On the fock space representation of occupations times for non reversible markov processes

1988 ◽  
pp. 134-138
Author(s):  
Yves Le Jan
Keyword(s):  
Markov Processes ◽  
Fock Space ◽  
Space Representation ◽  
Reversible Markov Processes

Exploring Representation Theory of Unitary Groups via Linear Optical Passive Devices

2006 ◽  
Vol 13 (04) ◽  
pp. 415-426 ◽  
Author(s):  
P. Aniello ◽  
C. Lupo ◽  
M. Napolitano
Keyword(s):  
Lie Algebras ◽  
Fock Space ◽  
Fixed Number ◽  
Unitary Groups ◽  
Space Representation ◽  
Remarkable Case ◽  
Mathematical Structures ◽  
Passive Devices ◽  
Optical Modes ◽  
Linear Optical

In this paper, we investigate some mathematical structures underlying the physics of linear optical passive (LOP) devices. We show, in particular, that with the class of LOP transformations on N optical modes one can associate a unitary representation of U (N) in the N-mode Fock space, representation which can be decomposed into irreducible sub-representations living in the subspaces characterized by a fixed number of photons. These (sub-)representations can be classified using the theory of representations of semi-simple Lie algebras. The remarkable case where N = 3 is studied in detail.

scholarly journals Limit Theorems for Reversible Markov Processes

1973 ◽  
Vol 1 (6) ◽  
pp. 1014-1025
Author(s):  
Michael L. Levitan ◽  
Lawrence H. Smolowitz
Keyword(s):  
Markov Processes ◽  
Limit Theorems ◽  
Reversible Markov Processes

An operation which inverts Bernoulli multiplication and associated stationary reversible Markov processes

1992 ◽  
Vol 29 (01) ◽  
pp. 234-238 ◽  
Author(s):  
R. P. Littlejohn
Keyword(s):  
Time Series ◽  
Markov Processes ◽  
Marginal Distribution ◽  
Ovulation Rate ◽  
Simple Operation ◽  
Reversible Markov Processes

A simple operation is described which inverts Bernoulli multiplication. It is used to define two classes of stationary reversible Markov processes with general marginal distribution. These are compared to the DAR(1) process of Jacobs and Lewis (1978). LJAR(1) is used to model ovulation rate time series.

scholarly journals A TWO-PARAMETER DEFORMED SUSY ALGEBRA FOR SUp/q(n)-COVARIANT (p,q)-DEFORMED FERMIONIC OSCILLATORS

2005 ◽  
Vol 20 (08) ◽  
pp. 613-622 ◽  
Author(s):  
ABDULLAH ALGIN ◽  
METIN ARIK
Keyword(s):  
Quantum Group ◽  
Fock Space ◽  
Space Representation ◽  
Oscillator Algebra ◽  
Two Parameter

We construct a two-parameter deformed SUSY algebra by constructing SUSY generators which are bilinears of n (p,q)-deformed fermions covariant under the quantum group SU p/q(n) and n undeformed bosons. The Fock space representation of the algebra constructed is discussed and the total deformed Hamiltonian for such a system is obtained. Some physical applications of the quantum group covariant two-parameter deformed fermionic oscillator algebra are also considered.

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