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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Cavity Input-Output Formalism: Physical significance and intuitive understanding

I have spent a lot of time trying to understand the input-output formalism for cavities. I sort of understand the idea Fields inside an optical cavity(our system) will have losses because the mirrors ...
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Can reduced dynamics lead to a map that is not completely positive?

This question is a follow-up to this one. The setup is the same as in that question. We consider a map from a certain set of density operators $\rho_S$ on a Hilbert space $\mathcal{H}_S$ to the ...
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How can an entangled initial state lead to non-positive reduced dynamics?

According to https://arxiv.org/abs/1206.3794, the standard treatment models the time evolution of open quantum systems as follows: starting with a system in the initial state $\rho_0$ on the Hilbert ...
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Collapse operators of two-level atom

Currently I am learning about the Lindbladian. I want to derive the optical bloch equations for a two-level atom interacting with monochromatic light from the Lindbladian. However I am having troubles ...
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Arbitrariness of Quantum Heat Current

Given a Hamiltonian $H$ for a closed quantum system, we know that the spectrum is invariant under any constant shift in energy $H'=H+c$. However, when talking about open quantum system where the ...
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Does the time-energy uncertainty principle apply to open systems?

Suppose I have a system that takes on discrete energy levels (and superpositions thereof) and is isolated. Now suppose the system takes on a specific eigenstate of its Hamiltonian. By the Schrodinger ...
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Can we consider the Hamiltonian of a single qubit as zero?

I am studying the Daniel Lidar`s lecture notes about open quantum systems. In the part that I have already attached it here, it considers the Hamiltonian of the single qubit as zero to implement into ...
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To verify the completely positivity: about conditionally completely positive

I'm reading the paper Assessing Non-Markovian Quantum Dynamics, by M.M. Wolf (PRL 101, 150402 (2008), arXiv:0711.3174). It mentions how to decide whether a generator is a valid Lindbladian generator, ...
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How to differentiate exponentials of Lindblad operators? [duplicate]

Suppose I have a time evolution generate by a Lindbladian $\mathcal{L}(x)$, parameterised by $x\in \mathbb{R}$. Suppose I wish to differentiate $k$ times with respect to $x$, how do I got about this? ...
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Is there a physical intuition behind the disentanglement of Werner states and the sudden death of entanglement?

It is possible to write two-qubit Werner states in terms of a mixture between a Bell state and the maximally mixed state: \begin{equation} \rho_W = \lambda |\Psi_-\rangle \langle\Psi_-| + \frac{1-\...
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How to quantify the one-way flow of information in Markovian dynamics

It is said that in the Born-Markovian dynamics (Master equation), the information flow is one way, i.e. from the system to the environment. How to understand this sentence? Is there a quantity of the ...
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How shift the system Hamiltonian change the interaction term?

I'm reading this paper about a model of a qubit coupled to an Ising spin bath. The interaction between the system qubit and the bath is described by the Ising Hamiltonian: $$H_{I}^{\prime}=\alpha \...
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Fokker-Planck equation for the Wigner function to covariance matrix

I cannot understand the derivation in Louis Garbe article (https://arxiv.org/abs/1910.00604) about how to obtain the covariance matrix equation from Fokker-Planck equation for the Wigner function in ...
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Covariance matrix of Fokker-Planck equation [closed]

Rewrite the Lindblad equation above into a Fokker-Planck equation for the Wigner function is: \begin{equation} \frac{\partial W}{\partial t}(x,p)=-\omega_0p\frac{\partial W}{\partial x} - \omega_0(Xg^...
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Does relation between non-hermetian Hamiltonian and curved space suggests lingering quantum gravity?

I have just discovered an article describing a recent discovery linking non-hermitian hamiltonian and curved space. The article doesn't say that directly, but that sounds like a suspiciously big step ...
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Is $\mathcal{L}^{*}_{L}(\rho) = 0$ $\forall$ $\rho$ $\in\{\rho: \langle\mathcal{L}_{L}(V)\rangle_{\rho}= 0\}$ true?

[Context: I have observed the fact, $\mathcal{L}^{*}_{L}(\rho) = 0$ $\forall$ $\rho$ $\in\{\rho: \langle\mathcal{L}_{L}(V)\rangle_{\rho}= 0\}$ (meaning of the symbols are below) true numerically, ...
1 vote
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On the dynamics of open quantum systems

I was going through the book "The theory of open quantum systems" by Breuer and Petruccione, and I am having problems with convincing myself of equation 3.49. In short, I am reading about ...
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Problem dealing with creation and annihilation operators of two uncoupled oscillators [closed]

I encountered a expression of the form while computing the Lindbladian of two uncoupled harmonic oscillators $$2 b^{\dagger}a a^{\dagger}a^{\dagger}b-a^{\dagger}a^{\dagger}b b^{\dagger}a-a^{\dagger}b ...
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Trace distance of two infinite rank tensor product states

Let $\sigma$ and $\rho$ be both density operators acting on different Hilbert spaces, $H_{1}$ and $H_{2}$ respectively. Also, let said operators have infinite rank. In the infinite dimensional case ...
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Possibility of the quantum phase transition with the linear equations of motion in the classical limit

Let us say we have a Lindblad equation for the density matrix $$ \dot{\rho}=-\frac{i}{\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} ...
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Is the Lindblad equation invariant under the unitary transformation?

