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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16
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2answers
542 views

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}\...
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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. ...
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3answers
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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. ...
13
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511 views

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] -...
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5answers
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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; ...
12
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1answer
907 views

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 ...
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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 ...
9
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1answer
235 views

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 $C$ ...
8
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1answer
589 views

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{\...
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1answer
522 views

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 ...
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756 views

What is an Open Quantum System?

What is an Open Quantum System? The simple quantum text book examples like Simple Harmonic Oscillator potential and H-atom, seem to me open quantum systems, since the particle interacts with the ...
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1answer
272 views

Lindbladian and Dynamical semigroups

I am attempting to learn a bit more about open quantum systems. Often we derive master equations or Heisenberg-Langevin equations where we have something like \begin{align} \dot{\rho}(t) = \mathcal{...
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Equivalence of quantum state diffusion and heterodyne trajectory

According to Breuer-Petruccione, the SDE quantum trajectory evolution for heterodyne detection $$d\psi=-iH\psi dt-\frac{\gamma}{2}\left(C^\dagger C-\langle C^\dagger \rangle_{\psi} C+\frac{1}{2}\...
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1answer
219 views

What is the difference between the three types of bosonic reservoirs : sub-ohmic, ohmic and super-ohmic?

I want to ask what is the difference between the three types of bosonic reservoirs that we use in the theory of quantum decoherence: sub-ohmic, ohmic and super-ohmic. I know that there is a parameter "...
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1answer
325 views

Classical approximation of coupling to a quantum bath

This question is a follow up / more focused variant of the question posed here. With some feedback from other users I realized that the question posed was too broad to answer rigorously, and I have ...
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2answers
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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 ...
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1answer
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Pure dephasing $\gamma_\phi$ in a master equation and noise power spectral densities

In its simplest form, my question is regarding a two level system of transition frequency $\omega_0$ given by the Hamiltonian \begin{equation} H = \frac{\hbar \omega_0}{2}\sigma_z \end{equation} ...
5
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3answers
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Green Function in Open Quantum Systems

Imagine an open quantum system interacting with an environment that admits a density matrix (Markovian) description in terms of Lindbladians ($c$ and $c^\dagger$). Is there a meaningful way to define ...
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1answer
252 views

Clarifications needed on why certain arguments related to quantum maps dubbed as false [closed]

As I was learning more about the evolution of open quantum systems, I came across this question. Reading through the answers, I found this paper by A. Shaji and E.C.G. Sudarshan. The mathematical ...
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1answer
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Book recommendations for learning about open quantum systems

Recently I'm curious about the topic of open quantum system which is not talked about in common quantum mechanics textbooks, i.e. Master equation, Lindblad equation, reduced density matrix, ...
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1answer
237 views

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 ...
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What makes quantum decoherence different from dissipation?

From my understanding quantum decoherence and dissipation are completely different ways of modelling information loss to the environment. Dissipation can be modeled using the Caldeira-Leggett model ...
5
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1answer
202 views

Can an arbitrary quantum system of finite size be made to reliably relax to its ground state? Is there a physical principle prohibiting this?

I am talking about the possibility of reliably cooling an arbitrary quantum system of FINITE size (for example, localized on earth), to its ground state through any means, like exposure to a special ...
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Kraus Operators from Lindblad equation

One should be able to formulate the time evolution given by Lindblad equation in terms of Kraus Operators. But how does one do that in practise i.e given $H$ and Lindblad operators $L_\mu$, how does ...
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How to understand the failure of Leibniz rule in Lindblad type Heisenberg equation?

Dual to the well-known Lindblad master equation for density matrices, the equation for operators (in the sense of Heisenberg equation) is written as $$ \frac{d}{dt}\hat{A}=i[H,\; \hat{A}]+\sum_i \...
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1answer
922 views

Solving the Lindblad quantum master equation in matrix form

I have just started learning density matrix and quantum master equations, and I am given a problem set that asks to find the solution to the Lindblad equation with $H$, $L_+$, $L_-$, $L_z$, and $\rho(...
4
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3answers
477 views

Complete positivity: why is the condition sufficient for quantum maps?

I know that when we define quantum maps, we need the map to be completly positive, to ensure that if our system $A$ is entangled with some extra system $B$, the evolution on $H_A \otimes H_B$ will ...
4
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1answer
166 views

Why should the dynamics of open quantum systems be always linear?

There is a need to use open quantum systems in describing the reality since, in general, the real systems are often found correlated with the environment whose properties cannot be realized in closed ...
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1answer
552 views

Born-Markov Approximation: Why is $\rho_{I}(s) \to \rho_{I}(t)$ taken, and not $\rho(s) \to \rho(t)$?

I am following along Chapter 3 of Breuer and Petruccione's book. For a Hilbert space $\mathcal{H}_{S} \otimes \mathcal{H}_{R}$ and Hamiltonian $$ H = H_{S} \otimes \mathbb{I}_{R} + \mathbb{I}_{S} \...
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1answer
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What is the relationship between the Drude form and the exponential form of Ohmic spectral density?

