Can the Wigner function be determined by properties for translation and parity transformation on lattice phase space?
نویسنده
چکیده
We show that the Fano operator for one dimensional quantum system is uniquely determined by assuming the reasonable behavior under translation and parity transformation on phase space. Contrarily, for the system with lattice phase space the same procedure does not work.
منابع مشابه
Determination of the Wigner Function from Photon Statistics *
We present an experimental realisation of the direct scheme for measuring the Wigner function of a single quantized light mode. In this method, the Wigner function is determined as the expectation value of the photon number parity operator for the phase space displaced quantum state. The Wigner function provides a complete representation of the quantum state in the form that is analogous to a c...
متن کاملAutonomous generation of all Wigner functions and marginal probability densities of Landau levels
Generation of Wigner functions of Landau levels and determination of their symmetries and generic properties are achieved in the autonomous framework of deformation quantization. Transformation properties of diagonal Wigner functions under space inversion, time reversal and parity transformations are specified and their invariance under a four-parameter subgroup of symplectic transformations ar...
متن کاملStatistical uncertainty in quantum optical photodetection measurements
We present a complete statistical analysis of quantum optical measurement schemes based on photodetection. Statistical distributions of quantum observables determined from a finite number of experimental runs are characterized with the help of the generating function, which we derive using the exact statistical description of raw experimental outcomes. We use the developed formalism to point ou...
متن کاملua nt - p h / 06 02 22 7 v 4 7 N ov 2 00 7 Stationary quantum Markov process for the Wigner function on a lattice phase space
As a stochastic model for quantum mechanics we present a stationary quantum Markov process for the time evolution of the Wigner function on a lattice phase space Z N ×Z N with N odd. By introducing a phase factor extension to the phase space, each particle can be treated independently. This is an improvement on earlier methods that require the whole distribution function to determine the evolut...
متن کاملFinite Dimensional Schwinger Basis, Deformed Symmetries, Wigner Function, and an Algebraic Approach to Quantum Phase
Schwinger’s finite (D) dimensional periodic Hilbert Space representations are studied on the toroidal lattice with specific emphasis on the deformed oscillator subalgebras and the generalized representations of the Wigner function. These subalgebras are shown to be admissible endowed with the non-negative norm of Hilbert space vectors. Hence, they provide the desired canonical basis for the alg...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008