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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Lindblad from infinitesimal Kraus sum representation

I have a few basic queries regarding a proof in the set of notes MIT: Open Quantum Systems, the following is stated: We can derive the Lindblad equation from an infinitesimal evolution described by ...
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BITS: A liter of air (…) has a thermodynamic entropy of 5 J/K. How many bits would be necessary to represent the microstate of a liter of air? [closed]

I just started the first chapter of the book 'Quantum Processes, Systems & Information' B. Schumacher, M. Westmoreland; and I wanna know if my answer is correct. [Exercise 1.3] I used the formula ...
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Is the establishment of entanglement inevitable with the passage of time?

Derivation of the Lindblad master equation starts with the assumption that at an initial time $t=0$, the total density matrix is the product of the density matrices of the system $\rho_S$ and that of ...
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64 views

Expectation Values in the Quantum Trajectory Formalism

If I want to know the expectation value of an operator O in the quantum trajectory formalism, I average over $N$ trajectories, where I call one such trajectory $\Psi_n$: \begin{equation} \langle O \...
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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 ...
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What is the characteristics time scale of a quantum system, in context of the Markovian approximation?

In the theory of open quantum system, we make the markovian approximation when the timescale of the memory of the reservoir is small. But this timescale is measured with respect to the characteristic ...
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95 views

Eigenvalues of generators [closed]

If I have a hamiltonian like $\omega\sigma_z$ and 2 Lindblad operators as $\gamma\sigma_-$ and $\gamma\sigma_+$ how can I find eigenvalues of generators? I think I should put the general form of $\rho$...
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Why are there so few ion-trap experiments studying quantum trajectories?

The quantum trajectory theory describes the behaviour of a quantum system under continuous monitoring. Initially it is theoretically studied in quantum optics and single atom scenario (e.g., ion trap ...
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Time-evolution operator written through a commutator [duplicate]

I found this expression for the time-evolution operator: $$\begin{split} U(t) & = T_{\leftarrow}\exp\left[-i\int_0^t ds H(s)\right] \\ &= \exp\left[-\frac{1}{2}\int_0^t ds\int_0^t ds' [H(s),H(...
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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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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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Can quantum systems interact with multiple environments of different types?

If it can, how can we write the Hamiltonian of the total System is it just (for example with N bath) $$ H_{tot} = H_{s} + H_{B_{1}} + H_{B_{2}} + ... + H_{B_{N}} + H_{I_{1}} + H_{I_{2}} + ... +H_{I_{N}...
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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 ...
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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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Why are simple models of coupled pendulums incapable of describing irreversible energy dissipation?

Consider two pendulums $A$ and $B$ coupled by a spring and also regard $A+B$ to be a completely isolated system. Let us start the system in an initial configuration where only one of the pendulums (...
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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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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 ...
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Density operator of a system $S$ coupled to a bath $B$

In the second equation of section 8.1 in this MIT OCW lecture notes, I can't understand how they went from $$\rho_{S}(t)=Tr_{B}\{\rho_{SB}(t)\}=\sum_{k}\langle k|U_{SB}(\rho_{S}(0)\otimes|0\rangle\...
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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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Finding density matrix of open system with nearest-neighbor hopping interactions

I want to find the density matrix of the system for an open system with nearest-neighbor hopping interactions using a hamiltonian in the interaction picture. I know that I have to solve a master ...
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51 views

What is an example of a system with non-vanishing topological entanglement entropy at finite temperatures?

In this paper: https://doi.org/10.1088/1367-2630/14/3/033044 it is show that for Kitaev toric code looses topological entanglement entropy over long times if it is thermally opened. What is an example ...
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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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Time evolution of a tripartite quantum state

Question: How do we write the unitary evolution of a tripartite system in Hilbert Space $\mathcal{H}_A \otimes \mathcal{H}_B \otimes \mathcal{H}_C$ when it is subject to two unitary evolution ...
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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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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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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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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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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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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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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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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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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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458 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{\...