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.

Filter by
Sorted by
Tagged with
3
votes
1answer
51 views

Is there a way to quantify decoherence in the Heisenberg picture?

In the usual picture of decoherence: $\bullet$ you start with a state $| \psi(0) \rangle = | \psi_{S}(0) \rangle \otimes | \psi_{E}(0) \rangle$ for the system and environment (assumed to be ...
0
votes
0answers
13 views

Are there any recommended texts for introduction to Lindblandian dynamics for third year undergraduate? [duplicate]

I am looking to learn Lindbladian dynamics and apply it to a system with multiple baths. Are there any texts available that only assume undergraduate Quantum Mechanics knowledge (My school offers ...
2
votes
0answers
64 views

Derivation of Jump Operators in Master Equation

I'm trying to understand the process of deriving the master equation in this article. The system in general is composed of two interacting qubits each of which is coupled to their local thermal bath ...
1
vote
0answers
55 views

The “Algorithm” for Derivation of the Master Equation

I'm trying to come up with a master equation for a spin system. So, I'm trying to understand in general how can we derive the master equation and the Lindblad operators if we know the system, bath and ...
1
vote
1answer
44 views

What does the master equation for this quantum autonomous absorption refrigerator imply?

I'm following this paper: https://arxiv.org/abs/0908.2076, about building minimal and autonomous quantum absorption refrigerators. The setup is 3 qubits, each coupled to their own baths, and with some ...
1
vote
0answers
20 views

Master Equation Second Order Approximation

I have a problem deriving the master equation using projection operator technique. If we are given the master equation which reads: $$ \dot{\rho}= -\frac{i}{\hbar}[H_S+H_B+H_I,\rho]+\mathcal{D}\rho $$ ...
2
votes
1answer
51 views

Expected value in usual quantum mechanics vs quantum information

In standard Quantum Mechanics, one computes the expected value of an operator $A$ (arbitrary state $|\Psi\rangle$) as $$ \langle\Psi|A|\Psi\rangle. $$ This has the virtue that we can compute for ...
4
votes
2answers
122 views

Lindblad equation unitary term (in practice)

The Lindblad equation is given by $$ \dot\rho=-{i\over\hbar}[H,\rho]+\sum_{i = 1}^{N^2-1} \gamma_i\left(L_i\rho L_i^\dagger -\frac{1}{2} \left\{L_i^\dagger L_i, \rho\right\} \right), $$ where $H$ is ...
1
vote
1answer
35 views

Why do the odd moments of the interaction Hamiltonian vanish w.r.t. a reference state?

When deriving the Nakajima-Zwanzig equation in The Theory of Open Quantum Systems by Breuer and Pettrucione, in Eq. 9.10, they state that In many cases it may also be assumed that the odd moments of ...
0
votes
0answers
33 views

Difference between reactive (coherent) and dissipative coupling in open quantum systems?

I am unsure about the physical interpretation of the different types of coupling, I understand that reactive coupling is manifested by a term within the Hamiltonian and dissipative is via a term in ...
1
vote
0answers
73 views

How do you compute saddle point approximation of path integral for open quantum system?

Note: the question in this post is basically originated from here. Please refer to it first if you don't get the sense. I'd like to know how you compute the saddle point approximation in the path ...
0
votes
1answer
36 views

Dimensions of a non-hermitian Hamiltonian

I have recently started studying the non-hermitian hamiltonians and I came across an example- $H=p^2+ix^3$ (where $h=1$ and $m=1/2$) I know that hamiltonian is the total energy of the system. So how ...
3
votes
1answer
135 views

Is $ \hbar \rightarrow 0 $ in path integral merely technical thing? Is there any justification? (especially in open quantum theory)

I wonder whether the limit $ \hbar \rightarrow 0 $ in path integral is merely technical stuff when we explain the classical limit of quantum mechanics, or there may be any physical meaning or sense ...
3
votes
1answer
87 views

How is it acceptable that the Lindblad equation typically depends on a Cauchy principal value?

According to the standard lore, (Markovian) open quantum dynamics are usually modeled by the Lindblad equation $$ {\displaystyle {\dot {\rho }}=-{i \over \hbar }[H,\rho ]+\sum _i\gamma _{i}\left(L_{i}\...
3
votes
1answer
85 views

Bath interaction observable and noise stochastic force

To derive quantum master equation using perturbative and born approximation we get the equation for state evolution as (from Liouville-von Neumann) $$ \frac{d}{dt}\rho(t)=-i[H_I(t),\rho(0)]-\int_0^t ...
1
vote
1answer
16 views

Why does the Franck-Condon matrix appear to not be unitary when written in the basis of phonon states?

Preliminary: The Franck-Condon (FC) matrix can be defined as \begin{align} X & = e^{-x(b^{\dagger} - b)}, \label{eq: FC 1} \end{align} where $b^{\dagger}$ and $b$ are standard bosonic creation ...
2
votes
1answer
58 views

Common subsystem-bath interaction operators?

Im new to the field of quantum open systems and I wanted to know what are the most common operators for describing the subsystem-bath interaction. To narrow down a bit my question, say we have as a ...
3
votes
1answer
73 views

Quantum relaxation to equilibrium?

