Lindblad Equation Research Articles

Quantum wires with local particle loss: Transport manifestations of fluctuation-induced effects

We investigate the transport properties of a quantum wire of weakly interacting fermions in the presence of local particle loss. We calculate current and conductance in this system due to applied external chemical potential bias that can be measured in experimental realizations of ultracold fermions in quasi one-dimensional traps. Using a Keldysh field theory approach based on the Lindblad equation, we establish a perturbative scheme to study the effect of imbalanced reservoirs. Logarithmically divergent terms are resummed using a renormalization group method, and a novel powerlaw behavior for the conductance as a function of the potential bias across the wire is found. In contrast to the equilibrium case of a potential barrier in a Luttinger liquid, the conductance exhibits a scaling behavior, which depends on the interaction strength and on the loss probability. Repulsive interactions reduce the conductance of the wire while attractive interactions enhance it. However, perfect reflectivity and transparency are only reached in the absence of particle loss. Published by the American Physical Society 2024

Understanding gravitationally induced decoherence parameters in neutrino oscillations using a microscopic quantum mechanical model

In this work, a microscopic quantum mechanical model for gravitationally induced decoherence introduced by Blencowe and Xu is investigated in the context of neutrino oscillations. The focus is on the comparison with existing phenomenological models and the physical interpretation of the decoherence parameters in such models. The results show that for neutrino oscillations in vacuum gravitationally induced decoherence can be matched with phenomenological models with decoherence parameters of the form Γ ij ∼ Δ m 4 ij E -2. When matter effects are included, the decoherence parameters exhibit a dependence on the varying matter density across the Earth layers. This behavior can be explained by the nature of the coupling between neutrinos and the gravitational wave environment, as suggested by linearised gravity. On a theoretical level, these different models can be characterised by a different choice of Lindblad operators, with the model with decoherence parameters that do not include matter effects being less suitable from the point of view of linearised gravity. Consequently, in the case of neutrino oscillations in matter, the microscopic model does not agree with many existing phenomenological models that assume constant decoherence parameters in matter. Nonetheless, we identify the KamLAND experimental setup as particularly well-suited to establish the first experimental constraints on the model parameters, namely the neutrino coupling to the gravitational wave environment and its temperature, based on a prior analysis using the phenomenological model.

Quarkonium polarization in medium from open quantum systems and chromomagnetic correlators

We study the spin-dependent in-medium dynamics of quarkonia by using the potential nonrelativistic QCD (pNRQCD) and the open quantum system framework. We consider the pNRQCD Lagrangian valid up to the order rM0=r and r0M=1M in the double power counting. By considering the Markovian condition and applying the Wigner transformation upon the diagonal spin components of the quarkonium density matrix with the semiclassical expansion, we systematically derive the Boltzmann transport equation for quarkonia with polarization dependence in the quantum optical limit. Unlike the spin-independent collision terms governed by certain chromoelectric field correlators, new gauge invariant correlators of chromomagnetic fields determine the recombination and dissociation terms with polarization dependence at the order we are working. We also derive a Lindblad equation describing the in-medium transitions between spin-singlet and spin-triplet heavy quark-antiquark pairs in the quantum Brownian motion limit. The Lindblad equation is governed by new transport coefficients defined in terms of the chromomagnetic field correlators. Our formalism is generic and valid for both weakly coupled and strongly coupled quark gluon plasmas. It can be further applied to study spin alignment of vector quarkonia in heavy ion collisions. Published by the American Physical Society 2024

Flux qubit based detector of microwave photons

A theory of detection of microwave photons with a flux qubit based detector is presented. We consider a semiclassical approximation with the electromagnetic field being in a coherent state. The flux qubit is considered as a multilevel quantum system (qudit). By solving the Lindblad equation, we describe the time evolution of occupations of the qudit's levels for readout and reset stages of detection. When considering the reset stage, the time evolution is described by multiple avoided-level crossings, thus providing a multilevel Landau-Zener-Stückelberg-Majorana (LZSM) problem. In addition to numerical calculations, we present an approximate solution for the description of the reset stage dynamics based on the adiabatic-impulse approximation and rate equation approach. Our theory may be useful for the theoretical description of driven-dissipative dynamics of qudits, including applications such as single-photon detection. Published by the American Physical Society 2024