I have been studying open quantum systems for some time now. I have learnt about something known as spectral density that confers information about the physical structure and are found in the ...
4
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1answer
302 views

Examples of non-Hermitian Hamiltonians in open systems?

I have often heard the statement that non-Hermitian Hamiltonians can be used to describe open systems, since the dynamics are non-unitary. However, I have not been able to find any examples of a non-...
4
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2answers
472 views

Quantum input-output theory : Why do we multiply by density of mode to have a number of photon **per unit of time**

In this paper, https://journals.aps.org/pra/abstract/10.1103/PhysRevA.31.3761, we work with input-output theory. I will first summarize the physics of it and then ask my question. In input-output ...
4
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2answers
661 views

Lindblad and Input-Output Formalism in Quantum Optics

I'm confused about how to apply the Lindblad formalism and the input-output formalism in practice, and how one goes between the two. Suppose I have a cavity (C) coupled to a reservoir (R), with the ...
4
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1answer
112 views

Is it possible to formulate quantum mechanics in the equilibrium state?

The standard formulation of quantum theory takes measurement as "part of the postulates" (see for example this post). It is known that measurement is always associated with an increase in entropy (...
4
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2answers
433 views

Green's functions in the Keldysh-formalism and quantum stochastic calculus

Introduction The Keldysh path integral can be thought of as a reformulation of the quantum optical master equation, which describes the markovian time evolution of the density operator of an open ...
4
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1answer
181 views

Classical noise approximation of a system coupled to a quantum environment

I have a question based on the principles described in "Quantum simulator of an open quantum system using superconducting qubits: exciton transport in photosynthetic complexes" by Mostame et al. In ...
4
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1answer
184 views

Why is the frequency bandwidth of the environment important for Markovianity?

In the derivation of Spontaneous Emission in two level systems in Quantum Optics (be it Wigner Weisskopf or a different approach, such as density operators to find the master equation), one makes (...
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Open Quantum Systems: Born-Approximation and the preservation of Trace, Hermicity and Positivity

This is related to a previous question of mine. We consider a density matrix $\sigma(t)$ operating on a Hilbert space $\mathscr{H}_{s}\otimes \mathscr{H}_b$ with Hamiltonian $H = H_s \otimes \mathbb{...
4
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0answers
71 views

Bounds on the effect of strong coupling

I am interested in bounding the effects of system-environment interaction. Suppose I have an initial state $\rho \in \mathcal{H}_S \otimes \mathcal{H}_E$ where the system and environment might be ...
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0answers
620 views

Understanding quantum stochastic master equations

I'm teaching myself open quantum systems and the concept of a stochastic master equation has arisen. As someone who has studied classical stochastic processes a fair bit, this seems, at least to my ...
4
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1answer
614 views

How to determine the collapse operator for a Lindblad equation

Given a Hamiltonian $H$, how can I relate the collapse operator for the Lindblad equation to a given environmental effect? Also, how can I relate the constant $\gamma$ in front of the sum of the ...
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1answer
957 views

What are the open problems in the field of quantum thermodynamics? [closed]

I came across the Lindblad equation and found it very interesting. What are the open problems in the field of quantum thermodynamics?
3
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1answer
68 views

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 ...
3
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1answer
402 views

When a time local quantum master equation is completely positive?

I know that a time-local quantum master equation can be put in a "Lindblad-like" form, which is a Lindblad equation whose coefficients can be negative and time-dependent. If all the coefficients are ...
3
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1answer
1k views

Lindblad equation derivation

I'm reading A simple derivation of the Lindblad equation. It introduces a Hamiltonian for a system consisting of a principal system $S$, a heat bath $B$ and an interaction term: $\hat{H}=\hat{H}_S+\...
3
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1answer
82 views

How do I show the separability of this density matrix?

I am stuck since a longer time regarding this exercise where I need to work with a density matrix of the given form $$\displaystyle \rho_{AB}(X)= \frac{1}{N+\text{tr}X^2}\left( {\begin{array}{cc} ...
3
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1answer
63 views

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 ...
3
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1answer
127 views

Why entropy decreases in this coupled quantum systems?

I have calculated the exact time evolution of a simple 1-D qubit lattice (2008 paper) and this is what I've found for $\rho(t)$ containing one excitation of 2 qubit site $(|1\rangle,|2\rangle)$ + 1 ...
3
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1answer
91 views

Relation between correlation functions and Poincaré recurrence time

When deducing Markovian quantum master equation, supposing the total Hamiltonian is the following form: $H=H_{S}+H_{B}+H_{I}$ where $H_{S}$ is the Hamiltonian for the quantum system, $H_{B}$ is ...
3
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0answers
29 views

Fluctuation dissipation theorems in dynamic processes: a comparison

I do not understand what the first and the second fluctuation- dissipation theorems physically represent and what are the differences between the first and the second on the physical side. As a ...