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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Why do quantum computation models based on open quantum systems receive so little attention?

In almost all research on (universal) quantum computation the common models assumed from the outset are either the quantum circuit model with unitary gates, the measurement-based one-way model or the ...
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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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Cauchy Principal Value in the derivation of Born-Markov master equations

I am deriving some Born-Markov master equations, but I'm facing a kind of strange problem. The structure is correct, but I need to find the coefficients that appear in my particular problem. One of ...
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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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Non-Markovian noise coupled to atomic system

I want to calculate the density matrix element's average over all the realization of Gaussian colored noise when the atomic system is coupled to the said noise. I know how to do it for atomic energy ...
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Approximate solution to the resolvent of an open quantum system

I have an open system which evolves according to some master equation: $$ \partial_t\rho(t) = \mathcal{L}\rho(t) $$ where $\mathcal{L}$ is the Liouvillian of the system which generates completely ...
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How to obtain a unitary time evolution that leads to the Lindblad equation on tracing out?

It is known that given the time evolution of an open quantum system by Kraus Operators, one can rewrite it as a unitary time evolution of a bigger system. That is, given Kraus operators on the Hilbert ...
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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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Direct Derivation of Kraus Operator from Interaction Hamiltonian

For the dynamics of open quantum systems, the Kraus operators $K_\kappa$ can be derived from the unitary orbit $U(t)\rho U(t)^\dagger$ for $\rho=\rho_S\otimes\rho_E$ of the composite system given by ...
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103 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-...
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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 ...
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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{...
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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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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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Any method that can show the time evolution of a open many body system?

the master equation seems is a choice but this method seems only give a mean field result which can not show obviously the effect of specific interaction between particles. So, I am wondering is there ...
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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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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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93 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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52 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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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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67 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 ...
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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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226 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 ...
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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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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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191 views

How do we know that, if only $\rho_A$ evolves, then the evolution of $\rho_{AB}$ is given by $(\mathcal{L}_A \otimes 1)(\rho_{AB})$?

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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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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329 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 ...