Machine learning approach to the Floquet-Lindbladian problem.

Similar to its classical version, quantum Markovian evolution can be either time-discrete or time-continuous. Discrete quantum Markovian evolution is usually modeled with completely positive trace-preserving maps, while time-continuous evolution is often specified with superoperators referred to as "Lindbladians." Here, we address the following question: Being given a quantum map, can we find a Lindbladian that generates an evolution identical-when monitored at discrete instances of time-to the one induced by the map? It was demonstrated that the problem of getting the answer to this question can be reduced to an NP-complete (in the dimension N of the Hilbert space, the evolution takes place in) problem. We approach this question from a different perspective by considering a variety of machine learning (ML) methods and trying to estimate their potential ability to give the correct answer. Complimentarily, we use the performance of different ML methods as a tool to validate a hypothesis that the answer to the question is encoded in spectral properties of the so-called Choi matrix, which can be constructed from the given quantum map. As a test bed, we use two single-qubit models for which the answer can be obtained using the reduction procedure. The outcome of our experiment is that, for a given map, the property of being generated by a time-independent Lindbladian is encoded both in the eigenvalues and the eigenstates of the corresponding Choi matrix.

Random generators of Markovian evolution: A quantum-classical transition by superdecoherence.

Continuous-time Markovian evolution appears to be manifestly different in classical and quantum worlds. We consider ensembles of random generators of N-dimensional Markovian evolution, quantum and classical ones, and evaluate their universal spectral properties. We then show how the two types of generators can be related by superdecoherence. In analogy with the mechanism of decoherence, which transforms a quantum state into a classical one, superdecoherence can be used to transform a Lindblad operator (generator of quantum evolution) into a Kolmogorov operator (generator of classical evolution). We inspect spectra of random Lindblad operators undergoing superdecoherence and demonstrate that, in the limit of complete superdecoherence, the resulting operators exhibit spectral density typical to random Kolmogorov operators. By gradually increasing strength of superdecoherence, we observe a sharp quantum-to-classical transition. Furthermore, we define an inverse procedure of supercoherification that is a generalization of the scheme used to construct a quantum state out of a classical one. Finally, we study microscopic correlation between neighboring eigenvalues through the complex spacing ratios and observe the horseshoe distribution, emblematic of the Ginibre universality class, for both types of random generators. Remarkably, it survives both superdecoherence and supercoherification.

Chaotic spin-photonic quantum states in an open periodically modulated cavity.

When applied to dynamical systems, both classical and quantum, time periodic modulations can produce complex non-equilibrium states which are often termed "chaotic." Being well understood within the unitary Hamiltonian framework, this phenomenon is less explored in open quantum systems. Here, we consider quantum chaotic states emerging in a leaky cavity when the intracavity photonic mode is coherently pumped with the pumping intensity varying periodically in time. We show that a single spin when placed inside the cavity and coupled to the mode can moderate transitions between regular and chaotic regimes-that are identified by using quantum Lyapunov exponents or features of photon emission statistics-and thus can be used to control the degree of chaos.

Asymptotic densities of planar Lévy walks: A nonisotropic case.

Lévy walks are a particular type of continuous-time random walks which results in a super-diffusive spreading of an initially localized packet. The original one-dimensional model has a simple schematization that is based on starting a new unidirectional motion event either in the positive or in the negative direction. We consider two-dimensional generalization of Lévy walks in the form of the so-called XY model. It describes a particle moving with a constant velocity along one of the four basic directions and randomly switching between them when starting a new motion event. We address the ballistic regime and derive solutions for the asymptotic density profiles. The solutions have a form of first-order integrals which can be evaluated numerically. For specific values of parameters we derive an exact expression. The analytic results are in agreement with the results of finite-time numerical samplings.

Photon waiting-time distributions: A keyhole into dissipative quantum chaos.

Open quantum systems can exhibit complex states, for which classification and quantification are still not well resolved. The Kerr-nonlinear cavity, periodically modulated in time by coherent pumping of the intracavity photonic mode, is one of the examples. Unraveling the corresponding Markovian master equation into an ensemble of quantum trajectories and employing the recently proposed calculation of quantum Lyapunov exponents [I. I. Yusipov et al., Chaos 29, 063130 (2019)], we identify "chaotic" and "regular" regimes there. In particular, we show that chaotic regimes manifest an intermediate power-law asymptotics in the distribution of photon waiting times. This distribution can be retrieved by monitoring photon emission with a single-photon detector so that chaotic and regular states can be discriminated without disturbing the intracavity dynamics.

Pulse radiolysis study on the reactivity of NO3˙ radical toward uranous(iv), hydrazinium nitrate and hydroxyl ammonium nitrate at room temperature and at 45 °C.

