scholarly journals Scattering of polarized laser light by an atomic gas in free space: A quantum stochastic differential equation approach

2007 ◽  
Vol 75 (5) ◽  
Author(s):  
Luc Bouten ◽  
John Stockton ◽  
Gopal Sarma ◽  
Hideo Mabuchi
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Free Space ◽  
Laser Light ◽  
Equation Approach ◽  
Quantum Stochastic Differential Equation ◽  
Atomic Gas

scholarly journals Pure Gaussian state generation via dissipation: a quantum stochastic differential equation approach

2012 ◽  
Vol 370 (1979) ◽  
pp. 5324-5337 ◽  
Author(s):  
Naoki Yamamoto
Keyword(s):  
Differential Equation ◽  
Steady State ◽  
Stochastic Differential Equation ◽  
Cluster State ◽  
Dissipative System ◽  
Complete Characterization ◽  
Gaussian State ◽  
Quantum State Transfer ◽  
Quantum Stochastic Differential Equation ◽  
Gaussian System

Recently, the complete characterization of a general Gaussian dissipative system having a unique pure steady state was obtained. This result provides a clear guideline for engineering an environment such that the dissipative system has a desired pure steady state such as a cluster state. In this paper, we describe the system in terms of a quantum stochastic differential equation (QSDE) so that the environment channels can be explicitly dealt with. Then, a physical meaning of that characterization, which cannot be seen without the QSDE representation, is clarified; more specifically, the nullifier dynamics of any Gaussian system generating a unique pure steady state is passive. In addition, again based on the QSDE framework, we provide a general and practical method to implement a desired dissipative Gaussian system, which has a structure of quantum state transfer.

Quantum Stochastic Differential Equation is Unitarily Equivalent to a Symmetric Boundary Value Problem in Fock Space

1998 ◽  
Vol 01 (02) ◽  
pp. 175-199 ◽  
Author(s):  
Alexander M. Chebotarev
Keyword(s):  
Differential Equation ◽  
Schrödinger Equation ◽  
Boundary Value Problem ◽  
Stochastic Differential Equation ◽  
Schrodinger Equation ◽  
Fock Space ◽  
Boundary Value ◽  
Weak Limit ◽  
Quantum Stochastic Differential Equation ◽  
Markov Evolution

We show a new remarkable connection between the symmetric form of a quantum stochastic differential equation (QSDE) and the strong resolvent limit of the Schrödinger equations in Fock space: the strong resolvent limit is unitarily equivalent to QSDE in the adapted (or Ito) form, and the weak limit is unitarily equivalent to the symmetric (or Stratonovich) form of QSDE. We also prove that QSDE is unitarily equivalent to a symmetric boundary value problem for the Schrödinger equation in Fock space. The boundary condition describes standard jumps in phase and amplitude of components of Fock vectors belonging to the range of the resolvent. The corresponding Markov evolution equation (the Lindblad or Markov master equation) is derived from the boundary value problem for the Schrödinger equation.

On the theory and application of one-step numerical schemes for solving quantum stochastic differential equation (QSDE)

2014 ◽  
Vol 07 (03) ◽  
pp. 1450037
Author(s):  
T. O. Akinwumi ◽  
B. J. Adegboyegun
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Stochastic Differential Equation ◽  
Numerical Experiments ◽  
Numerical Schemes ◽  
Quantum Stochastic Differential Equation ◽  
One Step ◽  
Definition Of ◽  
Convergent Sequences ◽  
Solution Techniques

This paper presents one-step numerical schemes for solving quantum stochastic differential equation (QSDE). The algorithms are developed based on the definition of QSDE and the solution techniques yield rapidly convergent sequences which are readily computable. As well as developing the schemes, we perform some numerical experiments and the solutions obtained compete favorably with exact solutions. The solution techniques presented in this work can handle all class of QSDEs most especially when the exact solution does not exist.

scholarly journals Fitting of von Bertalanffy growth model: Stochastic differential equation approach

2017 ◽  
Vol 64 (3) ◽  
Author(s):  
Prajneshu Gupta ◽  
Himadri Ghosh ◽  
N. N. Pandey
Keyword(s):  
Differential Equation ◽  
Rainbow Trout ◽  
Stochastic Differential Equation ◽  
Computer Code ◽  
Von Bertalanffy ◽  
Equation Approach ◽  
Length Relationship ◽  
Length Data ◽  
Von Bertalanffy Growth Model ◽  
Modelling Approach

In this paper, the well-known von Bertalanffy growth (VBG) model for estimating age-length relationship in fisheries is considered. It is emphasised that nonlinear estimation procedures should be adopted for fitting the von Bertalanffy nonlinear statistical (VBNS) model rather than the age-old Ford-Walford plot. Some limitations of employing VBNS modelling approach are highlighted. Employment of stochastic differential equation (SDE) approach, which does not suffer from these limitations, is advocated for fitting the VBG model. The methodology for fitting the von Bertalanffy SDE (VBSDE) model is described. Relevant computer code for fitting this model is written in SAS package and the same is included as an Appendix. Finally, as an illustration, superiority of VBSDE model over VBNS model for fitting and forecasting purposes is shown for rainbow trout (Onchorhynchus mykiss) age-length data.

A jump stochastic differential equation approach for influence prediction on heterogenous networks

2020 ◽  
Vol 18 (8) ◽  
pp. 2341-2359
Author(s):  
Yaohua Zang ◽  
Gang Bao ◽  
Xiaojing Ye ◽  
Hongyuan Zha ◽  
Haomin Zhou
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Equation Approach

ON THE HAMILTONIAN OPERATOR ASSOCIATED TO SOME QUANTUM STOCHASTIC DIFFERENTIAL EQUATIONS

2000 ◽  
Vol 03 (04) ◽  
pp. 483-503 ◽  
Author(s):  
M. GREGORATTI
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Unitary Group ◽  
Open Quantum System ◽  
Hamiltonian Operator ◽  
Stochastic Evolution ◽  
Quantum Stochastic Differential Equation ◽  
Special Cases ◽  
Densely Defined ◽  
Full Domain

We consider the quantum stochastic differential equation introduced by Hudson and Parthasarathy to describe the stochastic evolution of an open quantum system together with its environment. We study the (unbounded) Hamiltonian operator generating the unitary group connected, as shown by Frigerio and Maassen, to the solution of the equation. We find a densely defined restriction of the Hamiltonian operator; in some special cases we prove that this restriction is essentially self-adjoint and in one particular case we get the whole Hamiltonian with its full domain.

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