ترغب بنشر مسار تعليمي؟ اضغط هنا

Well-posedness and convergence of the Lindblad master equation for a quantum harmonic oscillator with multi-photon drive and damping

68   0   0.0 ( 0 )
 نشر من قبل Pierre Rouchon
 تاريخ النشر 2015
  مجال البحث فيزياء
والبحث باللغة English




اسأل ChatGPT حول البحث

We consider the model of a quantum harmonic oscillator governed by a Lindblad master equation where the typical drive and loss channels are multi-photon processes instead of single-photon ones; this implies a dissipation operator of order 2k with integer k>1 for a k-photon process. We prove that the corresponding PDE makes the state converge, for large time, to an invariant subspace spanned by a set of k selected basis vectors; the latter physically correspond to so-called coherent states with the same amplitude and uniformly distributed phases. We also show that this convergence features a finite set of bounded invariant functionals of the state (physical observables), such that the final state in the invariant subspace can be directly predicted from the initial state. The proof includes the full arguments towards the well-posedness of the corresponding dynamics in proper Banach spaces of Hermitian trace-class operators equipped with adapted nuclear norms. It relies on the Hille-Yosida theorem and Lyapunov convergence analysis.



قيم البحث

اقرأ أيضاً

169 - Dustin Keys , Jan Wehr 2019
The paper studies a class of quantum stochastic differential equations, modeling an interaction of a system with its environment in the quantum noise approximation. The space representing quantum noise is the symmetric Fock space over L^2(R_+). Using the isomorphism of this space with the space of square-integrable functionals of the Poisson process, the equations can be represented as classical stochastic differential equations, driven by Poisson processes. This leads to a discontinuous dynamical state reduction which we compare to the Ghirardi-Rimini-Weber model. A purely quantum object, the norm process, is found which plays the role of an observer (in the sense of Everett [H. Everett III, Reviews of modern physics, 29.3, 454, (1957)]), encoding all events occurring in the system space. An algorithm introduced by Dalibard et al [J. Dalibard, Y. Castin, and K. M{o}lmer, Physical review letters, 68.5, 580 (1992)] to numerically solve quantum master equations is interpreted in the context of unravellings and the trajectories of expected values of system observables are calculated.
The measurement of a quantum system becomes itself a quantum-mechanical process once the apparatus is internalized. That shift of perspective may result in different physical predictions for a variety of reasons. We present a model describing both sy stem and apparatus and consisting of a harmonic oscillator coupled to a field. The equation of motion is a quantum stochastic differential equation. By solving it we establish the conditions ensuring that the two perspectives are compatible, in that the apparatus indeed measures the observable it is ideally supposed to.
104 - Giovanni Rastelli 2016
We apply the Born-Jordan and Weyl quantization formulas for polynomials in canonical coordinates to the constants of motion of some examples of the superintegrable 2D anisotropic harmonic oscillator. Our aim is to study the behaviour of the algebra o f the constants of motion after the different quantization procedures. In the examples considered, we have that the Weyl formula always preserves the original superintegrable structure of the system, while the Born-Jordan formula, when producing different operators than the Weyls one, does not.
We present a general quantum fluctuation theorem for the entropy production of an open quantum system whose evolution is described by a Lindblad master equation. Such theorem holds for both local and global master equations, thus settling the dispute on the thermodynamic consistency of the local quantum master equations. The theorem is genuinely quantum, as it can be expressed in terms of conservation of an Hermitian operator, describing the dynamics of the system state operator and of the entropy change in the baths. The integral fluctuation theorem follows from the properties of such an operator. Furthermore, it is valid for arbitrary number of baths and for time-dependent Hamiltonians. As such, the quantum Jarzynski equality is a particular case of the general result presented here. Moreover, our result can be extended to non-thermal baths, as long as microreversibility is preserved. We finally present some numerical examples to showcase the exact results previously obtained.
This article reviews recent work on the Kac master equation and its low dimensional counterpart, the Kac equation.
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