Concentrated nitric acid solutions subjected to radiation produce radicals of extreme importance in the reprocessing of spent nuclear fuel. Knowledge of the different rate constants of the reactions involved in this chemistry is needed to improve the efficiency of the process and to define safe operating practices. Pulse radiolysis measurements are performed to find the rate constant of the reaction between NO3˙ radicals and U(iv) in highly concentrated nitrate solution. The optimal stabilization conditions toward thermal oxidation are defined for the considered solutions at room temperature and at 45 °C by adding anti-nitrous agents such as hydrazinium nitrate (HN) and hydroxyl ammonium nitrate (HAN). The decay of the NO3˙ radical is monitored and its reaction rates with HN, HAN and U(iv) are found to be 1.3 × 105, 1.5 × 107 and 1.6 × 106 M-1 s-1 at room temperature. The latter value is more than 10 times lower than the one currently used in numerical codes for simulation of the long-term radiolytic degradation associated with the reprocessing and storage of spent nuclear waste. At 45 °C, conditions similar to the reprocessing of spent fuel, the values of the rate constants of NO3˙ radical toward HN, HAN and U(iv) increase and are found to be 2.6 × 105, 2.9 × 107 and 9.3 × 106 M-1 s-1.

Linking 7-Nitrobenzo-2-oxa-1,3-diazole (NBD) to Triphenylphosphonium Yields Mitochondria-Targeted Protonophore and Antibacterial Agent.

Appending lipophilic cations to small molecules has been widely used to produce mitochondria-targeted compounds with specific activities. In this work, we obtained a series of derivatives of the well-known fluorescent dye 7-nitrobenzo-2-oxa-1,3-diazole (NBD). According to the previous data [Denisov et al. (2014) Bioelectrochemistry, 98, 30-38], alkyl derivatives of NBD can uncouple isolated mitochondria at concentration of tens of micromoles despite a high pKa value (~11) of the dissociating group. Here, a number of triphenylphosphonium (TPP) derivatives linked to NBD via hydrocarbon spacers of varying length (C5, C8, C10, and C12) were synthesized (mitoNBD analogues), which accumulated in the mitochondria in an energy-dependent manner. NBD-C10-TPP (C10-mitoNBD) acted as a protonophore in artificial lipid membranes (liposomes) and uncoupled isolated mitochondria at micromolar concentrations, while the derivative with a shorter linker (NBD-C5-TPP, or C5-mitoNBD) exhibited no such activities. In accordance with this data, C10-mitoNBD was significantly more efficient than C5-mitoNBD in suppressing the growth of Bacillus subtilis. C10-mitoNBD and C12-mitoNBD demonstrated the highest antibacterial activity among the investigated analogues. C10-mitoNBD also exhibited the neuroprotective effect in the rat model of traumatic brain injury.

Unfolding a quantum master equation into a system of real-valued equations: Computationally effective expansion over the basis of SU(N) generators.

Dynamics of an open N-state quantum system is often modeled with a Markovian master equation describing the evolution of the system density operator. By using generators of SU(N) group as a basis, the density operator can be transformed into a real-valued "coherence-vector." A generator of the dissipative evolution, so-called "Lindbladian," can be expanded over the same basis and recast in the form of a real matrix. Together, these expansions result is a nonhomogeneous system of N^{2}-1 real-valued linear ordinary differential equations. Now one can, e.g., implement standard high-performance algorithms to integrate the system of equations forward in time while being sure in exact preservation of the trace (norm) and Hermiticity of the density operator. However, when performed in a straightforward way, the expansion turns to be an operation of the time complexity O(N^{10}). The complexity can be reduced when the number of dissipative operators is independent of N, which is often the case for physically meaningful models. Here we present an algorithm to transform quantum master equation into a system of real-valued differential equations and propagate it forward in time. By using a specific scalable model, we evaluate computational efficiency of the algorithm and demonstrate that it is possible to handle the model system with N=10^{3} states on a single node of a computer cluster.

Quantum Lyapunov exponents beyond continuous measurements.

Quantum systems, when interacting with their environments, may exhibit nonequilibrium states that are tempting to be interpreted as quantum analogs of chaotic attractors. However, different from the Hamiltonian case, the toolbox for quantifying dissipative quantum chaos remains limited. In particular, quantum generalizations of Lyapunov exponents, the main quantifiers of classical chaos, are established only within the framework of continuous measurements. We propose an alternative generalization based on the unraveling of quantum master equation into an ensemble of "quantum trajectories," by using the so-called Monte Carlo wave-function method. We illustrate the idea with a periodically modulated open quantum dimer and demonstrate that the transition to quantum chaos matches the period-doubling route to chaos in the corresponding mean-field system.