Entropy production of quantum reset models

We analyze the entropy production of Quantum Reset Models (QRMs) corresponding to quantum dynamical semigroups driven by Lindbladians motivated by a probabilistic description of dissipation in an external environment. We investigate the strict positivity of entropy production for Lindbladians given as sums of QRMs, when the Hamiltonian of the total Lindbladian is split as an affine combination of Hamiltonians of the individual QRMs. In this setup, we derive conditions on the coefficients of the combination and on the reset states ensuring either positive or zero entropy production. Second, we deal with a tri-partite system subject at its ends to two independent QRMs and a weak coupling Hamiltonian. The latter is split as an affine combination of individual Hamiltonians, and we provide necessary and sufficient conditions ensuring strict positivity of the entropy production to leading order, with the possible exception of one affine combination. We apply these results to a physically motivated model and exhibit explicit expressions for the leading orders steady-state solution, entropy production and entropy fluxes. Moreover, these approximations are numerically shown to hold beyond the expected regimes.

Block quantum dynamical semigroups of completely positive definite kernels

Block quantum dynamical semigroups of completely positive definite kernels

Photo-induced dynamics with continuous and discrete quantum baths.

The ultrafast quantum dynamics of photophysical processes in complex molecules is an extremely challenging computational problem with a broad variety of fascinating applications in quantum chemistry and biology. Inspired by recent developments in open quantum systems, we introduce a pure-state unraveled hybrid-bath method that describes a continuous environment via a set of discrete, effective bosonic degrees of freedom using a Markovian embedding. Our method is capable of describing both, a continuous spectral density and sharp peaks embedded into it. Thereby, we overcome the limitations of previous methods, which either capture long-time memory effects using the unitary dynamics of a set of discrete vibrational modes or use memoryless Markovian environments employing a Lindblad or Redfield master equation. We benchmark our method against two paradigmatic problems from quantum chemistry and biology. We demonstrate that compared to unitary descriptions, a significantly smaller number of bosonic modes suffices to describe the excitonic dynamics accurately, yielding a computational speed-up of nearly an order of magnitude. Furthermore, we take into account explicitly the effect of a δ-peak in the spectral density of a light-harvesting complex, demonstrating the strong impact of the long-time memory of the environment on the dynamics.

Kadanoff-Baym Equations for Interacting Systems with Dissipative Lindbladian Dynamics.

The extraordinary quantum properties of nonequilibrium systems governed by dissipative dynamics have become a focal point in contemporary scientific inquiry. The nonequilibrium Green's functions (NEGF) theory provides a versatile method for addressing driven nondissipative systems, utilizing the powerful diagrammatic technique to incorporate correlation effects. We here present a second-quantization approach to the dissipative NEGF theory, reformulating Keldysh ideas to accommodate Lindbladian dynamics and extending the Kadanoff-Baym equations accordingly. Generalizing diagrammatic perturbation theory for many-body Lindblad operators, the formalism enables correlated and dissipative real-time simulations for the exploration of transient and steady-state changes in the electronic, transport, and optical properties of materials.

Entropy production in the mesoscopic-leads formulation of quantum thermodynamics.

Understanding the entropy production of systems strongly coupled to thermal baths is a core problem of both quantum thermodynamics and mesoscopic physics. While many techniques exist to accurately study entropy production in such systems, they typically require a microscopic description of the baths, which can become numerically intractable to study for large systems. Alternatively an open-systems approach can be employed with all the nuances associated with various levels of approximation. Recently, the mesoscopic leads approach has emerged as a powerful method for studying such quantum systems strongly coupled to multiple thermal baths. In this method, a set of discretized lead modes, each locally damped, provide a Markovian embedding. Here we show that this method proves extremely useful to describe entropy production of a strongly coupled open quantum system. We show numerically, for both noninteracting and interacting setups, that a system coupled to a single bath exhibits a thermal fixed point at the level of the embedding. This allows us to use various results from the thermodynamics of quantum dynamical semigroups to infer the nonequilibrium thermodynamics of the strongly coupled, non-Markovian central systems. In particular, we show that the entropy production in the transient regime recovers the well-established microscopic definitions of entropy production with a correction that can be computed explicitly for both the single- and multiple-lead cases.

Markovian dynamics for a quantum/classical system and quantum trajectories

Quantum trajectory techniques have been used in the theory of open systems as a starting point for numerical computations and to describe the monitoring of a quantum system in continuous time. We extend this technique to develop a general approach to the dynamics of quantum/classical hybrid systems. By using two coupled stochastic differential equations, we can describe a classical component and a quantum one which have their own intrinsic dynamics and which interact with each other. A mathematically rigorous construction is given, under the restriction of having a Markovian joint dynamics and of involving only bounded operators on the Hilbert space of the quantum component. An important feature is that, if the interaction allows for a flow of information from the quantum component to the classical one, necessarily the dynamics is dissipative. We show also how this theory is connected to a suitable hybrid dynamical semigroup, which reduces to a quantum dynamical semigroup in the purely quantum case and includes Liouville and Kolmogorov–Fokker–Planck equations in the purely classical case. Moreover, this semigroup allows to compare the proposed stochastic dynamics with various other proposals based on hybrid master equations. Some simple examples are constructed in order to show the variety of physical behaviors which can be described; in particular, a model presenting hidden entanglement is introduced.

