Two-state System Research Articles

Morris-Shore transformation for nondegenerate systems

The Morris-Shore (MS) transformation is a powerful tool for decomposition of the dynamics of multistate quantum systems to a set of two-state systems and uncoupled single states. It assumes two sets of states wherein any state in the first set can be coupled to any state in the second set but the states within each set are not coupled between themselves. Another important condition is the degeneracy of the states in each set, although all couplings between the states from different sets can be detuned from resonance by the same detuning. The degeneracy condition limits the application of the MS transformation in various physically interesting situations, e.g. in the presence of electric and/or magnetic fields or light shifts, which lift the degeneracy in each set of states, e.g. when these sets comprise the magnetic sublevels of levels with nonzero angular momentum. This paper extends the MS transformation to such situations, in which the states in each of the two sets are nondegenerate. To this end, we develop an alternative way for the derivation of Morris-Shore transformation, which can be applied to non-degenerate sets of states. We present a generalized eigenvalue approach, by which, in the limit of small detunings from degeneracy, we are able to generate an effective Hamiltonian that is dynamically equivalent to the non-degenerate Hamiltonian. The effective Hamiltonian can be mapped to the Morris-Shore basis with a two-step similarity transformation. After the derivation of the general framework, we demonstrate the application of this technique to the popular Lambda three-state system, and the four-state tripod, double-Lambda and diamond systems. In all of these systems, our formalism allows us to reduce their quantum dynamics to simpler two-state systems even in the presence of various detunings, e.g. generated by external fields of frequency drifts.

High-fidelity composite quantum gates for Raman qubits

We present a general systematic approach to design robust and high-fidelity quantum logic gates with Raman qubits using the technique of composite pulses. We use two mathematical tools -- the Morris-Shore and Majorana decompositions -- to reduce the three-state Raman system to an equivalent two-state system. They allow us to exploit the numerous composite pulses designed for two-state systems by extending them to Raman qubits. We construct the NOT, Hadamard, and rotation gates by means of the Morris-Shore transformation with the same uniform approach: sequences of pulses with the same phases for each gate but different ratios of Raman couplings. The phase gate is constructed by using the Majorana decomposition. All composite Raman gates feature very high fidelity, beyond the quantum computation benchmark values, and significant robustness to experimental errors. All composite phases and pulse areas are given by analytical formulas, which makes the method scalable to any desired accuracy and robustness to errors.

Uncertainty Relation for Errors Focusing on General POVM Measurements with an Example of Two-State Quantum Systems.

A novel uncertainty relation for errors of general quantum measurement is presented. The new relation, which is presented in geometric terms for maps representing measurement, is completely operational and can be related directly to tangible measurement outcomes. The relation violates the naïve bound for the position-momentum measurement, whilst nevertheless respecting Heisenberg’s philosophy of the uncertainty principle. The standard Kennard–Robertson uncertainty relation for state preparations expressed by standard deviations arises as a corollary to its special non-informative case. For the measurement on two-state quantum systems, the relation is found to offer virtually the tightest bound possible; the equality of the relation holds for the measurement performed over every pure state. The Ozawa relation for errors of quantum measurements will also be examined in this regard. In this paper, the Kolmogorovian measure-theoretic formalism of probability—which allows for the representation of quantum measurements by positive-operator valued measures (POVMs)—is given special attention, in regard to which some of the measure-theory specific facts are remarked along the exposition as appropriate.

Mixed Quantum-Classical Dynamics with Machine Learning-Based Potentials via Wigner Sampling.

Machine learning-based approaches for surface hopping (SH) offer the prospect of SH simulations with ab initio accuracy, but with a computational cost more similar to classical molecular dynamics simulations. However, such approaches in the adiabatic basis are difficult due to the need to fit a machine learning model to reproduce the nonadiabatic coupling, which rapidly changes in the vicinity of a conical intersection. Previous approaches have typically dealt with this difficulty by either computing the hopping probabilities using methods that do not require the explicit nonadiabatic coupling or by employing adaptive sampling. In this study, we introduce a new approach using a simple modification of Wigner sampling to generate appropriate training data. Test SH simulations on the two-state spin-boson Hamiltonian system show that Wigner sampling with an appropriately selected data set can reduce the size of the training data set by up to a factor of 7.5 per degree of freedom compared to previously linear sampling-based approaches.

