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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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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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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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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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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107 views

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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921 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(...
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111 views

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{...
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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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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 ...
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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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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 ...
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88 views

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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52 views

Is there an open quantum system analogue of the equilibration time bounds for classical ergodic Markov chains?

Background For classical ergodic discrete Markov chains, we can bound the time taken to reach the stationary distribution to the spectral properties of the transition matrix. I will outline this ...
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560 views

Quantum regression theorem/formula for Lindblad dynamics

I have been trying to understand the proof of the quantum regression theorem or formula for a Lindblad evolution. If $V(t,0)$ is the propagator, $\rho_S(t) = V(t,0)\rho_S(0)$, the formula is: $\...
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914 views

From the Heisenberg-Langevin equation to the Lindblad equation

In a open quantum system, one can easily derive the Heisenberg-Langevin equation of motion which describes the time evolution of creation/annihilation operators (in say, a cavity) $$\dot{a}(t) = i[H,...
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144 views

Does the Lindblad equation satisfy a fluctuation dissipation relation?

The fluctuation dissipation relation is usually stated in terms of an identity that relates the retarded, advanced and either the Keldysh or time-ordered correlators. This is easily enforced in ...
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298 views

Transition rate of two level system subjected to noise

(this question is simpler than its length implies. I did this on purpose to provide a nice complete development for future readers) The setup Suppose we have a two-level quantum system with ...
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Projecting Density Matrix into Edge States Subspace

I'm reading and trying to understand the paper by Diehl, S., Rico, E., Baranov, M. et al. "Topology by dissipation in atomic quantum wires". Nature Phys 7, 971–977 (2011). https://doi.org/10....
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20 views

Semi-group in quantum open systems

In the literature of Open Quantum System, one often comes across the following ($t_2>t_1,>0$): Semi-group property of a map: $A(t_1+t_2,0) = A(t_2,0) A(t_1,0)$. What does this mean physically,...
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37 views

Is a temperature change in quantum statistical dynamics related to a nonunitary evolution of the problem?

Consider a quantum composite problem given in terms of a system $\hat{H}_s$ interacting via $\hat{H}_I$ with a bath $\hat{H}_B$ in terms of a Hamiltonian $\hat{H}=\hat{H}_s+\hat{H}_I+\hat{H}_B$. ...
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91 views

Input-output theory: interpretation of the final expression

I am trying to understand this paper- https://journals.aps.org/pra/abstract/10.1103/PhysRevA.30.1386 I will try to give my understanding of the paper first. We start with the quantum Langevin ...
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22 views

Formalism for an open system with non-adiabatic (non periodic) time dependence

Most non-equilibrium statistical processes of open time dependent systems are approached by Markovian dynamics of a system where time dependence of the system is assumed to be adiabatic (if Floquet ...
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53 views

Is hermicity of the reduced density matrix preserved here?

I am following along Breuer and Petruccione's book . I would like to know if the property $\rho^{\dagger} = \rho$ is preserved for evolution that is described by the Born Approximation. For a Hilbert ...
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64 views

Tracing $\rho (t)$ with respect to the Bath when system and bath are coupled in an open quantum system

Consider a system S that is coupled to a bath B. Let {$|s_i\rangle 's$} and {$|b_j\rangle 's$} be the eigen states of the system and bath hamiltonians respectively (i.e) \begin{align} \hat{H}_{S}|s_i\...
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Cast Caldeira-Leggett master equation to Lindblad form

Consider a Brownian motion particle, whose motion is described by $\frac{d}{dt}\rho_{S}=-\frac{i}{\hbar}[H_{S},\rho_{S}]+\sum_{i,j}a_{i,j}(F_{i}\rho_{S}F_{j}^{\dagger}-\frac{1}{2}\{F_{j}^{\dagger}F_{...
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53 views

Is one allowed to split path integrals in the Feynman-Vernon Influence theory

In QFT the propagator $J(t,t_0,x_f,x_i) = \langle x_f | U(t,t_0) | x_i \rangle$ fulfills the property $$ J(t,t_0,x_f,x_i) = \int_{-\infty}^{\infty}dx' J(t,t',x_f,x')J(t',t_0,x',x_i) $$ and can be ...
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Is the whole universe a closed quantum system?

