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QUANTUM STOCHASTIC INTEGRAL EQUATIONS WITH EXPONENTIAL NOISE
, 1995A. Boukas
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Gauge Integral Structures for Stochastic Calculus and Quantum Electrodynamics
, 2021Patrick Joseph Muldowney
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Stochastic Mechanics: The Unification of Quantum Mechanics with Brownian Motion
SpringerBriefs in Physics, 2023We unify Brownian motion and quantum mechanics in a single mathematical framework. In particular, we show that non-relativistic quantum mechanics of a single spinless particle on a flat space can be described by a Wiener process that is rotated in the ...
F. Kuipers
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Quantum stochastic integration and quantum stochastic differential equations
Mathematical Proceedings of the Cambridge Philosophical Society, 1994AbstractQuantum stochastic integrals are constructed using the non-commutativeLp-space theory of Haagerup. The existence and uniqueness of the solution to quantum stochastic differential equations driven by quasi-Wiener noises, or noises satisfying generalized standing hypotheses, is established as is the Markov behaviour of the solution.
Barnett, Chris +2 more
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ContHutch++: Stochastic trace estimation for implicit integral operators
SIAM Journal on Numerical Analysis, 2023Hutchinson's estimator is a randomized algorithm that computes an $\epsilon$-approximation to the trace of any positive semidefinite matrix using $\mathcal{O}(1/\epsilon^2)$ matrix-vector products. An improvement of Hutchinson's estimator, known as Hutch+
Jennifer Zvonek +2 more
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Quantum mechanics from stochastic processes
The European Physical Journal Plus, 2023We construct an explicit one-to-one correspondence between non-relativistic stochastic processes and solutions of the Schrödinger equation and between relativistic stochastic processes and solutions of the Klein–Gordon equation.
F. Kuipers
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Multidimensional Quantum Stochastic Integrals
AIP Conference Proceedings, 2011Quantum stochastic analogues (H,A{Az}z∈R+,m,R+), of a classical stochastic base may be formed whereby a classical sample space Ω is replaced by a Hilbert Space H, σ‐field F is replaced by a von Neumann algebra b, the filtration {FI}i∈I by a filtration {Bz}z of von Neumann subalgebras of the von Neumann algebra B and the probability measure P with gage ...
William Joseph Spring +2 more
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Stochastic path-integral simulation of quantum scattering
Physical Review A, 1993We present a path-integral solution for the exact propagation of the Wigner distribution in phase space, which is an improved version of results obtained [Maslov, Bertrand, Combe, and co-workers, J. Sov. Math. 13, 315 (1980); 19, 55 (1982); Lett. Math. Phys. 7, 327 (1983); Physica 124A, 561 (1984)] and is suitable for Monte Carlo simulations.
, Schmidt, , Möhring
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Symmetrized double quantum stochastic product integrals
Journal of Mathematical Physics, 2000A theory is developed of product integrals of the form ∏a<s<b ∏c<t<d(1+g[h] (ds,dt)). Here [a,b[ and [c,d[ are disjoint finite subintervals of R+, and g[h] is a formal power series in the indeterminate h whose constant term is zero and whose coefficients are elements of L⊗L, where ℒ is the space of basic differentials of a ...
Hudson, R. L., Pulmannová, S.
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On a causal quantum stochastic double product integral related to Lévy area
Annales de l'Institut Henri Poincaré D, 2018We study the family of causal double product integrals Pi(a < x < y < b) (1 + i lambda/2 (dP(x)dQ(y) - dQ(x)dP(y)) + i mu/2 (dP(x)dP(y) + dQ(x)dQ(y))), where P and Q are the mutually nonco ...
R. Hudson, Y. Pei
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