83 Citations
Quantum Lévy–Itô algebras and non-commutative stochastic analysis
- Mathematics
- 2012
We review the basic concepts of quantum probability and revise the classical and quantum stochastic (QS) calculus using the universal Itô B*-algebra approach. A non-commutative generalization of Lévy…
Malliavin Calculus and Skorohod Integration for Quantum Stochastic Processes
- Mathematics
- 2001
A derivation operator and a divergence operator are defined on the algebra of bounded operators on the symmetric Fock space over the complexification of a real Hilbert space and it is shown that they…
Q-Adapted Quantum Stochastic Integrals and Differentials in Fock Scale
- Physics, MathematicsArXiv
- 2011
The Fock-Guichardet formalism for the quantum stochastic integration is introduced, and the four fundamental processes of the dynamics are introduced in the canonical basis as the operator-valued measures of the QS integration over a space-time.
Noncommutative dynamics is the unified dynamics of quantum and classical systems on a C *-algebra represented in a Hilbert space Γ with a generating state vector
- Mathematics
- 2010
We review the basic concepts of quantum stochastics using the universal Itô *-algebra approach. The main notions and results of classical and quantum stochastics are reformulated in this unifying…
Multiple Q-Adapted Integrals and Ito Formula of Noncommutative Stochastic Calculus in Fock Space
- Mathematics
- 2011
We study the continuity property of multiple Q-adapted quantum stochastic integrals with respect to noncommuting integrands given by the non-adapted multiple integral kernels in Fock scale. The…
Noncommutative dynamics and generalized master equations
- Mathematics
- 2010
We review the basic concepts of quantum probability and stochastics using the universal Itô B*-algebra approach. The main notions and results of classical and quantum stochastics are reformulated in…
Quantum stochastic calculus with maximal operator domains.
- Mathematics
- 2004
Quantum stochastic calculus is extended in a new formulation in which its stochastic integrals achieve their natural and maximal domains. Operator adaptedness, conditional expectations and stochastic…
Quantum Stochastic Calculus with Maximal Operator Domains 1
- Mathematics
- 2004
Quantum stochastic calculus is extended in a new formulation in which its stochastic integrals achieve their natural and maximal domains. Operator adaptedness, conditional expectations and stochastic…
A canonical dilation of the Schrödinger equation
- Mathematics, PhysicsRussian Journal of Mathematical Physics
- 2014
In this paper we shall re-visit the well-known Schrödinger equation of quantum mechanics. However, this shall be realized as a marginal dynamics of a more general, underlying stochastic counting…
A canonical dilation of the Schrödinger equation
- Mathematics, Physics
- 2014
In this paper we shall re-visit the well-known Schrödinger equation of quantum mechanics. However, this shall be realized as a marginal dynamics of a more general, underlying stochastic counting…
References
SHOWING 1-10 OF 30 REFERENCES
A new form and a ⋆-algebraic structure of quantum stochastic integrals in Fock space
- Mathematics
- 1988
An algebraic definition of the basic quantum process for the noncommutative stochastic calculus is given in terms of the Fock representation of a Lie ⋆-algebra of matrices in a pseudo-Euclidean…
Quantum Ito's formula and stochastic evolutions
- Mathematics
- 1984
Using only the Boson canonical commutation relations and the Riemann-Lebesgue integral we construct a simple theory of stochastic integrals and differentials with respect to the basic field operator…
Cohomology of power sets with applications in quantum probability
- Mathematics
- 1989
Square integrable Wiener functionals may be represented as sums of multiple Itô integrals. This leads to an identification of such functionals with square integrable functions on the symmetric…
Reconstruction theorem for a quantum stochastic process
- Mathematics, Physics
- 1985
This paper gives a physically interpretable--in real time--definition of a QSP as families of representations of the observable algebra 'B' in a common (large) system by indicating a universal method…
Generalized stochastic integrals and the malliavin calculus
- Mathematics
- 1986
SummaryThe paper first reviews the Skorohod generalized stochastic integral with respect to the Wiener process over some general parameter space T and it's relation to the Malliavin calculus as the…
Quantum Markov processes on Fock space described by integral kernels
- Mathematics
- 1985
A description is introduced of operators on Fock space by way of integral kernels. In terms of these kernels, the quantum stochastic differential equation for a Markov process over the n×n matrices…