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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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....
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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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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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2 votes
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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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How is it acceptable that the Lindblad equation typically depends on a Cauchy principal value?

According to the standard lore, (Markovian) open quantum dynamics are usually modeled by the Lindblad equation $$ {\displaystyle {\dot {\rho }}=-{i \over \hbar }[H,\rho ]+\sum _i\gamma _{i}\left(L_{i}\...
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3 votes
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Bath interaction observable and noise stochastic force

To derive quantum master equation using perturbative and born approximation we get the equation for state evolution as (from Liouville-von Neumann) $$ \frac{d}{dt}\rho(t)=-i[H_I(t),\rho(0)]-\int_0^t ...
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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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4 votes
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Quantum relaxation to equilibrium?

Source and context: Im reading “The Theory of Quantum Open Systems” by Breuer and Petruccione. As an application of the just derived Lindblad equation for the dynamics of the reduced density matrix $\...
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“Secular” approximation in the Lindblad equation for an open quantum system

Some context: I am deriving the Lindblad equation following “The Theory of Open Quantum Systems” by Breuer and Petruccione (somebody transcribed the section I am reading in this link). My question: I ...
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What is the explicit form of exponential superoperators in Liouville space?

In the theory of open quantum systems, operators acting on a density matrix $\rho$ are often called superoperators. For example, the time evolution of a closed system may be written as $\rho(t)=U^\...
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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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2 votes
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Where does the expression $\mathrm{Tr}(K) = \sum_{j=1}^{n}\langle\psi_j|K|\psi_j\rangle$ for the partial trace come from?

During my studies of composite quantum systems I find some expressions that leave me with a little doubt. For example: Let K be a linear operator defined in the Hilbert space H. Where H is given by $H ...
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How to extend a quantum operation to an auxiliary Hilbert space?

In Breuer and Petruccione's book 'The theory of open quantum systems', section 2.4.3, 'representation theorem of quantum operations', a quantum operation $\phi_m$ corresponding to a measurement ...
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Time scales in Master equation

In the Lindblad master equation $$\dot\rho=\frac{i}{\hbar}[H,\rho]+\sum_{i=1}^{N^2-1}\gamma_i \left(L_i\rho L_i^{\dagger}-\frac{1}{2}\left\{L_i^{\dagger}L_i,\rho\right\}\right)$$ where $\dot{\rho} = \...
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