By the whole universe I mean everything besides $|0\rangle$, if not what is the environment then? How do they interact? If the whole universe is a closed system, can we assign a single Hamiltonian to ...
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481 views

Going from stochastic Schrödinger equation to master equation

I am currently reading the book "Quantum measurement and control" by Wiseman and Milburn (https://www.amazon.ca/Quantum-Measurement-Control-Howard-Wiseman/dp/1107424151) and something is really ...
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112 views

On Stinespring's Theorem

Wherein the proof of Stinespring's theorem does complete positivity enter? Suppose my map is not completely positive but the Kraus operators follow the trace preservation condition as $\sum_{n = 1}^{...
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77 views

Noisy limit of sinusoidal modulation of the frequency of a two level system

I've been reading the paper Motional Averaging in a Superconducting Qubit by Li et al. from 2011, in which they study what happens when they modulate the frequency of a two level system. Specifically, ...
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22 views

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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31 views

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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66 views

The master equation and continuous measurements

To derive the master equation under a continuous measurement we first define the two measurement operators $$M_0=\mathbb{I}-\left(R~/~2+iH\right)dt \tag 1$$ $$M_1=c\sqrt{dt}, \tag 2 $$ where $M_0$ ...
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Markov Approximation and Master Equation Derivation

In deriving the master equation, I am coming across the Markov Approximation which says: Suppose environment $E$ and system $S$ interact and exchange some energy with each other. Then $E$ would ...
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Approximation in master equation

Can someone explain to me how it works the fact that the nonzero part of the term to be neglected in the master equation for open systems can be absorbed into the Hamiltonian of the system as stated ...
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28 views

Action of tensor product of operators on entangled state

Let $S$ be a system described by the density operator $\rho_S$. Consider the operator $$\mathcal{L_t}\left[ \rho_S \right] = \gamma (t) \left[ \sigma_z \rho_S \sigma_z - \rho_S\right] $$ where $\...
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42 views

Strongly continuous dynamical maps

Let's say we have a bipartite system $\rho(0)=\rho_A \otimes \rho_B$ The evolution of system $A$ alone will be described by a dynamical map $\Phi_t$, such as: $\rho_A(t)=\Phi_t(\rho_A(0))$ If ...
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51 views

When would an open system reach the steady state calculated from master equation?

From the master equation for density matrix, it seems that one can have steady state solution requiring the derivative of density matrix equals to zero, but I want to know whether a real open system ...
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131 views

Transient solution system of differential equations obtained from master equation

I have to solve the following equation (or at least obtain an approximate estimate) for the diagonal terms of the density matrix. We consider that the initial state is a coherent state $\rho_{n,n}(0)=...
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61 views

Spontanous emission Hamiltonian model

I am looking for a clear (and not too long) model of spontaneous emission, for an atom modeled by a two level system in a cavity where the field is multimode I am looking for model bases on ...
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1answer
110 views

Counterterms in quantum brownian motion

In the part "Quantum Brownian motion" of the book, The theroy of open quantum systems written by Breuer, the author investigates on the Caldeira-Leggett model: The Hamiltonian of the particle is $H_{...
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76 views

Physics behind assumptions in deduction of quantum master equation

In Breuer's book, he deduces quantum master equation using following steps: $(1). \frac{d}{dt}\rho(t)=-i[H_{I},\rho(t)]$ then the solution for equ.(1) can be written as $(2).{\rho(t)}=\rho(0)-i\...
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237 views

Noise add to the Lindblad equation or Liouville-Von Neumann equation

I am working on an open system and I would like to use the Lindblad master equation but also I would like to add noise to it. If is possible. All the books and papers I did read about tells me that ...
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37 views

Is recombination and quantum dissipation the same?

I have been reading two articles on the quantum transport in the FMO complex [1]. Each of these papers models a different processes that affects the quantum transport of the excitons in the FMO ...
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1answer
231 views

How to find the Heisenberg picture from the master equation without Lindblad structure?

My question is closely related to this post and this one too. I understand that with a Lindbladian type master equation, it is possible to find the differential equation for an observable. However, my ...
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114 views

Open Quantum Systems: Limitations of Self-Energy Method

In low field quantum transport, steady state regime, a popular method to compute Non-Equilibrium Green's functions to study transport, as introduced by Datta (see for reference pdf), accounts for open ...
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109 views

Effects of light wavelength on the Hamiltonian of the FMO complex

Recently, I have been interested in the energy transfer within the FMO complex. I was wondering, how could the wavelength of the light that excites the complex affect the energy transfer efficiency. ...
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311 views

how to arrive at first-order correlation function with the above master equation?

My question arose when I was reading a paper called " Multi-photon Blockade of the dressing of the dressed states'. This is the states this paper used: This is the master equation this paper has ...
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18 views

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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1answer
68 views

Transformation to rotating frame

I want to apply a transformation to the rotating frame of a two level system such that a state in the transformed frame is $ |\hat{\phi} \rangle = U |\phi \rangle$, where U is the generator of ...