Characterisation of gradient flows for a given functional

Let X be a vector field and Y be a co-vector field on a smooth manifold M. Does there exist a smooth Riemannian metric gαβ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$g_{\\alpha \\beta }$$\\end{document} on M such that Yβ=gαβXα\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Y_\\beta = g_{\\alpha \\beta } X^\\alpha $$\\end{document}? The main result of this note gives necessary and sufficient conditions for this to be true. As an application of this result we provide a gradient-flow characterisation for dissipative quantum systems. Namely, we show that finite-dimensional ergodic Lindblad equations admit a gradient flow structure for the von Neumann relative entropy if and only if the condition of bkm-detailed balance holds.

Computer Simulation of Charge Transfer In a DNA Molecule within a Simple Model of an Open Quantum System

The quantum-statistical model proposed earlier by Skourtis and Nitzan to describe a charge (hole) propagation in a fragment of artificial DNA molecule has been generalized and further investigated. A numerical simulation of a charge transport was carried out taking into account two different dissipative processes, including the capture of the charged carrier by the environment and the decoherence of its quantum wave properties due to the influence of stochastic fields of the environment. The interaction of the carrier with the environment is regulated by a small set of phenomenological parameters whose values vary in the process of simulation. Within this model, the propagation of a hole carrier in DNA is described by solving the quantum Franke-Kossakovski–Lindblad–Glauber–Sudarshan equation (hereinafter referred to as the Lindblad equation) for the carrier density matrix using the Lindblad MPO Solver program. Results of numerical analysis of the model are in a good agreement with experimental observations and demonstrate two different types of the charged carrier motion, presumably tunneling and incoherent hopping. The model is put in more general context and non-unitary dynamics of the hole carrier is treated within the framework of a theory of continuous quantum measurements by the environment in an open quantum system. The main concepts of the theory of decoherence and superselection for open quantum systems and the prospects for their application for further study of various mechanisms of motion of a charged carrier in DNA are briefly discussed.

Recovering an accurate Lindblad equation from the Bloch-Redfield equation for general open quantum systems

Recovering an accurate Lindblad equation from the Bloch-Redfield equation for general open quantum systems

Symmetry-preserving quadratic Lindbladian and dissipation driven topological transitions in Gaussian states

The dynamical evolution of an open quantum system can be governed by the Lindblad equation of the density matrix. In this paper, we propose to characterize the density matrix topology by the topological invariant of its modular Hamiltonian. Since the topological classification of such Hamiltonians depends on their symmetry classes, a primary issue we address is determining the requirement for the Lindbladian operators, under which the modular Hamiltonian can preserve its symmetry class during the dynamical evolution. We solve this problem for the fermionic Gaussian state and for the modular Hamiltonian being a quadratic operator of a set of fermionic operators. When these conditions are satisfied, along with a nontrivial topological classification of the symmetry class of the modular Hamiltonian, a topological transition can occur as time evolves. We present two examples of dissipation-driven topological transitions where the modular Hamiltonian lies in the AIII class with U(1) symmetry and the DIII class without U(1) symmetry. By a finite size scaling, we show that this density matrix topology transition occurs at a finite time. We also present the physical signature of this transition.

The standard block RG and DMRG for open systems

For physical models that can be described by a lattice, a coarse-graining transformation is defined according to the numerical Wilson renormgroup. We formulated a numerical RG method for open quantum systems. To create it, on the one hand, we used the information about how the Hamiltonian is transformed in the standard method defined for Hamiltonian systems and, on the other hand, the knowledge how the Hamiltonian enters the right part of the GKLS equation. After that we have shown exactly how the environment given by Lindblad operators can be inscribed into a well known alternative to the standard method – the DMRG. In the prospects using the methods of numerical renormgroup for open systems allow us to investigate the time behaviour of quantum entanglement. Using the DMRG example for the Ising model in the transverse field, we have demonstrated the behaviour of entanglement for a small iteration number.

