scholarly journals $C\sp{2}$-preserving strongly continuous Markovian semigroups

1973 ◽  
Vol 180 ◽  
pp. 359-359
Author(s):  
W. M. Priestley
Keyword(s):  
Markovian Semigroups

DIRICHLET FORMS AND SYMMETRIC MARKOVIAN SEMIGROUPS ON ℤ2-GRADED VON NEUMANN ALGEBRAS

2003 ◽  
Vol 15 (08) ◽  
pp. 823-845 ◽  
Author(s):  
CHANGSOO BAHN ◽  
CHUL KI KO ◽  
YONG MOON PARK
Keyword(s):  
Von Neumann Algebras ◽  
Dirichlet Forms ◽  
Gauge Invariant ◽  
Von Neumann ◽  
Markovian Semigroups

We extend the construction of Dirichlet forms and symmetric Markovian semigroups on standard forms of von Neumann algebras given in [1] to the case of ℤ2-graded von Neumann algebras. As an application of the extension, we construct symmetric Markovian semigroups on CAR algebras with respect to gauge invariant quasi-free states and also investigate detailed properties such as ergodicity of the semigroups.

scholarly journals NON-POSITIVE SEMIGROUP DYNAMICS IN CONTINUOUS VARIABLE MODELS

2007 ◽  
Vol 05 (01n02) ◽  
pp. 189-198 ◽  
Author(s):  
F. BENATTI ◽  
R. FLOREANINI
Keyword(s):  
Time Evolution ◽  
Initial Conditions ◽  
External Environment ◽  
Continuous Variable ◽  
Positive Semigroup ◽  
Density Matrices ◽  
Initial State ◽  
Variable Model ◽  
Markovian Semigroups

Non-positive, Markovian semigroups are sometimes used to describe the time evolution of subsystems immersed in an external environment. A widely adopted prescription to avoid the appearance of negative probabilities is to eliminate from the admissible initial conditions those density matrices that would not remain positive by the action of the semigroup dynamics. Using a continuous variable model, we show that this procedure leads to physical inconsistencies when two subsystems are considered and their initial state is entangled.

scholarly journals Comparison of Cutoffs Between Lazy Walks and Markovian Semigroups

2013 ◽  
Vol 50 (4) ◽  
pp. 943-959 ◽  
Author(s):  
Guan-Yu Chen ◽  
Laurent Saloff-Coste
Keyword(s):  
Markov Chains ◽  
Total Variation ◽  
Discrete Time ◽  
Continuous Time ◽  
Transition Matrix ◽  
Mixing Time ◽  
Total Variation Distance ◽  
Variation Distance ◽  
Markovian Semigroups

We make a connection between the continuous time and lazy discrete time Markov chains through the comparison of cutoffs and mixing time in total variation distance. For illustration, we consider finite birth and death chains and provide a criterion on cutoffs using eigenvalues of the transition matrix.

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