We show that in classical mechanics, as well as in nonrelativistic quantum mechanics the equation of the relative motion for a two-body bound system at rest can be replaced by individual dynamical equations of the same kind as the first one, but with different parameters. We assume that in relativistic quantum mechanics the individual equations are Dirac equations with modified parameters in agreement with the individual Schrödinger equations. We find that products of solutions to the individual equations with correlated arguments are the quantum analogues of the classical representation of a bound system and represent suitable models for the bound state wave functions. As validity test for the new representation of bound states we suggest to use some observable differences between this one and the representation in terms of relative coordinates.
We comment on: E. Iyoda, K. Kaneko, and T. Sagawa, "Fluctuation Theorem for Many-Body Pure Quantum States", Phys. Rev. Lett. 119, 100601 (2017). We also respond to the reply by the afore mentioned authors: "arXiv:1712.05172". The response at hand concludes our discussion of the subject on the arXiv.
We discuss a recent test of the performance of the kinetic energy partition method (KEP) through its application to two separable quantum-mechanical models. We argue that one of the benchmark models is exceedingly simple for testing any realistic approximate method and that almost any reasonable approach yields better results. In the second example our exact benchmark eigenvalues disagree considerably with those chosen by the authors for comparison, which casts doubts on the accuracy of their KEP approach.
In J. Math. Phys. 13, 1608-1621 (1972), Erdahl considered the convex structure of the set of $N$-representable 2-body reduced density matrices in the case of fermions. Some of these results have a straightforward extension to the $m$-body setting and to the more general quantum marginal problem. We describe these extensions, but can not resolve a problem in the proof of Erdahl's claim that every extreme point is exposed in finite dimensions. Nevertheless, we can show that when $2m \geq N$ every extreme point of the set of $N$-representable $m$-body reduced density matrices has a unique pre-ima…
In their recent paper [Nature Physics 15, 451 (2006)], Sakmann and Kasevich study the formation of fringe patterns in ultra-cold Bose gases and claim: `Here, we show how single shots can be simulated from numerical solutions of the time-dependent many-body Schrödinger equation.' It would be remarkable if they had solved this exponentially complex equation. Instead they solve nonlinear equations with the aim to approximate the solution of the Schrödinger equation. The authors proceed to criticize phase-space approaches to simulating quantum dynamics and claim the impossibility of interpreting s…
Comment on "Limits of the measurability of the local quantum electromagnetic-field amplitude"
有人认为，最近的重新分析的结果由Compagno和Escherico [Phys. Rev. A 57，1595（1998）]的玻尔-罗森菲尔德程序的电磁场的一个单一的时空平均分量的测量是不正确的，当现场测量时间短于所需的光穿过测量的测试机构。为此，时间平均的“自作用力”的测试机构，假设为简单的球形形状，评估的一般轨迹的一维求积允许的测试机构由Compagno和Atriico，并在封闭形式的限制阶状轨迹玻尔和Rosenfeld。
In a recent Letter [Dabelow and Reimann, Phys. Rev. Lett. 124, 120602 (2020)], a perturbative relaxation theory is applied to the Bose-Hubbard model and compared to data from a quantum simulator experiment [Trotzky et al. Nature Phys 8, 325 (2012)]. In this Comment, I argue that the discrepancy found is due to the quasi-local observable measured in the experiment being affected by a harmonic trapping potential that is unaccounted for in the analytic calculation. I support my claim with quasi-exact numerics computed using a parallel time-evolving block decimation algorithm (TEBD), and show that…
Reimann [Phys. Rev. Lett. 101, 190403 (2008)] claimed that generic isolated macroscopic quantum system will equilibrate under experimentally realistic conditions by proving a theorem. We here show that the proof is invalid for most many-body systems and is unable to demonstrate equilibration in realistic experiment.
In a recent paper (Phys. Rev. Lett. 123, 210602), Kozin and Kyriienko claim to realize "genuine" ground state time crystals by studying models with long-ranged and infinite-body interactions. Here we point out that their models are doubly problematic: they are unrealizable ${\it and}$ they violate well established principles for defining phases of matter. Indeed with infinite body operators allowed, almost all quantum systems are time crystals. In addition, one of their models is highly unstable and another amounts to isolating, via fine tuning, a single degree of freedom in a many body system…
Comment on a letter to Nature Physics, where Sakmann and Kasevich claim to solve the many-body time dependent Schrödinger equation to simulate single experimental runs of interacting quantum systems.