Source and context: Im reading “The Theory of Quantum Open Systems” by Breuer and Petruccione. As an application of the just derived Lindblad equation for the dynamics of the reduced density matrix $\...
1
vote
0answers
57 views

“Secular” approximation in the Lindblad equation for an open quantum system

Some context: I am deriving the Lindblad equation following “The Theory of Open Quantum Systems” by Breuer and Petruccione (somebody transcribed the section I am reading in this link). My question: I ...
1
vote
1answer
81 views

What is the explicit form of exponential superoperators in Liouville space?

In the theory of open quantum systems, operators acting on a density matrix $\rho$ are often called superoperators. For example, the time evolution of a closed system may be written as $\rho(t)=U^\...
0
votes
0answers
50 views

Memory effects in open quantum systems: Markovian approximation question

Setting: Quantum system $S$ composed of a subsystem of interest $A$ and a subsystem acting as the environment $B$ such that $S=A\cup B$. System $S$ is described by density matrix $\rho$ whereas ...
1
vote
1answer
36 views

Is the effective Hamiltonian obtained via Feshbach-Fano partitioning closed?

I am not familiar with Feshbach-Fano partitioning so this question may be trivial. The full Hamiltonian of an open quantum system consists of system+enviroment+interaction. This can be cast into an ...
2
votes
1answer
82 views

Where does the expression $\mathrm{Tr}(K) = \sum_{j=1}^{n}\langle\psi_j|K|\psi_j\rangle$ for the partial trace come from?

During my studies of composite quantum systems I find some expressions that leave me with a little doubt. For example: Let K be a linear operator defined in the Hilbert space H. Where H is given by $H ...
0
votes
1answer
65 views

How to extend a quantum operation to an auxiliary Hilbert space?

In Breuer and Petruccione's book 'The theory of open quantum systems', section 2.4.3, 'representation theorem of quantum operations', a quantum operation $\phi_m$ corresponding to a measurement ...
1
vote
0answers
41 views

Time scales in Master equation

In the Lindblad master equation $$\dot\rho=\frac{i}{\hbar}[H,\rho]+\sum_{i=1}^{N^2-1}\gamma_i \left(L_i\rho L_i^{\dagger}-\frac{1}{2}\left\{L_i^{\dagger}L_i,\rho\right\}\right)$$ where $\dot{\rho} = \...
1
vote
3answers
97 views

Dyson expansion for the density matrix

I am following these notes and I am stuck on going from equation (37) to (38). In a nutshell, given $$ \frac{d \tilde{\rho}(t)}{dt} =-i\alpha[\tilde{H}_I(t),\tilde{\rho}(t)], \quad (*) $$ where $\...
2
votes
0answers
80 views

Non-Hermitian Hamiltonian diagonalization

Edit : 2x2 simple system instead, simplification of the question. I would like to study a system into its diagonal form, but this system is represented by a non-Hermitian Hamiltonian $\tilde{\mathcal{...
6
votes
1answer
180 views

Why do time evolution semigroups have to be contracting?

Studying the theory of open quantum systems, some textbooks start by introducing the notion of a semigroup for the time evolution operator $T_t$. The next step then usually is to impose that such a ...
0
votes
1answer
37 views

Correspondence between ground state and steady state in quantum systems

An open quantum system $S$ is usually studied by considering a system of interest effectively interacting with an environment $E$. The environment is treated effectively because of the difficulty of ...
0
votes
0answers
29 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 ...
1
vote
0answers
47 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 ...
2
votes
1answer
102 views

How do I show the separability of this density matrix?

I am stuck since a longer time regarding this exercise where I need to work with a density matrix of the given form $$\displaystyle \rho_{AB}(X)= \frac{1}{N+\text{tr}X^2}\left( {\begin{array}{cc} ...
1
vote
1answer
50 views

Example of an infinite volume Lindblad system

What is an explicit example of a Lindbladian \begin{align*} L(\rho) = - i \lbrack H_A, \rho \rbrack + G \sum_{j} V_j \rho V_j^* - \frac{1}{2}(V_j^* V_j \rho + \rho V_j^* V_j) \end{align*} acting on ...
0
votes
1answer
126 views

Solving linear Lindblad equations in the Heisenberg picture?

I'm interested in solving the explicit time dependence of operators in a simple open system described by a Lindblad equation. The concrete example I'm interested in is a harmonic oscillator with the ...
1
vote
1answer
105 views

Super-ohmic bosonic bath correlation function

In quantum Brownian motion, bosonic/harmonic oscillator bath and interaction described by Hamiltonian $$ H_B = \sum_{n}\hbar\omega_n(b_n^\dagger b_n) \\ H_I = -\sigma_x \otimes B $$ and $$ B = \sum_n \...
1
vote
1answer
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 ...
1
vote
1answer
80 views

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 ...
0
votes
1answer
53 views

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 ...
1
vote
1answer
70 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 \...
3
votes
1answer
103 views

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 ...
1
vote
1answer
93 views

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 ...
1
vote
1answer
114 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 $\rho$...
2
votes
1answer
61 views

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 ...
0
votes
0answers
70 views

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(...
5
votes
1answer
212 views

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 ...
3
votes
0answers
33 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 ...
1
vote
1answer
51 views

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}...
3
votes
1answer
74 views

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 ...
3
votes
0answers
103 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 ...
0
votes
1answer
44 views

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 (...