The quantum jump method, also known as the

Monte Carlo Monte Carlo ( ; ; or colloquially ; , ; ) is an official administrative area of Monaco, specifically the Ward (country subdivision), ward of Monte Carlo/Spélugues, where the Monte Carlo Casino is located. Informally, the name also refers to ...

wave function (MCWF) is a technique in

computational physics Computational physics is the study and implementation of numerical analysis to solve problems in physics. Historically, computational physics was the first application of modern computers in science, and is now a subset of computational science ...

used for simulating

open quantum system In physics, an open quantum system is a quantum-mechanical system that interacts with an external quantum system, which is known as the ''environment'' or a ''bath''. In general, these interactions significantly change the dynamics of the system a ...

s and

quantum dissipation Quantum dissipation is the branch of physics that studies the quantum analogues of the process of irreversible loss of energy observed at the classical level. Its main purpose is to derive the laws of classical dissipation from the framework of qua ...

. The quantum jump method was developed by Dalibard, Castin and Mølmer at a similar time to the similar method known as

Quantum Trajectory Theory In physics, a quantum (: quanta) is the minimum amount of any physical entity (physical property) involved in an interaction. The fundamental notion that a property can be "quantized" is referred to as "the hypothesis of quantization". This me ...

developed by Carmichael. Other contemporaneous works on wave-function-based

approaches to open quantum systems include those of Dum, Zoller and Ritsch and Hegerfeldt and Wilser.The associated primary sources are, respectively: * * * *

Method

The quantum jump method is an approach which is much like the master-equation treatment except that it operates on the wave function rather than using a

density matrix In quantum mechanics, a density matrix (or density operator) is a matrix used in calculating the probabilities of the outcomes of measurements performed on physical systems. It is a generalization of the state vectors or wavefunctions: while th ...

approach. The main component of this method is evolving the system's wave function in time with a pseudo-Hamiltonian; where at each time step, a quantum jump (discontinuous change) may take place with some probability. The calculated system state as a function of time is known as a quantum trajectory, and the desired

as a function of time may be calculated by averaging over many simulated trajectories. For a Hilbert space of dimension N, the number of wave function components is equal to N while the number of density matrix components is equal to N². Consequently, for certain problems the quantum jump method offers a performance advantage over direct master-equation approaches.

References

External links

mcsolve
Quantum jump (

) solver from QuTiP for

Python Python may refer to: Snakes * Pythonidae, a family of nonvenomous snakes found in Africa, Asia, and Australia ** ''Python'' (genus), a genus of Pythonidae found in Africa and Asia * Python (mythology), a mythical serpent Computing * Python (prog ...

.
QuantumOptics.jl
the quantum optics toolbox in

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.
Quantum Optics Toolbox
for

Matlab MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementat ...

Quantum mechanics Computational physics Monte Carlo methods {{Quantum-stub

Method

References

Further reading

External links