Realization of Unitary q-White Noise on Fock Space

1991 ◽  
pp. 377-386
Author(s):  
Michael Schürmann
Keyword(s):  
White Noise ◽  
Fock Space

scholarly journals White noise delta functions and continuous version theorem

1993 ◽  
Vol 129 ◽  
pp. 1-22
Author(s):  
Nobuaki Obata
Keyword(s):  
White Noise ◽  
Harmonic Analysis ◽  
Quantum Physics ◽  
Fock Space ◽  
Continuous Version ◽  
Infinite Dimensional ◽  
Schwartz Distribution ◽  
Delta Functions ◽  
Gelfand Triple ◽  
Gaussian Space

The recently developed Hida calculus of white noise [5] is an infinite dimensional analogue of Schwartz’ distribution theory besed on the Gelfand triple (E) ⊂ (L2) = L2 (E*, μ) ⊂ (E)*, where (E*, μ) is Gaussian space and (L2) is (a realization of) Fock space. It has been so far discussed aiming at an application to quantum physics, for instance [1], [3], and infinite dimensional harmonic analysis [7], [8], [13], [14], [15].

COMPLEX WHITE NOISE ANALYSIS

2001 ◽  
Vol 04 (03) ◽  
pp. 347-375
Author(s):  
MYLAN REDFERN
Keyword(s):  
Stochastic Processes ◽  
White Noise ◽  
Fock Space ◽  
Noise Analysis ◽  
White Noise Analysis ◽  
Space Decomposition ◽  
New Space ◽  
Class Of Functions

This paper describes a new space, [Formula: see text], of complex Wiener distributions for the analysis of multi-parameter generalized stochastic processes [Formula: see text]. For a certain class of functions [Formula: see text] and complex Wiener integrals Φ1, …, Φm, F(Φ1, …, Φm) is defined as an element of [Formula: see text] and its Fock space decomposition determined.

A NOTE ON CONVOLUTION OPERATORS IN WHITE NOISE CALCULUS

2011 ◽  
Vol 14 (04) ◽  
pp. 661-674 ◽  
Author(s):  
NOBUAKI OBATA ◽  
HABIB OUERDIANE
Keyword(s):  
Laplace Transform ◽  
White Noise ◽  
Convolution Operator ◽  
Fock Space ◽  
Wick Product ◽  
Convolution Product ◽  
Convolution Operators ◽  
S Transform ◽  
The Laplace Transform ◽  
White Noise Calculus

We derive some characteristic properties of the convolution operator acting on white noise functions and prove that the convolution product of white noise distributions coincides with their Wick product. Moreover, we show that the S-transform and the Laplace transform coincide on Fock space.

QUANTUM STOCHASTIC ANALYSIS VIA WHITE NOISE OPERATORS IN WEIGHTED FOCK SPACE

2002 ◽  
Vol 14 (03) ◽  
pp. 241-272 ◽  
Author(s):  
DONG MYUNG CHUNG ◽  
UN CIG JI ◽  
NOBUAKI OBATA
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
White Noise ◽  
Fock Space ◽  
Existence Of A Solution ◽  
Quantum Stochastic Differential Equation ◽  
Unique Existence ◽  
Regularity Properties ◽  
Weighted Fock Space ◽  
White Noises

White noise theory allows to formulate quantum white noises explicitly as elemental quantum stochastic processes. A traditional quantum stochastic differential equation of Itô type is brought into a normal-ordered white noise differential equation driven by lower powers of quantum white noises. The class of normal-ordered white noise differential equations covers quantum stochastic differential equations with highly singular noises such as higher powers or higher order derivatives of quantum white noises, which are far beyond the traditional Itô theory. For a general normal-ordered white noise differential equation unique existence of a solution is proved in the sense of white noise distribution. Its regularity properties are investigated by means of weighted Fock spaces interpolating spaces of white noise distributions and associated characterization theorems for S-transform and for operator symbols.

scholarly journals The q-Gamma White Noise

2016 ◽  
Vol 66 (1) ◽  
pp. 81-90
Author(s):  
Hakeem A. Othman
Keyword(s):  
White Noise ◽  
Fock Space ◽  
Infinite Dimensional ◽  
Chaos Decomposition ◽  
Noise Measure ◽  
Interacting Fock Space

Abstract For 0 < q < 1 and 0 < α < 1, we construct the infinite dimensional q-Gamma white noise measure γα,q by using the Bochner-Minlos theorem. Then we give the chaos decomposition of an L2 space with respect to the measure γα,q via an isomorphism with the 1-mode type interacting Fock space associated to the q-Gamma measure.

scholarly journals Quantum white noises—White noise approach to quantum stochastic calculus

1993 ◽  
Vol 129 ◽  
pp. 23-42 ◽  
Author(s):  
Zhiyuan Huang
Keyword(s):  
Hilbert Space ◽  
White Noise ◽  
Fock Space ◽  
Stochastic Calculus ◽  
Quantum Stochastic Calculus ◽  
Integrable Functions ◽  
Boson Fock Space ◽  
Square Integrable Functions ◽  
Complex Valued ◽  
White Noises

Let H = L2 (R) be the Hilbert space of all complex-valued square integrable functions defined on R, Ф = Γ(H) be the Boson Fock space over H. For each h ∈ H, denote by ε(h) the corresponding exponential vector:in particular ε(0) is the Fock vacuum.

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