# Tag Info

Accepted

### Lindblad equation for Heisenberg operators?

$\def\dd{{\rm d}} \def\LL{\mathcal{L}} \def\ii{{\rm i}} \def\ee{{\rm e}}$ The trick here is very simple and physically motivated. You simply demand that the expectation value of an operator $A$ is the ...
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### Ohmic spectral density

I like to think of the spectral density as a filter for the bosonic field frequencies, it tells you "how much" of each frequency there is. In this case, if $S=1$ you have a linear increase ...
• 466
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### Why should the dynamics of open quantum systems be always linear?

First of all, let me point out that there are theories that propose nonlinear extensions to quantum mechanics (for instance Weinberg's nonlinear quantum mechanics). But there are very strong arguments ...
• 15.5k
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### Fastest numerical method to solve Lindblad Master Equation?

Are you familiar with the Stochastic simulation method (quantum trajectories)? It reduces the cost from evolving and $N\times N$ density matrix, to wavefunctions $|\psi\rangle$ of only $N$ elements. ...
• 1,545
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### Hermitian and non-Hermitian jump operators in Lindblad master equation

Writing the Lindblad equation in non-diagonal form with Hermitian operators is always possible. This follows from the simple observation that an arbitrary operator can be expanded in a Hermitian ...
• 15.5k

### What is an open quantum system?

The examples you give are of two particle systems. The open quantum system presupposes a many body state. The underlying nature of reality is quantum mechanical , thus all particles in the universe, ...
• 233k
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### Pure dephasing $\gamma_\phi$ in a master equation and noise power spectral densities

$\def\ii{{\rm i}} \def\dd{{\rm d}} \def\ee{{\rm e}}$ It turns out that the case of pure dephasing is exactly solvable, and one can obtain nice solutions under certain conditions. In particular, I ...
• 15.5k
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### Is the Heisenberg picture of an open-system very different than that of a closed one?

Indeed, for a product operator $\hat{C} = \hat{A}\hat{B}$, it is not true that $\hat{C}(t) = \hat{A}(t) \hat{B}(t)$ for a general (i.e. non-unitary) evolution in the Heisenberg picture. It is ...
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### Lindblad and Input-Output Formalism in Quantum Optics

There is already a nice answer but I feel that some important aspects deserve additional attention. My answer is simply a list of observations: Master equations involve approximations: It is ...
• 11.5k
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### Born-Markov Approximation: Why is $\rho_{I}(s) \to \rho_{I}(t)$ taken, and not $\rho(s) \to \rho(t)$?

Roughly speaking, it is the SchrÃ¶dinger-picture density operator which has rapidly oscillating phase factors. Transforming to the interaction picture removes these phase factors. The residual time ...
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### Why do time evolution semigroups have to be contracting?

I do not know the general context, but I see that the book deals with open systems. The probability is not conserved, in general, for open systems. However it cannot increase (it remains a probability)...
• 70.7k
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### Consistency of Lindblad-type operator evolution equations

The adjoint Liouvillian generates a perfectly acceptable operator evolution from a quantum-mechanical point of view. However, the Leibniz rule no longer applies with respect to the operator product, ...
• 15.5k
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### Classical approximation of coupling to a quantum bath

$\def\ii{{\rm i}} \def\dd{{\rm d}} \def\ee{{\rm e}} \def\Tr{{\rm Tr}}$As far as I know and would expect, the replacement of a quantum heat reservoir with a noisy classical field cannot be rigorously ...
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• 15.5k

### What is an open quantum system?

The distinction between an open and a closed quantum system is mostly about whether information about the system is copied into the outside world, not about interaction per se. Suppose, for example, ...
• 7,114
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I have done more reading and see an important point I missed above. In my last line for $\dot{\rho_A(t)}$ I made the step $$\text{Tr}_B(\mathcal{L}[\rho(t)]) = \mathcal{L}_A[\rho_A(t)]$$ This step ...
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### Correspondence between ground state and steady state in quantum systems

The system + environment will not go into its ground state if it is isolated. In fact, it will not even go to an equilibrium state but keep evolving under the unitary dynamics govered by the total ...
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