Physics Stack Exchange
Physics Stack Exchange

Questions tagged [open-quantum-systems]

The study of open quantum systems is concerned with understanding and predicting the dynamics of quantum systems that are coupled significantly to their surroundings, leading to effects such as dissipation and decoherence.

All quantum systems are coupled to their surroundings to some extent. In some cases, this coupling is so weak that the system can be treated as approximately isolated, so that the usual laws of unitary quantum evolution apply. However, in many cases, the influence of the environment cannot be ignored and the system no longer evolves unitarily, in which case the quantum system is called open. The study of open quantum systems is concerned with understanding and predicting the dynamics of such open systems, including the most important effects arising due to their unavoidable interaction with the environment, such as decoherence and energy dissipation.

307 questions
23
votes
3 answers

What is the physical meaning of the Lindblad operator?

I read the wikipedia article on the Lindblad operator, but I still don't understand what this operator is supposed to describe. I therefore considered setting up an example in order to get the idea. So let $H$ be the Hamiltonian of the first $n$…
user167575
  • 373
  • 1
  • 3
  • 7
20
votes
2 answers

Lindblad equation for Heisenberg operators?

Very related to this question: Is it possible to go from the Master Equation formalism to Heisenberg-Langevin equations I don't yet have enough reputation to comment so I'm asking the new question here. I'm coming from a physics background on this…
Jagerber48
  • 16,234
18
votes
3 answers

What information is contained in the quantum spectral density?

Consider a harmonic oscillator system with Hamiltonian $$\hat{H} = \frac{1}{2} A \hat{u}^2 + \frac{1}{2} B \hat{v}^2 \qquad [\hat{u}, \hat{v}]=i \gamma $$ where $A$, $B$, and $\gamma$ are all real. This system has resonance frequency $\omega_0 =…
DanielSank
  • 25,766
16
votes
2 answers

Caldeira-Leggett Dissipation: frequency shift due to bath coupling

I am trying to understand the Caldeira-Leggett model. It considers the Lagrangian $$L = \frac{1}{2} \left(\dot{Q}^2 - \left(\Omega^2-\Delta \Omega^2\right)Q^2\right) - Q \sum_{i} f_iq_i + \sum_{i}\frac{1}{2} \left(\dot{q}^2 - \omega_i^2q^2\right)$$…
Smerdjakov
  • 547
13
votes
2 answers

Numerical Simulation of Stochastic Master Equation using Stochastic Schrödinger Equation (Wave Function Monte Carlo)

Consider a time independent system coupled to a Markovian bath, the equation of motion for the density matrix of the system has to take the form \begin{equation} \dot{\rho} = - i \left[H,\rho\right] - \sum_m \left(c_m^{\dagger}c_m\rho+ \rho…
loewe
  • 746
12
votes
1 answer

Ohmic spectral density

I am witting a paper about the non-Markovian effects of open quantum systems (a qubit interacting with a bosonic environment). I am using a spectral density of the form below: $$ J(\omega) = \frac{\omega^S}{\omega_C^{S-1}}e^{-\omega/\omega_C} $$ I…
Zeinab
  • 121
12
votes
1 answer

Why does a damped quantum harmonic oscillator have the same decay rate as the equivalent classical system?

$\newcommand{ket}[1]{|#1\rangle} \newcommand{bbraket}[3]{\langle #1 | #2 | #3 \rangle}$ Why does the decay rate for a damped quantum harmonic oscillator exactly match the classical limit? Background Consider a localized quantum system $S$ connected…
DanielSank
  • 25,766
11
votes
1 answer

Hermitian and non-Hermitian jump operators in Lindblad master equation

Is there a way of rotating non-Hermitian jump operators for a Lindblad master equation (LME) to a basis where they are Hermitian? In other words, I have a (diagonal) LME: $$ \dot{\rho} = -i [\mathcal{H}, \rho] + \sum_{\alpha} \gamma_{\alpha} \left[…
PolMol
  • 113
  • 6
11
votes
5 answers

Negativity of the real part of eigenvalues of Lindblad operators

I'm looking for a proof of the fact that the real part of eigenvalues of Lindblad operators is always negative. So far I have only found handwavy arguments such as "things should not blow up at infinitely long-time".
Jean Pierre Polnareff
  • 153
  • 5
11
votes
2 answers

Is the Heisenberg picture of an open-system very different than that of a closed one?

For a closed system the time evolution (in the Heisenberg picture) of an operator $A$ is given by $$A(t) = U^{\dagger}(t)AU(t)$$ with $U^{\dagger} U = 1\!\!1$, so that for some other operator $C$ we have: $$C(t) = (AB)(t) = A(t)B(t)$$ However for…
user29918
  • 221
11
votes
1 answer

Using open system dynamics to define a quantum state

Background The density matrix of a closed quantum system with Hilbert space $\mathscr H$ evolves according to the von Neumann equation \begin{align*} i\hbar\dot\rho=[H,\rho]. \end{align*} Given a solution $\rho(t)$ to the above equation, the…
TLDR
  • 3,836
11
votes
5 answers

How can one model quantum walks in photosynthesis?

I have been working on quantum biology and found something interesting that I would like to write an equation for. Scientists have wondered how plants have such a high efficiency in photosynthesis; they always thought that the photons' energy…
TanMath
  • 1,785
10
votes
4 answers

What is an open quantum system?

What is an open quantum system? The simple quantum textbook examples like Simple Harmonic Oscillator potential and H-atom, seem to me open quantum systems, since the particle interacts with the potential. How is exactly the problem of open quantum…
Seeker
  • 592
9
votes
2 answers

Fastest numerical method to solve Lindblad Master Equation?

The Lindblad Master Equation is a generalization of the Schrodinger Equation for open quantum systems, given by $$ \frac{\mathrm{d} \rho}{\mathrm{d}t} = -i \left[ H, \rho\right] + \sum_k \gamma_k \left( L_k \rho L_k^\dagger - \frac{1}{2} \left\{…
Ronan
  • 462
9
votes
2 answers

How to efficiently check if a superoperator is Lindbladian?

Superoperators are linear maps on the vector space of linear operator. The Lindbladian superoperators are the important subset that can be expressed in the form $$\mathcal{L}[\rho] = -i (H \rho - \rho H) + \sum_i L_i\rho L_i^\dagger -…
Jess Riedel
  • 3,764
1
2 3
…
20 21