Hybrid quantum-classical systems: Quasi-free Markovian dynamics

In the case of a quantum-classical hybrid system with a finite number of degrees of freedom, the problem of characterizing the most general dynamical semigroup is solved, under the restriction of being quasi-free. This is a generalization of a Gaussian dynamics, and it is defined by the property of sending (hybrid) Weyl operators into Weyl operators in the Heisenberg description. The result is a quantum generalization of the Lévy–Khintchine formula; Gaussian and jump contributions are included. As a byproduct, the most general quasi-free quantum-dynamical semigroup is obtained; on the classical side the Liouville equation and the Kolmogorov–Fokker–Planck equation are included. As a classical subsystem can be observed, in principle, without perturbing it, information can be extracted from the quantum system, even in continuous time; indeed, the whole construction is related to the theory of quantum measurements in continuous time. While the dynamics is formulated to give the hybrid state at a generic time [Formula: see text], we show how to extract multi-time probabilities and how to connect them to the quantum notions of positive operator-valued measure and instrument. The structure of the generator of the dynamical semigroup is analyzed, in order to understand how to go on to non-quasi-free cases and to understand the possible classical-quantum interactions; in particular, all the interaction terms which allow to extract information from the quantum system necessarily vanish if no dissipation is present in the dynamics of the quantum component. A concrete example is given, showing how a classical component can input noise into a quantum one and how the classical system can extract information on the behavior of the quantum one.

Lindblad dynamics from spatio-temporal correlation functions in nonintegrable spin- 1/2 chains with different boundary conditions

We investigate the Lindblad equation in the context of boundary-driven magnetization transport in spin-1/2 chains. Our central question is whether the nonequilibrium steady state of the open system, including its buildup in time, can be described on the basis of the dynamics in the closed system. To this end, we rely on a previous study [Heitmann , ], in which a description in terms of spatio-temporal correlation functions was suggested in the case of weak driving and small system-bath coupling. Because this work focused on integrable systems and periodic boundary conditions, we here extend the analysis in three directions: (1) We consider nonintegrable systems, (2) we take into account open boundary conditions and other bath-coupling geometries, and (3) we provide a comparison to time-evolving block decimation. While we find that nonintegrability plays a minor role, the choice of the specific boundary conditions can be crucial due to potentially nondecaying edge modes. Our large-scale numerical simulations suggest that a description based on closed-system correlation functions is a useful alternative to already existing state-of-the-art approaches. Published by the American Physical Society 2024

Decoherence rate in random Lindblad dynamics

Open quantum systems undergo decoherence, which is responsible for the transition from quantum to classical behavior. The time scale in which decoherence takes place can be analyzed using upper limits to its rate. We examine the dynamics of open chaotic quantum systems governed by random Lindblad operators sourced from Gaussian and Ginibre ensembles with Wigner-Dyson symmetry classes. In these systems, the ensemble-averaged purity decays monotonically as a function of time. This decay is governed by the decoherence rate, which is upper-bounded by the dimension of their Hilbert space and is independent of the ensemble symmetry. These findings hold upon mixing different ensembles, indicating the universal character of the decoherence rate limit. Moreover, our findings reveal that open chaotic quantum systems governed by random Lindbladians tend to exhibit the most rapid decoherence, regardless of the initial state. This phenomenon is associated with the concentration of the decoherence rate near its upper bound. Our work identifies primary features of decoherence in dissipative quantum chaos, with applications ranging from quantum foundations to high-energy physics and quantum technologies. Published by the American Physical Society 2024

Understanding and Generalizing Unique Decompositions of Generators of Dynamical Semigroups

We generalize the result of Gorini, Kossakowski, and Sudarshan [J. Math. Phys. 17:821, 1976] that every generator of a quantum-dynamical semigroup decomposes uniquely into a closed and a dissipative part, assuming the trace of both vanishes. More precisely, we show that given any generator [Formula: see text] of a completely positive dynamical semigroup and any matrix [Formula: see text] there exists a unique matrix [Formula: see text] and a unique completely positive map [Formula: see text] such that (i) [Formula: see text], (ii) the superoperator [Formula: see text] has trace zero, and (iii) [Formula: see text] is a real number. The key to proving this is the relation between the trace of a completely positive map, the trace of its Kraus operators, and expectation values of its Choi matrix. Moreover, we show that the above decomposition is orthogonal with respect to some [Formula: see text]-weighted inner product.

Optimized noise-assisted simulation of the Lindblad equation with time-dependent coefficients on a noisy quantum processor

Optimized noise-assisted simulation of the Lindblad equation with time-dependent coefficients on a noisy quantum processor