A simple derivation of the Lindblad equation

Brasil, Carlos Alexandre; Fanchini, Felipe F.; Napolitano, Reginaldo de Jesus

doi:10.1590/s1806-11172013000100003

Cited by 37 publications

(30 citation statements)

References 9 publications

(7 reference statements)

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Refs. [47,[88][89][90][91], we pay special attention to the physical assumptions the Lindblad formalism relies on, and show how they concretely enter into the calculation.…”

Section: A Deriving the Lindblad Equationmentioning

confidence: 99%

Observational constraints on quantum decoherence during inflation

Martin

Vennin

2018

J. Cosmol. Astropart. Phys.

152

View full text Add to dashboard Cite

Since inflationary perturbations must generically couple to all degrees of freedom present in the early Universe, it is more realistic to view these fluctuations as an open quantum system interacting with an environment. Then, on very general grounds, their evolution can be modelled with a Lindblad equation. This modified evolution leads to quantum decoherence of the system, as well as to corrections to observables such as the power spectrum of curvature fluctuations. On one hand, current cosmological observations constrain the properties of possible environments and place upper bounds on the interaction strengths. On the other hand, imposing that decoherence completes by the end of inflation implies lower bounds on the interaction strengths. Therefore, the question arises of whether successful decoherence can occur without altering the power spectrum. In this paper, we systematically identify all scenarios in which this is possible. As an illustration, we discuss the case in which the environment consists of a heavy test scalar field. We show that this realises the very peculiar configuration where the correction to the power spectrum is quasi scale invariant. In that case, the presence of the environment improves the fit to the data for some inflationary models but deteriorates it for others. This clearly demonstrates that decoherence is not only of theoretical importance but can also be crucial for astrophysical observations.

show abstract

“…Refs. [47,[88][89][90][91], we pay special attention to the physical assumptions the Lindblad formalism relies on, and show how they concretely enter into the calculation.…”

Section: A Deriving the Lindblad Equationmentioning

confidence: 99%

Observational constraints on quantum decoherence during inflation

Martin

Vennin

2018

J. Cosmol. Astropart. Phys.

152

View full text Add to dashboard Cite

show abstract

“…In general, simulations of single photon QWs in irregular arrays of waveguides are extremely difficult and therefore numerical solutions are necessary. Especially, if the propagation loss is included in numerically solving the Linblad equation it would require large resources including computing time and memory [40,41]. However, we can make use of the fact that single photon QWs do not exhibit any different behavior from classical wave propagation, and the light intensity distribution corresponds to the probability of detecting the photon at any position [42].…”

Section: Quantum Walks In Periodic and Quasiperiodic Multicore Ring Fmentioning

confidence: 99%

Quantum Walks in Periodic and Quasiperiodic Fibonacci Fibers

Nguyen

Khrapko

et al. 2020

Sci Rep

View full text Add to dashboard Cite

Quantum walk is a key operation in quantum computing, simulation, communication and information. Here, we report for the first time the demonstration of quantum walks and localized quantum walks in a new type of optical fibers having a ring of cores constructed with both periodic and quasiperiodic Fibonacci sequences, respectively. Good agreement between theoretical and experimental results have been achieved. The new multicore ring fibers provide a new platform for experiments of quantum effects in low-loss optical fibers which is critical for scalability of real applications with large-size problems. Furthermore, our new quasiperiodic Fibonacci multicore ring fibers provide a new class of quasiperiodic photonics lattices possessing both on-and offdiagonal deterministic disorders for realizing localized quantum walks deterministically. The proposed Fibonacci fibers are simple and straightforward to fabricate and have a rich set of properties that are of potential use for quantum applications. Our simulation and experimental results show that, in contrast with randomly disordered structures, localized quantum walks in new proposed quasiperiodic photonics lattices are highly controllable due to the deterministic disordered nature of quasiperiodic systems.

show abstract

“…where H S is the system of interest Hamiltonian, H R is the reservoir Hamiltonian, and H SR is the system-reservoir interaction Hamiltonian. As shown in Refs [33][34][35]49], by tracing over the reservoir degrees of freedom, considering a bilinear interaction between system and reservoir, and under the Markov approximation, the system density operator ρ S has its evolution described by the Sudarshan-Lindblad master equation…”

Section: Evolution Equation For a N Spin-1/2 Particles Interactinmentioning

confidence: 99%

“…which satisfies the requirements T r 3 ρ 3 (1, 2, 3) = ρ 2 (1, 2), T r 2 ρ 3 (1, 2, 3) = ρ 2 (1, 3) and T r 1 ρ 3 (1, 2, 3) = ρ 2 (2, 3). By introducing the correlation operator (49) in Eq. (50) we get ρ 3 (1, 2, 3) ≈ ρ 1 (1)ρ 1 (2)ρ 1 (3) + ρ 1 (1)χ(2, 3) + ρ 1 (2)χ(1, 3) + ρ 1 (3)χ(1, 2).…”

Section: Beyond the Mean-field Approximationmentioning

confidence: 99%

See 1 more Smart Citation

Many-particle Sudarshan-Lindblad equation: mean-field approximation, nonlinearity and dissipation in a spin system

Prataviera

Mizrahi

2014

Rev. Bras. Ensino Fís.

View full text Add to dashboard Cite

A system of N spin-1/2 particles interacting with a thermal reservoir is used as a pedagogical example for advanced undergraduate and graduate students. We introduce and illustrate some methods, approximations, and phenomena related to dissipation and nonlinearity in many-particle physics. We start our analysis from the dynamical Sudarshan-Lindblad quantum master equation for the density operator of a system S interacting with a thermal reservoir R. We derive the quantum version of the so-called Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) equations such that the master equation can be decomposed in a hierarchical set of N −1 equations (N > 1). The hierarchy is broken by introducing the mean-field approximation and reducing the problem to a nonlinear single particle system. In this scenario, the Hamiltonian is nonlinear (i.e., it depends on the state of S), although the superoperator responsible for the dissipation and decoherence of S remains unaffected. To provide a useful tool to students: (1) we discuss the physical approximations involved, (2) we derive the analytical solution to the mean values equations of motion resulting from the Hamiltonian, (3) we solve analytically the master equation in the stationary regime, (4) we obtain and discuss the solution of the nonlinear master equation, numerically, and finally, (5) we discuss the master equation beyond the mean-field approximation and show how to introduce higher order quantum correlations that have been previously neglected. That means that by changing t by −t, reverting the velocities, and replacing the initial conditions in the solution of the equation by the final ones does not lead us to the initial conditions after a time t has elapsed.

show abstract

A simple derivation of the Lindblad equation

Cited by 37 publications

References 9 publications

Observational constraints on quantum decoherence during inflation

Observational constraints on quantum decoherence during inflation

Quantum Walks in Periodic and Quasiperiodic Fibonacci Fibers

Many-particle Sudarshan-Lindblad equation: mean-field approximation, nonlinearity and dissipation in a spin system

Contact Info

Product

Resources

About