Let us say we have a Lindblad equation for the density matrix $$ \dot{\rho}=-\frac{i}{\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} ...
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Position representation of density operator in collapse models

I have been studying this paper for the past few days but really get stuck on one specific derivation that seems easy but I can't comprehend it. It's about quantum collapse models, so quite niche. We ...
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Memory effects in clopen quantum systems

A clopen quantum system may be defined as one where there is no global dissipation (e.g. a finite system of interacting spins without photonic coupling.) In the open quantum physics literature, it is ...
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Equation of motion for various operators in open quantum systems

I am trying to reproduce the calculations presented on page 4 in arXiv:1511.03347. The Hamiltonian (Eq. 2.4) is given by $H= \hbar \omega (a^{\dagger} a + \frac{1}{2}) - B \sqrt{\frac{\hbar g}{2 \...
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Analytical solution of the Fokker-Planck equation for a damped harmonic oscillator

I was having some trouble while trying to understand the solution for the Fokker-Planck equation for a damped harmonic oscillator, as given in chapter-3 of the textbook "Statistical Methods for ...
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General clarifications about the Lindblad equation

I would like to ask some clarifications about the Lindblad equation: Is the system guaranteed to reach a steady state after starting from a generic initial state under both unitary evolution and ...
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Evolution of a quantum system after decoherence

Decoherence leads to an almost diagonalization of the density matrix of a quantum system (in a certain basis) after an uncontrolled interaction with the environment. How does the quantum system evolve ...
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Given a Hamiltonian of a Spin System, How to check it is complete and also conserved? [closed]

Hi I am an engineering student trying some modelling in physics. Suppose you have a Hamiltonian of a spin system interacting with another two-level spin system as below. How do you know all the terms ...
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Show $I+\tau\mathcal{L}$ is completely positive when $\tau \leq 1/\lambda_{\mathrm{max}}(\mathcal{L})$

I am not very well-versed when in comes to open quantum systems which is why I need some help. In a paper, I encountered the following situation: Let $\mathcal{L}$ be a Lindbladian so the time ...
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Preserving normalisation for non-unitary dynamics in the Heisenberg picture

As the title says. Say I'm trying to calculate some 2 point correlator of some operator $\hat{\sigma}$: $$ \langle \hat{\sigma}(t)\hat{\sigma}(t+\tau) \rangle = \text{tr}[e^{L^{\dagger}\tau}(\hat{\...
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Linear response theory, but with measurement issue

In the standard linear response theory, the variation of an observable $A$ at time $t$ due to the perturbing Hamiltonian $H'$ is $$\langle \delta A(t) \rangle = \int_{-\infty}^t dt' \langle [A(t), H'(...
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Lindblad form for a Damped harmonic Oscillator

I'm considering a Lindblad-like master equation for a damped harmonic oscillator $$ \frac{d\rho(t)}{dt} = -i[H, \rho(t)]+\sum_{n,m=1}^2 h_{nm}[A_n \rho(t) A_m^\dagger - \frac12 \lbrace A_m^\...
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How to chose the collapse operators for an open quantum system?

Lets assume we have an open quantum system. In the Born-Markov-Approximation, the dynamics of the density operator is described by a Lindblad-Type equation \begin{equation} \dot{\rho} = - i[H, \rho] + ...
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Consistency of Lindblad-type operator evolution equations

One frequently comes across Lindblad-type operator evolution equations in the Heisenberg picture of the form $$ \frac{\mathrm{d}}{\mathrm{d}t} A =\mathcal{L}^{\dagger}(A), $$ where the adjoint ...
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When is the Liouvillian superoperator not diagonalisable?

An $n \times n$ matrix, $L$, is diagonalisable if it has $n$ linearly independent eigenvectors. I've recently been working with open quantum systems and come across the non-hermitian, Liouvillian ...
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Master equation approximation

In the Lindbladian master equation, one of the approximations is assuming $\rho(t)=\rho_S(t)\otimes\rho_B(t)$. However, if we try to solve the total state in a numerical way, using $\dot{\rho}(t)=-i[...
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Is there a simulation package for open quantum system dynamics using negative decay rate?

Consider the following situation: the model is described by a single qubit and the density matrix evolution is governed by the Lindblad equation. ${\displaystyle {\dot {\rho }}=-{i \over \hbar }[H,\...
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Time Derivative of the Hamiltonian for a Quantum Simple Harmonic Oscillator

I am reading an article on quantum refrigerator. Here is the link of the article. The arXiv version is available here. The working medium is an ensemble of non-interacting particles in a harmonic ...
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Projection of master equation onto eigenstates

I'm trying to understand the paper: "Quantum dot cavity-QED in the presence of strong electron-phonon interactions" by Wilson Ray and A. Imamoglu (https://journals.aps.org/prb/abstract/10....
6 votes
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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{...
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Technique for diagonalising this quadratic fermionic operator?

I want to diagonalise the following operator $$ \mathcal{L}= 2 \sum_k^N\epsilon_k(c^\dagger_{2k-1}c_{2k}-c_{2k}^\dagger c_{2k-1})+2iA\sum_k^N c^\dagger_{2k-1}c^\dagger_{2k}-B \sum^{2N}_kc^\dagger_kc_k,...
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Microscopic derivation of Lindblad operators for generalized subsystem induced by observable sub-algebra (a la Zanardi)

Consider a quantum system with two parts, the system $S$ and environment $E$, described by the tensor-product structure $\mathcal{H} = \mathcal{S}\otimes\mathcal{E}$. When the dynamics of reduced ...
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Two point measurement statistics in Quantum systems

I am reading a paper related to fluctuations in Quantum thermodynamics. I am unable to understand the math behind equation no. 10 where the probability density function for work distribution is ...
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Efficiency formula in Environment-assisted quantum transport (ENAQT)

I'm currently studying the book quantum effects in biology, in particular, I'm interested in the phenomena of Environment-assisted quantum transport (ENAQT) in photosynthesis. In ENAQT, they discuss ...
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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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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 ...
1 vote
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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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