We argue that the theories of Volokitin and Persson [Comment arXiv:1405:2525], of Dedkov and Kyasov [J. Phys.: Condens. Matter 20 (2008) 354006], and Pieplow and Henkel [New J. Phys. 15 (2013) 023027] agree on the electromagnetic force on a small, polarizable particle that is moving parallel to a planar, macroscopic body, as far as the contribution of evanescent waves is concerned. The apparent differences are discussed in detail and explained by choices of units and integral transformations. We point out in particular the role of Lorentz contraction in the procedure used by Volokitin and Pers…
This contributed conference proceeding reviews some results about a system of a few identical particles with spin trapped in one-dimensional potentials and experiencing two-body interactions. The focus is on how symmetry, integrability, and solvability depend on the trap shape, two-body interaction, the number of particles, and the number of spin components. A series of comments are presented that characterize the minimal symmetries possible for a composite system constructed from interacting single particles, with special focus on the contact interaction. For five and more particles with inte…
A recent work (2014 New J. Phys. 16 013006) claims that nonmonotonic structures found in the many-particle quantum-to-classical transition (2013 Proc. Natl Acad. Sci. USA 110 1227-1231; 2011 Phys. Rev. A 83 062111) are not exclusive to the many-body domain, but they also appear for single-photon as well as for semi-classical systems. We show that these situations, however, do not incorporate any quantum-to-classical transition, which makes the claims unsustainable.
In this comment we show that the approach presented by Fojón et al~\cite{Fojon10} is not as accurate as they claim. A straightforward calculation using the models considered buy those authors clearly shows that the spectral method, which the authors criticize, proves to be considerably better.
In a recent paper, PRL 114 100404, 2015, Raeisi and Mosca gave a limit for cooling with Heat-Bath Algorithmic Cooling (HBAC). Here we show how to exceed that limit by having correlation in the qubits-bath interaction.
The authors of the comment[Phys. Rev. A 97, 046101 (2018)] raise that the inconsistency in calculating some common quantum-speed-limit (QSL) bounds, which is presented in our paper [Phys. Rev. A 95, 052118 (2017)], does not exist in their paper [Phys. Rev. A 94, 052125 (2016)]. Therefore they insist that their criticism to some QSL bounds is still valid. We demonstrate all the QSL bounds mentioned in the comment are similar in essence. We also show the inconsistency which is presented in their original paper can not be used to support their criticism. Furthermore, we exhibit although the incon…
We present a quantum-mechanical generalization of the work penalty equation (Eq. (6) in Phys. Rev. Lett., 127, 190602 (2021)) with an alternative derivation.
We analyze the results obtained from a model consisting of the interaction between a moving electric quadrupole moment and a magnetic field. We argue that there are no bound states contrary to what the author stated. It is shown that the proposed method is unsuitable for obtaining all the bound states and that the existence of allowed cyclotron frequencies is an artifact of the approach.
The problem of boundary behaviour at the origin of coordinates is discussed for D-dimensional Schrodinger equation in the framework of hyper spherical formalism, which have been often considered last time. We show that the Dirichlet condition, which seems as natural, is not mathematically well justified, on the contrary to the 3-dimensional case. The stronger argument in favour of Dirichlet boundary condition is the requirement of time independence of wave functions norm. The problem remains open for singular potentials.
We provide an analytical proof of the entropic uncertainty relations presented by de Vicente and Sanchez-Ruiz in [Phys. Rev. A 77, 042110 (2008)] and also show that the replacement of Eq. (27) by Eq. (29) in that reference introduces solutions that do not take fully into account the contraints of the problem, which in turn leads to some mistakes in their treatment.
Comment on "Beyond-classical computation in quantum simulation"
Institute of Quantum Control (PGI-8), Forschungszentrum Jülich（于利希研究中心量子控制研究所）；Institute of Theoretical Physics, University of Regensburg（雷根斯堡大学理论物理研究所）；Institute for Theoretical Physics, University of Cologne（科隆大学理论物理研究所）
In a recent paper Castellanos-Jaramillo and Castellanos-Moreno proposed a simple quantum-mechanical model for an electron in the vicinity of an ionized nanostructure with a permanent electric dipole. They chose the interaction of the electron with the charge and the dipole in such a way that the resulting Schrödinger equation is separable into radial and angular parts. In this comment we show that those authors did not solve the angular eigenvalue equation with proper periodic boundary conditions and that they also made a mistake in the elimination of the first derivative in the radial equatio…
The authors claim that they "strictly" closed locality loophole, but their work does not close the locality loophole. there are at least two local transinformation explanations. The two explanations are the counter-examples of their claim. No reason can make a conclusion be right when there are counter-examples of the conclusion. And the two explanations also illustrate that the space-time diagrams of the paper have at least two problems.
