sentence contains the further details on the existence of the additional conserved charge for the various values of alpha. We have also removed the subindex of M_k in line 152: as there is a single charge, there is no need to add a counter to distinguish it from others as in the general case.