Zeno product formula revisited

نویسندگان

  • Pavel Exner
  • Takashi Ichinose
  • Hagen Neidhardt
  • Valentin A. Zagrebnov
چکیده

We introduce a new product formula which combines an orthogonal projection with a complex function of a non-negative operator. Under certain assumptions on the complex function the strong convergence of the product formula is shown. Under more restrictive assumptions even operator-norm convergence is verified. The mentioned formula can be used to describe Zeno dynamics in the situation when the usual non-decay measurement is replaced by a particular generalized observables in the sense of Davies.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Zeno Dynamics of Von Neumann Algebras

The dynamical quantum Zeno effect is studied in the context of von Neumann algebras. We identify a localized subalgebra on which the Zeno dynamics acts by automorphisms. The Zeno dynamics coincides with the modular dynamics of that subalgebra, if an additional assumption is satisfied. This relates the modular operator of that subalgebra to the modular operator of the original algebra by a varia...

متن کامل

New product formulæ and quantum Zeno dynamics with generalized observables

We demonstrate a pair of new product formulæ which combine a projection with a resolvent of a positive operator, or with an exponential function and spectral projections, respectively. The convergence is strong or even operator-norm under more restrictive assumptions. The second mentioned formula can be used to describe Zeno dynamics in the situation when the usual non-decay measurement is repl...

متن کامل

O ct 2 00 4 A Product Formula Related to Quantum Zeno Dynamics

We prove a product formula which involves the unitary group generated by a semibounded self-adjoint operator and an orthogonal projection P on a separable Hilbert space H, with the convergence in Lloc(R;H). It gives a partial answer to the question about existence of the limit which describes quantum Zeno dynamics in the subspace RanP . The convergence in H is demonstrated in the case of a fini...

متن کامل

ar X iv : m at h - ph / 0 30 20 60 v 1 2 5 Fe b 20 03 Product Formula Related to Quantum Zeno Dynamics

The fact that the decay of an unstable system can be slowed down, or even fully stopped in the ideal case, by frequently repeated measurements checking whether the system is still undecayed was noticed first by Beskow and Nilsson [BN]. It was only decade later, however, when Misra and Sudarshan [MS] caught the imagination of the community by linking the effect to the well-known Zeno aporia abou...

متن کامل

Dynamical Systems Revisited: Hybrid Systems with Zeno Executions

Results from classical dynamical systems are generalized to hybrid dynamical systems. The concept of ! limit set is introduced for hybrid systems and is used to prove new results on invariant sets and stability, where Zeno and non-Zeno hybrid systems can be treated within the same framework. As an example, LaSalle's Invariance Principle is extended to hybrid systems. Zeno hybrid systems are dis...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2005