Influence of amino acid sequence in a peptidic Cu+-responsive luminescent probe inspired by the copper chaperone CusF.

Copper(i) is a soft metal ion that plays an essential role in living organisms and Cu+-responsive probes are required to detect Cu+ ions in physiological conditions and understand its homeostasis as well as the diseases associated with its misregulation. In this article, we describe a series of cyclic peptides, which are structurally related to the copper chaperone CusF, and that behave as Cu+-repsonsive probes. These peptide probes comprise the 16-amino acid loop of CusF cyclized by a ß-turn inducer dipeptide and functionalized by a Tb3+ complex for its luminescence properties. The mechanism of luminescence enhancement relies on the modulation of the antenna effect between a tryptophan residue and the Tb3+ ion within the probe when Cu+ forms a cation-π interaction with the tryptophan. Here, we investigate the influence of the amino acid sequence of these cyclic peptides on the copper-induced modulation of Tb3+ emission and show that the rigid ß-turn inducer Aib-d-Pro and insertion of the Tb3+ complex close to its tryptophan antenna are required to obtain turn-on Cu+ responsive probes. We also show that the amino acid sequence, especially the number and position of proline residues has a significant impact on metal-induced luminescence enhancement and metal-binding constant of the probes.

Temperature effects on drift of suspended single-domain particles induced by the Magnus force.

We study the temperature dependence of the drift velocity of single-domain ferromagnetic particles induced by the Magnus force in a dilute suspension. A set of stochastic equations describing the translational and rotational dynamics of particles is derived, and the particle drift velocity that depends on components of the average particle magnetization is introduced. The Fokker-Planck equation for the probability density of magnetization orientations is solved analytically in the limit of strong thermal fluctuations for both the planar rotor and general models. Using these solutions, we calculate the drift velocity and show that the out-of-plane fluctuations of magnetization, which are not accounted for in the planar rotor model, play an important role. In the general case of arbitrary fluctuations, we investigate the temperature dependence of the drift velocity by numerically simulating a set of effective stochastic differential equations for the magnetization dynamics.

Localization in Open Quantum Systems.

In an isolated single-particle quantum system, a spatial disorder can induce Anderson localization. Being a result of interference, this phenomenon is expected to be fragile in the face of dissipation. Here we show that a proper dissipation can drive a disordered system into a steady state with tunable localization properties. This can be achieved with a set of identical dissipative operators, each one acting nontrivially on a pair of sites. Operators are parametrized by a uniform phase, which controls the selection of Anderson modes contributing to the state. On the microscopic level, quantum trajectories of a system in the asymptotic regime exhibit intermittent dynamics consisting of long-time sticking events near selected modes interrupted by intermode jumps.

Computation of the asymptotic states of modulated open quantum systems with a numerically exact realization of the quantum trajectory method.

Quantum systems out of equilibrium are presently a subject of active research, both in theoretical and experimental domains. In this work, we consider time-periodically modulated quantum systems that are in contact with a stationary environment. Within the framework of a quantum master equation, the asymptotic states of such systems are described by time-periodic density operators. Resolution of these operators constitutes a nontrivial computational task. Approaches based on spectral and iterative methods are restricted to systems with the dimension of the hosting Hilbert space dimH=N≲300, while the direct long-time numerical integration of the master equation becomes increasingly problematic for N≳400, especially when the coupling to the environment is weak. To go beyond this limit, we use the quantum trajectory method, which unravels the master equation for the density operator into a set of stochastic processes for wave functions. The asymptotic density matrix is calculated by performing a statistical sampling over the ensemble of quantum trajectories, preceded by a long transient propagation. We follow the ideology of event-driven programming and construct a new algorithmic realization of the method. The algorithm is computationally efficient, allowing for long "leaps" forward in time. It is also numerically exact, in the sense that, being given the list of uniformly distributed (on the unit interval) random numbers, {η_{1},η_{2},...,η_{n}}, one could propagate a quantum trajectory (with η_{i}'s as norm thresholds) in a numerically exact way. By using a scalable N-particle quantum model, we demonstrate that the algorithm allows us to resolve the asymptotic density operator of the model system with N=2000 states on a regular-size computer cluster, thus reaching the scale on which numerical studies of modulated Hamiltonian systems are currently performed.

Saccharide-induced modulation of photoluminescence lifetime in microgels.

