aqora

Non-Markovian Stochastic Schrodinger Equations

Jay Gambetta, Howard M. Wiseman

Jan 1, 20010 citations

The non-Markovian stochastic Schrödinger equation for open systems

Lajos Diósi, Walter T. Strunz

arXiv:quant-ph/9706050Physics Letters ANov 1, 1997283 citations

Perturbative approach to non-Markovian stochastic Schrödinger equations

Jay Gambetta, Howard M. Wiseman

In this paper we present a perturbative procedure that allows one to numerically solve diffusive non-Markovian stochastic Schr\"odinger equations, for a wide range of memory functions. To illustrate this procedure numerical results are presented for a classically driven two-level atom immersed in an environment with a simple memory function. It is observed that as the order of the perturbation is increased the numerical results for the ensemble average state ${\ensuremath{\rho}}_{\mathrm{red}}(t)$ approach the exact reduced state found via $\mathrm{Imamo}\mathrm{g}\ifmmode\bar\else\textasciimacron\fi{}{\mathrm{lu}}^{\ensuremath{'}}\mathrm{s}$ enlarged system method [Phys. Rev. A 50, 3650 (1994)].In this paper we present a perturbative procedure that allows one to numerically solve diffusive non-Markovian stochastic Schr\"odinger equations, for a wide range of memory functions. To illustrate this procedure numerical results are presented for a classically driven two-level atom immersed in an environment with a simple memory function. It is observed that as the order of the perturbation is increased the numerical results for the ensemble average state ${\ensuremath{\rho}}_{\mathrm{red}}(t)$ approach the exact reduced state found via $\mathrm{Imamo}\mathrm{g}\ifmmode\bar\else\textasciimacron\fi{}{\mathrm{lu}}^{\ensuremath{'}}\mathrm{s}$ enlarged system method [Phys. Rev. A 50, 3650 (1994)].

arXiv:quant-ph/0208169Physical Review ANov 18, 200232 citations

Markovian unraveling of non-Markovian stochastic Schr\"odinger equations

Antoine Tilloy

Non-Markovian stochastic Schrodinger equations (NMSSE) are important tools in quantum mechanics, from the theory of open systems to foundations. Yet, in general, they are but formal objects: their solution can be computed numerically only in some specific cases or perturbatively. This article is focused on the NMSSE themselves rather than on the open-system evolution they unravel and aims at making them less abstract. Namely, we propose to write the stochastic realizations of linear NMSSE as averages over the solutions of an auxiliary equation with an additional random field. Our method yields a non-perturbative numerical simulation algorithm for generic linear NMSSE that can be made arbitrarily accurate for reasonably short times. For isotropic complex noises, the method extends from linear to non-linear NMSSE and allows to sample the solutions of norm-preserving NMSSE directly.Non-Markovian stochastic Schrodinger equations (NMSSE) are important tools in quantum mechanics, from the theory of open systems to foundations. Yet, in general, they are but formal objects: their solution can be computed numerically only in some specific cases or perturbatively. This article is focused on the NMSSE themselves rather than on the open-system evolution they unravel and aims at making them less abstract. Namely, we propose to write the stochastic realizations of linear NMSSE as averages over the solutions of an auxiliary equation with an additional random field. Our method yields a non-perturbative numerical simulation algorithm for generic linear NMSSE that can be made arbitrarily accurate for reasonably short times. For isotropic complex noises, the method extends from linear to non-linear NMSSE and allows to sample the solutions of norm-preserving NMSSE directly.

Jan 8, 20170 citations

Time-local unraveling of non-Markovian stochastic Schrödinger equations

Antoine Tilloy

Non-Markovian stochastic Schrödinger equations (NMSSE) are important tools in quantum mechanics, from the theory of open systems to foundations. Yet, in general, they are but formal objects: their solution can be computed numerically only in some specific cases or perturbatively. This article is focused on the NMSSE themselves rather than on the open-system evolution they unravel and aims at making them less abstract. Namely, we propose to write the stochastic realizations of linear NMSSE as averages over the solutions of an auxiliary equation with an additional random field. Our method yields a non-perturbative numerical simulation algorithm for generic linear NMSSE that can be made arbitrarily accurate for reasonably short times. For isotropic complex noises, the method extends from linear to non-linear NMSSE and allows to sample the solutions of norm-preserving NMSSE directly.Non-Markovian stochastic Schrödinger equations (NMSSE) are important tools in quantum mechanics, from the theory of open systems to foundations. Yet, in general, they are but formal objects: their solution can be computed numerically only in some specific cases or perturbatively. This article is focused on the NMSSE themselves rather than on the open-system evolution they unravel and aims at making them less abstract. Namely, we propose to write the stochastic realizations of linear NMSSE as averages over the solutions of an auxiliary equation with an additional random field. Our method yields a non-perturbative numerical simulation algorithm for generic linear NMSSE that can be made arbitrarily accurate for reasonably short times. For isotropic complex noises, the method extends from linear to non-linear NMSSE and allows to sample the solutions of norm-preserving NMSSE directly.

arXiv:1701.01948QuantumSep 19, 201710 citations

Stochastic Schrödinger Equations

Wilfried Grecksch, Hannelore Lisei

WORLD SCIENTIFIC eBooksApr 26, 20203 citations

Markovian embedding procedures for non-Markovian stochastic Schrödinger equations

Related papers

Markovian embedding procedures for non-Markovian stochastic Schrödinger equations

Related papers