Smith, T.B.
(2006).
Generalized Q-functions.
Journal of Physics A: Mathematical and General, 39(44),
pp. 13747–13756.
Full text available as:
Abstract
The modulus squared of a class of wavefunctions defined on phase space is used to define a generalized family of Q or Husimi functions. A parameter lambda specifies orderings in a mapping from the operator psi)(sigma to the corresponding phase space wavefunction, where sigma is a given fiducial vector. The choice lambda = 0 specifies the Weyl mapping and the Q-function so obtained is the usual one when sigma is the vacuum state. More generally, any choice of of lambda in the range (-1,1) corresponds to orderings varying between standard and anti-standard. For all such orderings the generalized Q-functions are non-negative by construction. They are shown to be proportional to expectation of the system state rho with respect to a generalized displaced squeezed state which depends on lambda and position (p,q) in phase space. Thus, when a system has been prepared in the state rho, a generalized Q-function is proportional to the probability of finding it in the generalized squeezed state. Any such Q-function can also be written as the smoothing of the Wigner function for the system state rho by convolution with the Wigner function for the generalized squeezed state.
| Item Type: |
Journal Article
|
| ISSN: |
1751-8121 |
| Extra Information: |
Some of the symbols may not have transferred correctly into this bibliographic record and/or abstract. |
| Keywords: |
Wigner function; Q function; Weyl correspondence; squeezed state |
| Academic Unit/Department: |
Other Departments > Other Departments |
| Item ID: |
5859 |
| Depositing User: |
Tom Smith
|
| Date Deposited: |
14 Nov 2006 |
| Last Modified: |
06 Dec 2010 17:53 |
| URI: |
http://oro.open.ac.uk/id/eprint/5859 |
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