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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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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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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Lindblad superoperator and generated dynamics

In quantum mechanics, in order to evolve the state of an open system, I can use an equation like this $\dot\rho(t)=\mathcal{L}\rho(t)$, where $\mathcal{L}$ is the Lindblad superoperator. In general, $\...
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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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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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50 views

Computation of wavefunction after small time evolution [closed]

I have to simulate the wavefunction of a quantum driven duffing oscillator coupled to a bath of harmonic oscillators. The master equation is given by $\frac{d\rho}{dt}=\frac{i}{\hbar}[\rho,H_{sys}]-\...
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50 views

Does there exist a relation between the eigen-energies of two subsystems of a closed system?

I am rather new to the field of open quantum systems and I have a seemingly basic question for which I somehow cannot find a complete answer. Consider a closed system which we divide into two ...
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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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71 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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44 views

Expectation of Quantum Heat Bath Exponentials

Background I am studying the paper Lee et al (2012), located at arXiv:1207.7174. In this paper, we study the spin-boson model under a polaron transformation. The Hamiltonian is $$H = \frac{\epsilon}{...
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Master equation of a cavity interact with bath

When the evolution of the system is not unitary, one can describe this evolution by using the Master equation, wich contains the quantum jump operators (called also the Lindblad operators). The ...
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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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55 views

Does the principle of superposition hold for open quantum systems?

In closed systems, the dynamical equation is the Schrödinger equation, for which the principle of superposition holds. In open quantum systems, does the principle of superposition hold?
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Input Output formalism for a single-sided cavity in quantum optics, all modes same direction?

I have been trying to understand the input output formalism for a cavity by reading chapter 7 of Walls and Milburn (D. F. Walls and G. J. Milburn. Quantum optics. Springer, 2006.). There is something ...
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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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45 views

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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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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166 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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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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144 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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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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67 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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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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234 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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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{...