Full Counting Statistics and Fluctuation–Dissipation Relation for Periodically Driven Two-State Systems

We derive the fluctuation theorem for a stochastic and periodically driven system coupled to two reservoirs with the aid of a master equation. We write down the cumulant generating functions for both the current and entropy production in closed compact forms so as to treat the adiabatic and nonadiabatic contributions systematically. We derive the fluctuation theorem by taking into account the time reversal symmetry and the property that the instantaneous currents flowing into the left and the right reservoir are not equal. It is found that the fluctuation-dissipation relation derived from the fluctuation theorem involves an expansion with respect to the time derivative of the affinity.

Research on the Regulation of the New Development Bank’s Internal Governance

The Articles of Agreement on the New Development Bank is not only the Charter of the New Development Bank of the BRICs, but also a new rule of global financial governance. Its internal governance rules resemble its skeleton, supporting the decision-making and operation of the entire New Development Bank. On the basis of drawing lessons from the agreements of the existing international development financial institutions, there are many innovative practices in the internal governance rules of the New Development Bank. However, at the beginning, there are still some imperfections in the internal governance of the new development bank. Its legitimacy, accountability, and beneficial coordination among the three are outstanding, which are mainly manifested in: First, the New Development Bank has established a basic internal organizational structure of the board of directors, board of governors and presidents.Second, the lack of representativeness of directors, presidents and vice presidents weakens the legitimacy of the bank. Third, the rotation system of the president of BRICS countries affects the bank’s aid continuation of policy. Fourth, the voting mechanism of equal rights in the five countries reduces the efficiency of the bank, and the two-state veto system has led to a lack of leaders in decision-making rules.Under the current post-epidemic background, the New Development Bank, as the first global development financial institution established by developing countries, is playing an active role by providing emergency assistance loans and other means, especially the economic recovery of emerging market countries. In view of this, it is necessary to make a systematic and innovation analysis on the internal governance of the New Development Bank. The regulation of the internal governance of the New Development Bank should be carried out from the following aspects: First, to establish a coordinating supervisory agency, strengthen the coordination, supervision and mutual restriction of the existing mechanism of the New Development Bank, and implement a director system combining non-resident and resident directors. Second, to improve the representativeness of directors and presidents, and establish the election system of rotating presidents and the procedure of no-confidence cases. It includes optimizing the composition of rotating presidents, extending the period of rotation, establishing the procedure for no-confidence motions against rotating presidents, and adjusting the automatic rotation system for rotating presidents. Finally, to establish a more reasonable voting mechanism that weights basic voting rights and equity voting rights and an interest compensation mechanism of non-founding countries that replaces voting rights with interests.

An efficient way to incorporate the geometric phase in the time-dependent wave packet calculations in a diabatic representation.

We present a new approach to incorporate the geometric phase in the time-dependent wave packet calculations based on the analytic diabatic potential energy matrices for two-state systems connecting via a conical intersection. The approach only requires information on the location of the conical intersection and the adiabatic potential energy surface of the ground electronic state and merely takes the same computational cost as a diabatic calculation. Demonstrations of the benchmark H + H2/HD reactions show that the new approach can accurately include the geometric phase in dynamics calculation and can be easily extended to the cold regime where the GP effects become more pronounced. Due to its simplicity and numerical efficiency, the new approach has the potential to extend the dynamics study of the geometric effects to a wide range of reaction systems.

