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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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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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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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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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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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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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97 views

Hamiltonian in a Master Equation

I am going through this paper on the complete positive map with memory. The bath operators $\Gamma_k (t)$ are told to satisfy the correlation $\langle \Gamma_j(t) \Gamma_k(t^\prime) \rangle = a_k^2 e^{...
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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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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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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 ...
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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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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 ...
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Calculation of time-ordered propagations and correlators

I am reading the following paper M. H. S. Amin and D. V. Averin, “Macroscopic Resonant Tunneling in the Presence of Low Frequency Noise,” Phys. Rev. Lett., vol. 100, no. 19, p. 197001, May 2008. I ...
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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 (...
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59 views

How many elements can the set of asymptotic states of a reduced dynamics have?

Given a Hilbert space $\mathbb{C}^N$ and the reduced dynamics $\Lambda(t)$ of the open quantum system, we can define the set of asymptotic states as $$ \mathcal{A}=\left\{\tilde\rho \in \mathcal{S}(\...
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Constant bath density matrix for weak coupling : why

The problem : Consider an ensemble system + bath that has this Hamiltonian : $$H=\hbar \omega_0 h_S + \hbar \omega_B h_B + \hbar \gamma h_{int}(t) $$ The $h_S$ $h_B$ and $h_{int}$ are dimensionless ...
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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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Why it is necessary for a quantum map to exist that the initial state is a product state

In "Quantum Computation and Quantum Information" by Nielsen & Chuang, on page 358, as well as in "Exploring the quantum" by S.Haroche & J.M Raimond on page 177, they consider the following. ...
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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 ...
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133 views

Quantum map and preservation of trace

I am currently learning about quantum maps, ie maps that transform a density matrix into another one. Assume we are in the Hilbert space : $H_A \otimes H_B$. I call the quantum map on the density ...
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Generalized measurement and entanglement operation

I am reading Exploring the quantum By Serges Haroche & Jean-Michel Raimond They consider a system $A$ living in $H_A$ surrounded by an environment $B$ Thus the problem lives in $H_A \...
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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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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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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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Why do we use the rotating wave picture to make approxiamations in open quantum systems?

Why do we use the rotating wave picture to make approxiamations in open quantum systems? I understand why we use the Heisenberg picture when switching to the interaction picture. But why rotating ...
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134 views

Why is it impossible to formulate unitary QFT in a dynamical background?

I cannot recall the exact argument but I remember my professor saying something like unitary time evolution in a dynamical background "kicks" a state out of the Hilbert space constructed on curved ...
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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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Displacement transformation of Liouvillian superoperator

The displacement operator $D(\alpha)$ has the property $D^{\dagger}(\alpha) \hat{a} D(\alpha) = \hat{a} + \alpha$. We obtain the Hamiltonian $\hat{H}'$ in the displaced frame from the transformation $...
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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 $C$ ...
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Wigner flow for open quantum systems

In the paper by Friedman and Blencowe the Wigner flow for an open quantum system is derived. On page 3 the Wigner flow for the harmonic oscillator is derived. Substituting the potential $V = \frac{1}{...
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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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228 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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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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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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System-Environment Correlations for a Quantum Dynamical Semigroup

The density matrix for an open bipartite system can be written $$ \rho = \rho_S \otimes \rho_E + \rho_{corr} $$ and it is assumed that the system starts in a separable state $\rho(0) = \rho_S \otimes ...
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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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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 ...
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Spin-Boson coupling

Typically while coupling a single spin to a bunch of bosons (Harmonic oscillators) a $\sigma_x$ or $\sigma_z$ coupling operator is chosen for the system operator coupled to the position of the bosons, ...
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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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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 ...
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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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Time evolution operator for system -environment interaction

I am reading a paper https://journals.aps.org/prb/pdf/10.1103/PhysRevB.96.224302. In this paper the initial state of the system and environment is given as \begin{equation} |\Psi(0)\rangle=|\phi_{s}(...
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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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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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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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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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Question on Quantum Channels

A quantum channel describes the finite-time evolution of the reduced system of interest. Suppose one has the total unitary of the system and environment taken together, tracing out the environment ...
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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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271 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 ...
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Why is a continuum of bath modes required for irreversible dynamics?

In open quantum system dynamics it is often stated that a continuum of bath modes is required to obtain irreversible dynamics. Why is this the case? Is there a general theorem or precise statement ...