STOCHASTIC MEHLER KERNELS VIA OSCILLATORY PATH INTEGRALS

  • 발행 : 2001.03.01

초록

The configuration space and phase space oscillatory path integrals are computed in the case of the stochastic Schrodinger equation for the harmonic oscillator with a stochastic term of the form (K$\psi$(sub)t)(x) o dW(sub)t, where K is either the position operator or the momentum operator, and W(sub)t is the Wiener process. In this way formulae are derived for the stochastic analogues of the Mehler kernel.

키워드

참고문헌

  1. Potential Analysis v.4 Stationary phase method in infinite dimensions by finite dimensional opproximations: Applications to the Schrodinger equation S.Albeverio;A.B.de Monvel-Berthier;Z.Brzezniak
  2. Lecture Notes in Math v.523 Mathematical Theory of Feynman Path Integrals S.A.Albeverio;R,J.Hoegh-Krohn
  3. Comptes Rendus Acad.Sci.Paris v.323 Representation of the solutions of the Belackin quantum measurement equation by the Menski functional formula S.A.Albeberio;V.N.Kolokol'tsov
  4. Phys.Lett.A v.140 A new wave equation for a continuous nondemolition measurement V.P.Belvkin
  5. Kokl.Akad.Nauk Feynman path integral corresponding to the stochastic Schrodinger equation V.P.Belavkin;O.G,Smolyanov
  6. Phys Lett.A. v.129 Continuous quantum measurement and Ito formalism L.Diosi
  7. Ann,Inst,H,Poincare,Phys.Theor v.41 no.2 Feynman maps Cameron-Martin formulae and anharmonic oscillators K.D.Elworthy;A.Truman
  8. Comm.Math,Phys. v.93 Quantum Ito's formula and stochastic evolutions R,L.Hudson;K.T.Parthasarathy
  9. Math.Z. v.37 Notes on random functions R,E,A,C,Paley;N,Wiener;A,Zygmund
  10. PhD Thesis Topics on Stochastic Schrodinger Equations and Estimates for the Derivative of Diffusion Semigroups L.Rincon
  11. Feynman Path Integrals,Proc. INternat.Colloq.,Mareille,1978 ,Lecture Notes in Phys v.106 The polygonal path formulation of the Feynman path integral A,Truman;S.A.Albeverio(Ed);PhCombe(Ed)et al
  12. Seminar on Stochastic Analysis,Random Feilds and Qpplications, Centro Stefano Franscini,Ascona, Stochastic PDE's of Schrodinger type and stochastic Mehler kernels - a path integral approach A,Truman;T,Zastawniak;R.Dalang(ed);M.Dozzi(ed);F,Russo(ed)
  13. Stochastic Partial Drfferental Equations, LMS Lecture Note Series v.216 Stochasic Hamilton-Jacobi equations and related topics A,Truman;H.Z.Zhao;A.Etheridge(ed)
  14. Z.Wahrschein.Ver.Geb v.11 On the optimal filtering of diffusion processes M.Zakai
  15. Lett.Math.Phys. v.41 no.1 Fresnel type path integrals for the stochastic Schrodinger equation T.Zastawniak
  16. Univ.Iagel.Acta Math v.28 The equivalence of two approaches to the Feynman integral for the anharmonic oscillator T.Zastawiak