Four-State Model for Simulating Kinetic and Steady-State Voltage-Dependent Gating of Gap Junctions

Gap junction (GJ) channels, formed of connexin (Cx) proteins, provide a direct pathway for metabolic and electrical cell-to-cell communication. These specialized channels are not just passive conduits for the passage of ions and metabolites but have been shown to gate robustly in response to transjunctional voltage, Vj, the voltage difference between two coupled cells. Voltage gating of GJs could play a physiological role, particularly in excitable cells, which can generate large transients in membrane potential during the propagation of action potentials. We present a mathematical/computational model of GJ channel voltage gating to assess properties of GJ channels that takes into account contingent gating of two series hemichannels and the distribution of Vj across each hemichannel. From electrophysiological recordings in cell cultures expressing Cx43 or Cx45, the principal isoforms expressed in cardiac tissue, various data sets were fitted simultaneously using global optimization. The results showed that the model is capable of describing both steady-state and kinetic properties of homotypic and heterotypic GJ channels composed of these Cxs. Moreover, mathematical analyses showed that the model can be simplified to a reversible two-state system and solved analytically using a rapid equilibrium assumption. Given that excitable cells are arranged in interconnected networks, the equilibrium assumption allows for a substantial reduction in computation time, which is useful in simulations of large clusters of coupled cells. Overall, this model can serve as a tool for the studying of GJ channel gating and its effects on the spread of excitation in networks of electrically coupled cells.

A double well on-line simulation and activities for active learning of introductory quantum mechanics

Teaching introductory quantum mechanics is challenging, especially to students who have limited knowledge of mathematics. The challenges and approaches are evidenced in a wide range of literature. Our goal is to develop an active engagement module for introductory quantum mechanics that would cover the most important concepts: indeterminism, incompatibility, the difference between superposition and statistical mixture and the role of measurement. To accomplish this, we developed a free on-line simulation of a double well—a (pseudo) two-state system—which is able to evidence all of the above concepts. Students perform simulated experiments and build their knowledge from their observations. We present the simulation and the proposed experiments to address the above concepts. We provide a description of the activities and their outcomes as tested with high-school students in different settings. Qualitative analysis of learning outcomes offers evidence that between 60% and 100% of students can reach the following conclusions on their own. (i) The particle is only ever detected in one of the possible states. (ii) The outcome of one experiment cannot be predicted, only its probability can be predicted. (iii) For some pairs of quantities, knowing the value of one quantity exactly precludes the possibility of knowing the value of the other quantity exactly. (iv) A statistical mixture (of eigenstates) is not the same as a superposition state. (v) The measurement affects the time evolution of the system. The most difficult conclusion for students to reach is how exactly the measurement affects the system. The success rates presented here lead us to conclude that the simulated experiments can be very useful when designing an active engagement course on the concepts of quantum mechanics. While the development is done in high-school, we believe the results are also relevant for introductory university level, especially for non-physics students.

Discrete Langevin machine: Bridging the gap between thermodynamic and neuromorphic systems.

A formulation of Langevin dynamics for discrete systems is derived as a class of generic stochastic processes. The dynamics simplify for a two-state system and suggest a network architecture which is implemented by the Langevin machine. The Langevin machine represents a promising approach to compute successfully quantitative exact results of Boltzmann distributed systems by LIF neurons. Besides a detailed introduction of the dynamics, different simplified models of a neuromorphic hardware system are studied with respect to a control of emerging sources of errors.

An Overview of Emergent Order in Far-from-Equilibrium Driven Systems: From Kuramoto Oscillators to Rayleigh–Bénard Convection

Soft-matter systems when driven out of equilibrium often give rise to structures that usually lie in between the macroscopic scale of the material and microscopic scale of its constituents. In this paper we review three such systems, the two-dimensional square-lattice Ising model, the Kuramoto model and the Rayleigh–Bénard convection system which when driven out of equilibrium give rise to emergent spatio-temporal order through self-organization. A common feature of these systems is that the entities that self-organize are coupled to one another in some way, either through local interactions or through a continuous media. Therefore, the general nature of non-equilibrium fluctuations of the intrinsic variables in these systems are found to follow similar trends as order emerges. Through this paper, we attempt to find connections between these systems, and systems in general which give rise to emergent order when driven out of equilibrium. This study, thus acts as a foundation for modeling a complex system as a two-state system, where the states: order and disorder can coexist as the system is driven away from equilibrium.

A two-state multiserver retrial queueing model with balking

This paper discusses a two-state multiserver retrial queueing system with balking. Entering customer is admitted to join any idle server and receive his service immediately. On the other hand, if all the servers are busy, then the entering customer joins the orbit or balks from the system. Arrival of primary calls and repetition of repeating calls both follow Poisson distribution. Service times of each server follow exponential distribution. By solving the difference-differential equations recursively, we obtained transient probabilities of exact number of arrivals and exact number of departures at when all some or none servers are busy. Results for particular cases are also discussed.

