ترغب بنشر مسار تعليمي؟ اضغط هنا

Comment on Quantitative Condition is Necessary in Guaranteeing the Validity of the Adiabatic Approximation [arXiv:1004.3100]

196   0   0.0 ( 0 )
 نشر من قبل Jianda Wu
 تاريخ النشر 2011
  مجال البحث فيزياء
والبحث باللغة English




اسأل ChatGPT حول البحث

Recently, the authors of Ref.1[arXiv:1004.3100] claimed that they have proven the traditional adiabatic condition is a necessary condition. Here, it is claimed that there are some mistakes and an artificial over-strong constraint in [1], making its result inconvincible.

قيم البحث

اقرأ أيضاً

We analyze the validity of the adiabatic approximation, and in particular the reliability of what has been called the standard criterion for validity of this approximation. Recently, this criterion has been found to be insufficient. We will argue tha t the criterion is sufficient only when it agrees with the intuitive notion of slowness of evolution of the Hamiltonian. However, it can be insufficient in cases where the Hamiltonian varies rapidly but only by a small amount. We also emphasize the distinction between the adiabatic {em theorem} and the adiabatic {em approximation}, two quite different although closely related ideas.
In this paper, we continue our investigation on controlling the state of a quantum harmonic oscillator, by coupling it to a reservoir composed of a sequence of qubits. Specifically, we show that sending qubits separable from each other but initialise d at different states in pairs can stabilise the oscillator at squeezed states. However, only if entanglement is allowed in the reservoir qubit can we stabilise the oscillator at a wider set of squeezed states. This thus provides a proof for the necessity of involving entanglement in the reservoir qubits input to the oscillator, as regard to the stabilisation of quantum states in the proposed system setting. On the other hand, this system setup can be in turn used to estimate the coupling strength between the oscillator and reservoir qubits. We further demonstrate that entanglement in the reservoir input qubits contributes to the corresponding quantum Fisher information. From this point of view, entanglement is proved to play an indispensable role in the improvement of estimation precision in quantum metrology.
In order to analyze joint measurability of given measurements, we introduce a Hermitian operator-valued measure, called $W$-measure, such that it has marginals of positive operator-valued measures (POVMs). We prove that ${W}$-measure is a POVM {em if and only if} its marginal POVMs are jointly measurable. The proof suggests to employ the negatives of ${W}$-measure as an indicator for non-joint measurability. By applying triangle inequalities to the negativity, we derive joint measurability criteria for dichotomic and trichotomic variables. Also, we propose an operational test for the joint measurability in sequential measurement scenario.
44 - Kazuo Fujikawa 2007
Recently there have been some controversies about the criterion of the adiabatic approximation. It is shown that an approximate diagonalization of the effective Hamiltonian in the second quantized formulation gives rise to a reliable and unambiguous criterion of the adiabatic approximation. This is illustrated for the model of Marzlin and Sanders and a model related to the geometric phase which can be exactly diagonalized in the present sense.
The quantum adiabatic theorem states that if a quantum system starts in an eigenstate of the Hamiltonian, and this Hamiltonian varies sufficiently slowly, the system stays in this eigenstate. We investigate experimentally the conditions that must be fulfilled for this theorem to hold. We show that the traditional adiabatic condition as well as some conditions that were recently suggested are either not sufficient or not necessary. Experimental evidence is presented by a simple experiment using nuclear spins.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا