# 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.

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### Is there a way to quantify decoherence in the Heisenberg picture?

In the usual picture of decoherence: $\bullet$ you start with a state $| \psi(0) \rangle = | \psi_{S}(0) \rangle \otimes | \psi_{E}(0) \rangle$ for the system and environment (assumed to be ...
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### Are there any recommended texts for introduction to Lindblandian dynamics for third year undergraduate? [duplicate]

I am looking to learn Lindbladian dynamics and apply it to a system with multiple baths. Are there any texts available that only assume undergraduate Quantum Mechanics knowledge (My school offers ...
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### Derivation of Jump Operators in Master Equation

I'm trying to understand the process of deriving the master equation in this article. The system in general is composed of two interacting qubits each of which is coupled to their local thermal bath ...
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### The “Algorithm” for Derivation of the Master Equation

I'm trying to come up with a master equation for a spin system. So, I'm trying to understand in general how can we derive the master equation and the Lindblad operators if we know the system, bath and ...
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### What does the master equation for this quantum autonomous absorption refrigerator imply?

I'm following this paper: https://arxiv.org/abs/0908.2076, about building minimal and autonomous quantum absorption refrigerators. The setup is 3 qubits, each coupled to their own baths, and with some ...
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### Master Equation Second Order Approximation

I have a problem deriving the master equation using projection operator technique. If we are given the master equation which reads: $$\dot{\rho}= -\frac{i}{\hbar}[H_S+H_B+H_I,\rho]+\mathcal{D}\rho$$ ...
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### Expected value in usual quantum mechanics vs quantum information

In standard Quantum Mechanics, one computes the expected value of an operator $A$ (arbitrary state $|\Psi\rangle$) as $$\langle\Psi|A|\Psi\rangle.$$ This has the virtue that we can compute for ...
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### Lindblad equation unitary term (in practice)

The Lindblad equation is given by $$\dot\rho=-{i\over\hbar}[H,\rho]+\sum_{i = 1}^{N^2-1} \gamma_i\left(L_i\rho L_i^\dagger -\frac{1}{2} \left\{L_i^\dagger L_i, \rho\right\} \right),$$ where $H$ is ...
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### Why do the odd moments of the interaction Hamiltonian vanish w.r.t. a reference state?

When deriving the Nakajima-Zwanzig equation in The Theory of Open Quantum Systems by Breuer and Pettrucione, in Eq. 9.10, they state that In many cases it may also be assumed that the odd moments of ...
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### Difference between reactive (coherent) and dissipative coupling in open quantum systems?

I am unsure about the physical interpretation of the different types of coupling, I understand that reactive coupling is manifested by a term within the Hamiltonian and dissipative is via a term in ...
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### How do you compute saddle point approximation of path integral for open quantum system?

Note: the question in this post is basically originated from here. Please refer to it first if you don't get the sense. I'd like to know how you compute the saddle point approximation in the path ...
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### Dimensions of a non-hermitian Hamiltonian

I have recently started studying the non-hermitian hamiltonians and I came across an example- $H=p^2+ix^3$ (where $h=1$ and $m=1/2$) I know that hamiltonian is the total energy of the system. So how ...
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### Is $\hbar \rightarrow 0$ in path integral merely technical thing? Is there any justification? (especially in open quantum theory)

I wonder whether the limit $\hbar \rightarrow 0$ in path integral is merely technical stuff when we explain the classical limit of quantum mechanics, or there may be any physical meaning or sense ...
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### Why does the Franck-Condon matrix appear to not be unitary when written in the basis of phonon states?

Preliminary: The Franck-Condon (FC) matrix can be defined as \begin{align} X & = e^{-x(b^{\dagger} - b)}, \label{eq: FC 1} \end{align} where $b^{\dagger}$ and $b$ are standard bosonic creation ...
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### Common subsystem-bath interaction operators?

Im new to the field of quantum open systems and I wanted to know what are the most common operators for describing the subsystem-bath interaction. To narrow down a bit my question, say we have as a ...
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### Memory effects in open quantum systems: Markovian approximation question

Setting: Quantum system $S$ composed of a subsystem of interest $A$ and a subsystem acting as the environment $B$ such that $S=A\cup B$. System $S$ is described by density matrix $\rho$ whereas ...
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### Is the effective Hamiltonian obtained via Feshbach-Fano partitioning closed?

I am not familiar with Feshbach-Fano partitioning so this question may be trivial. The full Hamiltonian of an open quantum system consists of system+enviroment+interaction. This can be cast into an ...
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### Why do time evolution semigroups have to be contracting?

Studying the theory of open quantum systems, some textbooks start by introducing the notion of a semigroup for the time evolution operator $T_t$. The next step then usually is to impose that such a ...
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### Correspondence between ground state and steady state in quantum systems

An open quantum system $S$ is usually studied by considering a system of interest effectively interacting with an environment $E$. The environment is treated effectively because of the difficulty of ...
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### Derive master equation if one Lindblad term is already given

I have a following question: is it possible to derive master equation with Open Quantum systems approach if one Lindblad term is already given? For example, assume we have Liouville equation given ...
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### Derivation of Correlation function in Open Quantum Systems and Master Equation

I have a question and I have searched a long time about it without any success. It is about how to include convolution broadening incorrelation functions of bath operators, when using Open Quantum ...
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### Describing small, NRQM systems purely in terms of photons

Is there a canonical way to describe an open, non-relativistic quantum system with density matrix $\rho(t)$ entirely in terms of the light that it emits and absorbs (and vice versa?) Or is it possible ...
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### Lindblad from infinitesimal Kraus sum representation

I have a few basic queries regarding a proof in the set of notes MIT: Open Quantum Systems, the following is stated: We can derive the Lindblad equation from an infinitesimal evolution described by ...
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### Is the establishment of entanglement inevitable with the passage of time?

Derivation of the Lindblad master equation starts with the assumption that at an initial time $t=0$, the total density matrix is the product of the density matrices of the system $\rho_S$ and that of ...
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### Expectation Values in the Quantum Trajectory Formalism

If I want to know the expectation value of an operator O in the quantum trajectory formalism, I average over $N$ trajectories, where I call one such trajectory $\Psi_n$: \begin{equation} \langle O \...
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### How can we “isolate” a qubit

From Wikipedia : In ion quantum computer, if the ions are not properly isolated, noise can result from ions interacting with external electromagnetic fields, which creates random movement and destroys ...
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### What is the characteristics time scale of a quantum system, in context of the Markovian approximation?

In the theory of open quantum system, we make the markovian approximation when the timescale of the memory of the reservoir is small. But this timescale is measured with respect to the characteristic ...
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### Eigenvalues of generators [closed]

If I have a hamiltonian like $\omega\sigma_z$ and 2 Lindblad operators as $\gamma\sigma_-$ and $\gamma\sigma_+$ how can I find eigenvalues of generators? I think I should put the general form of $\rho$...
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### Why are there so few ion-trap experiments studying quantum trajectories?

The quantum trajectory theory describes the behaviour of a quantum system under continuous monitoring. Initially it is theoretically studied in quantum optics and single atom scenario (e.g., ion trap ...
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### In the theory of open quantum systems, what is really meant by *information backflow* from the environment to the system?

In the context of an Open Quantum System (OQS) i.e. a quantum system coupled to a quantum environment, what is really meant by information backflow from the environment to the system? I'm newly ...
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### In what sense is a quantum damped harmonic oscillator dissipative?

The classical Hamiltonian of a damped harmonic oscillator $$H=\frac{p^2}{2m}e^{-\gamma t}+\frac{1}{2}m\omega^2e^{\gamma t}x^2,~(\gamma>0)\tag{1}$$ when promoted to quantum version, remains ...
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### Why are simple models of coupled pendulums incapable of describing irreversible energy dissipation?

Consider two pendulums $A$ and $B$ coupled by a spring and also regard $A+B$ to be a completely isolated system. Let us start the system in an initial configuration where only one of the pendulums (...