STOCHASTIC DIFFERENTIAL EQUATIONS FOR THE CONTINUOUS SPONTANEOUS LOCALIZATION MODEL

2000 ◽  
Vol 15 (30) ◽  
pp. 1833-1842
Author(s):  
L. F. SANTOS ◽  
C. O. ESCOBAR
Keyword(s):  
Wave Function ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Quantum System ◽  
Open Quantum System ◽  
Random Potential ◽  
Free Particle ◽  
Localization Model ◽  
Spontaneous Localization ◽  
Continuous Spontaneous Localization

We extend Vink's method [J. C. Vink, Phys. Rev.A48, 1808 (1993)], developed for an isolated quantum system, to an open quantum system consisting of a free particle interacting with its surrounding through a random potential, which causes the spontaneous localization of its wave function. We then obtain the stochastic differential equations (SDE) underlying its evolution. These SDE help us to observe the effects of the environment upon the movement of the particle.

scholarly journals Experimental constrains on the Continuous Spontaneous Localization model from spontaneous radiation emission

2018 ◽  
Author(s):  
kristian Piscicchia ◽  
Angelo Bassi ◽  
Catalina Curceanu ◽  
Sandro Donadi ◽  
Andreas Pichler ◽  
...  
Keyword(s):  
Spontaneous Radiation ◽  
Radiation Emission ◽  
Localization Model ◽  
Spontaneous Localization ◽  
Continuous Spontaneous Localization

On characterizing quantum stochastic evolutions

1987 ◽  
Vol 102 (2) ◽  
pp. 363-369 ◽  
Author(s):  
R. L. Hudson ◽  
J. M. Lindsay
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Quantum System ◽  
Free Evolution ◽  
Quantum Dynamical ◽  
Quantum Dynamical Semigroups ◽  
Reversible Evolution ◽  
Boson Reservoir

It has recently been shown [7, 8, 4] that Markov dilations of quantum dynamical semigroups may be constructed by solving corresponding quantum stochastic differential equations. These equations may be interpreted as describing the evolution of a quantum system with a singular coupling to a Boson reservoir, moreover, when solutions are combined with the free evolution of the reservoir, a reversible evolution results which may be interpreted as that of the system plus reservoir. It is the purpose of the present paper to characterize the above stochastic evolutions essentially by a condition of with respect to the free evolution.

scholarly journals Effect of high frequency modes of medium on an open quantum system

2016 ◽  
Vol 31 (02) ◽  
pp. 1650002
Author(s):  
Nirupam Dutta ◽  
A. K. Chaudhuri ◽  
P. K. Panigrahi
Keyword(s):  
Wave Function ◽  
Density Matrix ◽  
Quantum System ◽  
Open System ◽  
High Frequency ◽  
Open Quantum System ◽  
Harmonic Oscillators ◽  
Open Quantum ◽  
Type Oscillation ◽  
High Frequency Modes

We present a method to calculate the real time effective propagator of a generic open quantum system, immersed in a medium using a wave function based framework. The medium is characterized by a set of harmonic oscillators having a continuous span of frequencies. This technique has been applied to the Caldeira–Leggett model showing that high frequency modes of the medium do not contribute towards decay of the population of states of the open system. In fact, they cause a Rabi-type oscillation. Moreover, our wave function based approach provides an excellent alternative to conventional formalisms involving the density matrix.

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