Sugar-responsive microgels were prepared by the covalent grafting of a poly(N-isopropylacrylamide) (pNIPAM) matrix with phenylboronic acid (PBA) as a saccharide sensing unit and a [Ru(bpy)3](2+) derivative (2,2'-bipyridine) as a luminescent reporter. Time-resolved emission studies reveal that the ruthenium complex has an unusually long lifetime (1.6 µs) and high quantum yield (∼0.17) in the PBA-microgel environment. In the presence of sugars, the microgels swell due to the formation of a sugar-boronate ester, leading to a more hydrophilic polymer chain. The swelling is accompanied by a decrease of the lifetime and the photoluminescence quantum yield, which cannot be explained solely by the swelling of the hydrogel. The emission properties of the ruthenium complex in PBA-functionalized microgels are compared to those in pNIPAM microgels lacking PBA moieties in various swelling states. The presence of PBA in the vicinity of [Ru(bpy)3](2+) is shown to have a predominant impact on its luminescence properties, mainly through a decrease of the polarity. Sugar-induced triggering of the boronate state thus leads to strong variations of the polarity and the luminescence characteristics.

Superdiffusive Dispersals Impart the Geometry of Underlying Random Walks.

It is recognized now that a variety of real-life phenomena ranging from diffusion of cold atoms to the motion of humans exhibit dispersal faster than normal diffusion. Lévy walks is a model that excelled in describing such superdiffusive behaviors albeit in one dimension. Here we show that, in contrast to standard random walks, the microscopic geometry of planar superdiffusive Lévy walks is imprinted in the asymptotic distribution of the walkers. The geometry of the underlying walk can be inferred from trajectories of the walkers by calculating the analogue of the Pearson coefficient.

Rotational properties of ferromagnetic nanoparticles driven by a precessing magnetic field in a viscous fluid.

We study the deterministic and stochastic rotational dynamics of ferromagnetic nanoparticles in a precessing magnetic field. Our approach is based on the system of effective Langevin equations and on the corresponding Fokker-Planck equation. Two key characteristics of the rotational dynamics, namely the average angular frequency of precession of nanoparticles and their average magnetization, are of interest. Using the Langevin and Fokker-Planck equations, we calculate both analytically and numerically these characteristics in the deterministic and stochastic cases, determine their dependence on the model parameters, and analyze in detail the role of thermal fluctuations.

Role of the interpretation of stochastic calculus in systems with cross-correlated Gaussian white noises.

We derive the Fokker-Planck equation for multivariable Langevin equations with cross-correlated Gaussian white noises for an arbitrary interpretation of the stochastic differential equation. We formulate the conditions when the solution of the Fokker-Planck equation does not depend on which stochastic calculus is adopted. Further, we derive an equivalent multivariable Ito stochastic differential equation for each possible interpretation of the multivariable Langevin equation. To demonstrate the usefulness and significance of these general results, we consider the motion of Brownian particles. We study in detail the stability conditions for harmonic oscillators with two white noises, one of which is additive, random forcing, and the other, which accounts for fluctuations of either the damping or the spring coefficient, is multiplicative. We analyze the role of cross correlation in terms of the different noise interpretations and confirm the theoretical predictions via numerical simulations. We stress the interest of our results for numerical simulations of stochastic differential equations with an arbitrary interpretation of the stochastic integrals.

Infinite densities for Lévy walks.

Motion of particles in many systems exhibits a mixture between periods of random diffusive-like events and ballistic-like motion. In many cases, such systems exhibit strong anomalous diffusion, where low-order moments 〈|x(t)|(q)〉 with q below a critical value q(c) exhibit diffusive scaling while for q>q(c) a ballistic scaling emerges. The mixed dynamics constitutes a theoretical challenge since it does not fall into a unique category of motion, e.g., the known diffusion equations and central limit theorems fail to describe both aspects. In this paper we resolve this problem by resorting to the concept of infinite density. Using the widely applicable Lévy walk model, we find a general expression for the corresponding non-normalized density which is fully determined by the particles velocity distribution, the anomalous diffusion exponent α, and the diffusion coefficient K(α). We explain how infinite densities play a central role in the description of dynamics of a large class of physical processes and discuss how they can be evaluated from experimental or numerical data.

Space-time velocity correlation function for random walks.

Space-time correlation functions constitute a useful instrument from the research toolkit of continuous-media and many-body physics. Here we adopt this concept for single-particle random walks and demonstrate that the corresponding space-time velocity autocorrelation functions reveal correlations which extend in time much longer than estimated with the commonly employed temporal correlation functions. A generic feature of considered random-walk processes is an effect of velocity echo identified by the existence of time-dependent regions where most of the walkers are moving in the direction opposite to their initial motion. We discuss the relevance of the space-time velocity correlation functions for the experimental studies of cold atom dynamics in an optical potential and charge transport on micro- and nanoscales.