Lindblad-type Equation Research Articles

Constraints on quantum spacetime-induced decoherence from neutrino oscillations

We investigate the implications of decoherence induced by quantum spacetime properties on neutrino oscillation phenomena. We develop a general formalism where the evolution of neutrinos is governed by a Lindblad-type equation and we compute the oscillation damping factor for various models that have been proposed in the literature. Furthermore, we discuss the sensitivity to these effects of different types of neutrino oscillation experiments, encompassing astrophysical, atmospheric, solar, and reactor neutrino experiments. By using neutrino oscillation data from long-baseline reactors and atmospheric neutrino observations, we establish stringent constraints on the energy scale governing the strength of the decoherence induced by stochastic metric fluctuations, amounting to, respectively, EQG≥2.6×1034 GeV and EQG≥2.5×1055 GeV. Published by the American Physical Society 2024

Controlling thermoelectric, heat, and energy currents through a quantum dot in sequential and cotunneling Coulomb-blockade regimes

Thermal transport through a Coulomb-blockade quantum dot (QD) coupled to two metallic leads is studied using five different approaches to the master equation in which sequential and coutuneling terms are taken into account. In the presence of intradot Coulomb interactions, a plateau in the thermo-particle, the heat, and the energy currents is seen. The current plateau diminishes at a high thermal bias between the leads. It is shown that the Pauli, the Redfield, the Lindblad-type equation with first order tunneling rates, and first-order von-Neumann master equations give very similar thermal transport indicating the conservation of coherency in the electron transport in sequential tunneling between the QD and leads. In contrast, the thermal transport is suppressed when coutuneling processes are taken into account via a second-order von-Neumann master equation. The consideration of second order effects with respect to the QD-leads coupling brings in a wealth of virtual processes at the contact to each lead. These virtual processes directly weaken the effects of the contribution of the first order direct processes to the overall transport, and introduce important other aspects of the transport, as level broadening, energy shifts, and lifetimes in the time-domain. As a result the current plateau formed via the Coulomb interaction diminishes, when second order and cotunneling processes are considered.

Effective Field Theory for jet substructure in heavy ion collisions

I develop an Effective Field Theory (EFT) framework to compute jet substructure observables for heavy ion collision experiments. As an example, I consider dijet events that accompany the formation of a weakly coupled long lived Quark Gluon Plasma (QGP) medium in a heavy ion collision and look at an observable insensitive to jet selection bias: the simultaneous measurement of jet mass along with the transverse momentum imbalance between the jets that are groomed to remove soft radiation. Treating the jet as an open quantum system, I write down a factorization formula within the SCET (Soft Collinear Effective Theory) framework in the forward scattering regime. The physics of the medium is encoded in a universal soft field correlator while the jet-medium interaction is captured by a medium induced jet function. The factorization formula leads to a Lindblad type equation for the evolution of the reduced density matrix of the jet in the Markovian approximation. The solution for this equation allows a resummation of large logarithms that arise due to the final state measurements imposed while simultaneously summing over multiple incoherent interactions of the jet with the medium.

Lindbladian approximation beyond ultraweak coupling

Away from equilibrium, the properties of open quantum systems depend on the details of their environment. A microscopic derivation of a master equation (ME) is therefore crucial. Of particular interest are Lindblad-type equations, not only because they provide the most general class of Markovian MEs, but also since they are the starting point for efficient quantum trajectory simulations. Lindblad-type MEs are commonly derived from the Born-Markov-Redfield equation via a rotating-wave approximation (RWA). However the RWA is valid only for ultraweak system-bath coupling and often fails to accurately describe nonequilibrium processes. Here we derive an alternative Lindbladian approximation to the Redfield equation, which does not rely on ultraweak system-bath coupling. Applying it to an extended Hubbard model coupled to Ohmic baths, we show that, especially away from equilibrium, it provides a good approximation in large parameter regimes where the RWA fails.

Master equation for open two-band systems and its applications to Hall conductance

Hall conductivity in the presence of a dephasing environment has recently been investigated with a dissipative term introduced phenomenologically. In this paper, we study the dissipative topological insulator (TI) and its topological transition in the presence of quantized electromagnetic environments. A Lindblad-type equation is derived to determine the dynamics of a two-band system. When the two-band model describes TIs, the environment may be the fluctuations of radiation that surround the TIs. We find the dependence of decay rates in the master equation on Bloch vectors in the two-band system, which leads to a mixing of the band occupations. Hence the environment-induced current is in general not perfectly topological in the presence of coupling to the environment, although deviations are small in the weak limit. As an illustration, we apply the Bloch-vector-dependent master equation to TIs and calculate the Hall conductance of tight-binding electrons in a two-dimensional lattice. The influence of environments on the Hall conductance is presented and discussed. The calculations show that the phase transition points of the TIs are robust against the quantized electromagnetic environment. The results might bridge the gap between quantum optics and topological photonic materials.

Floquet topological phases coupled to environments and the induced photocurrent

We consider the fate of a helical edge state of a spin Hall insulator and its topological transition in presence of a circularly polarized light when coupled to various forms of environments. A Lindblad type equation is developed to determine the fermion occupation of the Floquet bands. We find by using analytical and numerical methods that non-secular terms, corresponding to 2-photon transitions, lead to a mixing of the band occupations, hence the light induced photocurrent is in general not perfectly quantized in the presence of finite coupling to the environment, although deviations are small in the adiabatic limit. Sharp crossovers are identified at frequencies $\Omega$ and $\frac{1}{2}\Omega$ ($\Omega$ is the strength of light-matter coupling) with the former resembling to a phase transition.

Informational Description of the Flux Qubit Evolution

Lindblad-type equation is used to describe flux qubit evolution. In the frame of informational approach two types of flux qubit - three-junction qubit based on low-inductive π -interferometer and two-junction qubit based on low-inductive φ-interferometer - are considered and compared. Such approach to flux qubit analysis can be used to study the coherence state decay in the measurement procedure.

Jump-diffusion unravelling of a non-Markovian generalized Lindblad master equation

The “correlated-projection technique” has been successfully applied to derive a large class of highly non-Markovian dynamics, the so called non-Markovian generalized Lindblad-type equations or Lindblad rate equations. In this article, general unravelings are presented for these equations, described in terms of jump-diffusion stochastic differential equations for wave functions. We show also that the proposed unraveling can be interpreted in terms of measurements continuous in time but with some conceptual restrictions. The main point in the measurement interpretation is that the structure itself of the underlying mathematical theory poses restrictions on what can be considered as observable and what is not; such restrictions can be seen as the effect of some kind of superselection rule. Finally, we develop a concrete example and discuss possible effects on the heterodyne spectrum of a two-level system due to a structured thermal-like bath with memory.

Using the Renyi entropy to describe quantum dissipative systems in statistical mechanics

We develop a formalism for describing quantum dissipative systems in statistical mechanics based on the quantum Renyi entropy. We derive the quantum Renyi distribution from the principle of maximum quantum Renyi entropy and differentiate this distribution (the temperature density matrix) with respect to the inverse temperature to obtain the Bloch equation. We then use the Feynman path integral with a modified Mensky functional to obtain a Lindblad-type equation. From this equation using projection operators, we derive the integro-differential equation for the reduced temperature statistical operator, an analogue of the Zwanzig equation in statistical mechanics, and find its formal solution in the form of a series in the class of summable functions.