In a recent article [http://dx.doi.org/10.1103/PhysRevA.87.022340, Phys. Rev. A 87, 022340 (2013)], Yan et al have studied geometric discord for a well known class of bound entangled states. Based on their calculation, they claim "It is found that there exists a nondynamic sudden change in quantum discord" for these states. In this Comment, we criticize their work by pointing out that what has been calculated is actually a bound, and not the exact value of discord. Since, generally, it is not possible to infer the exact value (or property) of a quantity just from its bound, we can not conclude…
Reply on the ``Comment on `Loss-error compensation in quantum- state measurements' ''
评论的作者[G。M. D 'Ariano和C. Macchiavello将发表在Phys.Rev.A，quant-ph/9701009中]试图重新建立光学零差层析成像中损耗补偿的0.5效率界限。在我们的回答中，我们证明了这样一个严格的界限既不存在，也不是排除单个系统的状态重构所需要的界限[G。M. D 'Ariano和H. P. Yuen，Phys. Rev. Lett. 76，2832（1996）]。
Deffner and Lutz [J. Phys. A 46, 335302 (2013) and Phys. Rev. Lett. 111, 010402 (2013).] extended the Mandelstam-Tamm bound and the Margolus-Levitin bound to time-dependent and non-Markovian systems, respectively. Although the derivation of the Mandelstam-Tamm bound is correct, we point out that thier analysis of the Margolus-Levitin bound is incorrect. The Margolus-Levitin bound has not yet been established in time-dependent quantum systems, except for the adiabatic case.
Shegelski, Kavka, and Hynbida have developed a method for calculating the lifetime of a particle initially localized in a potential well exactly quantum mechanically by employing a heuristic expression for the lifetime <t>. Their method allows for the inclusion of a bound state, and their results for tunneling through a centrifugal barrier demonstrate the major role that bound states play in determining the lifetime. In this comment, I show that one can greatly simplify the analysis by calculating <t^2>^(1/2) instead. Results obtained are exact when no bound state is present. In the presence o…
In an article by García-Pintos et al. [Rev. Lett. 125, 040601 (2020)] the connection between the charging power of a quantum battery and the fluctuations of a "free energy operator" whose expectation value characterizes the maximum extractable work of the battery is studied. The result of the closed-system analysis shows that for a general charging process the battery will have a nonzero charging power if and only if the state of the battery is not an eigenstate of the free energy operator. In this Comment, we point out a few mistakes in the analysis and obtain the correct bound on the chargin…
Some difficulties, both numerical and conceptual, of the method to compute one dimensional wave functions by numerically integrating the quantum Hamilton-Jacobi equation, presented in the paper mentioned in the title, are analyzed. The origin of these difficulties is discussed, and it is shown how they can be avoided by means of another approach, based on different solutions of the same equation. Results for the same potentials, obtained by this latter method are presented and a comparison is made.
We prove that the inequality used recently by Wilk and Włodarczyk [Phys. Rev. A {\bf 79}, 062108 (2009)] to find a better lower bound in the uncertainty relations for the Rényi entropies is invalid. Thus, the problem of improving the bound given in our paper [Phys. Rev. A {\bf 74}, 052101 (2006)] remains unsolved.
An inequality for the lower bound of the average number of hyperfine component $μ=0$ particles in the ground state of spin-1 condensates under a magnetic field has been derived in ref.\cite{tasa13}. It is shown in this comment that, in a broad domain of parameters usually accessed in experiments, the lower bound appears to be negative. Thus the applicability of the inequality is very limited.
We perform a renormalization group analysis of the non-relativistic four-boson problem by means of a simple model with pointlike three- and four-body interactions. We investigate in particular the unitarity point where the scattering length is infinite and all energies are at the atom threshold. We find that the four-body problem behaves truly universally, independent of any four-body parameter. Our findings confirm the recent conjectures of Platter et al. and von Stecher et al. that the four-body problem is universal, now also from a renormalization group perspective. We calculate the corresp…