Theory of emittance exchange through coupling resonance crossing

In circular accelerators, transverse beam emittances can be exchanged by means of a coupling resonance crossing. It was first demonstrated experimentally at CERN accelerators, before a theoretical study revealed its mechanism. The existing theory of emittance exchange seems, however, to be deficient. In this study, we establish a theory of emittance exchange using the matrix formalism. Furthermore, we have found that the mechanism of emittance exchange is analogous to the transition dynamics of two-state quantum systems, thereby allowing the Landau-Zener formula to be applied for the prediction of transverse emittance values after nonadiabatic crossing.

On the Empirical Determination of a Gas–Liquid Supercritical Mesophase and its Phenomenological Definition

We respond to recent articles (Int. J. Thermophysics 39 139 2018, ibid.40 21 2019) that seek to deny the veracity of the empirical discovery and thermodynamic description of a gas–liquid supercritical mesophase. These IJT articles are misleading because they are based upon a false premise that the mesophase is a hypothetical concept. There is no “mesophase hypothesis” as wrongly stated in the title of article IJT, 40 21, 2019. Unlike the critical point continuity hypothesis of van der Waals (1873), or the universal critical point scaling hypothesis advocated by Anisimov and Sengers, and others since 1965, the supercritical mesophase is an empirical entity. If a hypothetical van der Waals fluid with the properties of a critical-state point with divergent isochoric heat capacity, and with the scaling properties of “universality” theory, were to exist, it could be used to vitiate the second law of thermodynamics. By contrast, the supercritical mesophase, discovered originally from computer experiments, is an empirically established equilibrium fluid region, of two-state systems of gas plus liquid, within a single Gibbs phase; the properties of which are determined by the laws of thermodynamics. Here, we provide a phenomenological definition of the gas–liquid supercritical mesophase that accords with the body of compelling experimental results over a 150-year period since van der Waals including modern computer experiments.

Multistate ring polymer instantons and nonadiabatic reaction rates.

We present two multistate ring polymer instanton (RPI) formulations, both obtained from an exact path integral representation of the quantum canonical partition function for multistate systems. The two RPIs differ in their treatment of the electronic degrees of freedom; while the Mean-Field (MF)-RPI averages over the electronic state contributions, the Mapping Variable (MV)-RPI employs explicit continuous Cartesian variables to represent the electronic states. We compute both RPIs for a series of model two-state systems coupled to a single nuclear mode with electronic coupling values chosen to describe dynamics in both adiabatic and nonadiabatic regimes. We show that the MF-RPIs for symmetric systems are in good agreement with the previous literature, and we show that our numerical techniques are robust for systems with non-zero driving force. The nuclear MF-RPI and the nuclear MV-RPI are similar, but the MV-RPI uniquely reports on the changes in the electronic state populations along the instanton path. In both cases, we analytically demonstrate the existence of a zero-mode, and we numerically find that these solutions are true instantons with a single unstable mode as expected for a first order saddle point. Finally, we use the MF-RPI to accurately calculate rate constants for adiabatic and nonadiabatic model systems with the coupling strength varying over three orders of magnitude.

Metallation-Induced Heterogeneous Dynamics of DNA Revealed by Single-Molecule FRET.

The metallation of nucleic acids is key to wide-ranging applications, from anticancer medicine to nanomaterials, yet there is a lack of understanding of the molecular-level effects of metallation. Here, we apply single-molecule fluorescence methods to study the reaction of an organo-osmium anticancer complex and DNA. Individual metallated DNA hairpins are characterised using Förster resonance energy transfer (FRET). Although ensemble measurements suggest a simple two-state system, single-molecule experiments reveal an underlying heterogeneity in the oligonucleotide dynamics, attributable to different degrees of metallation of the GC-rich hairpin stem. Metallated hairpins display fast two-state transitions with a two-fold increase in the opening rate to ≈2 s-1 , relative to the unmodified hairpin, and relatively static conformations with long-lived open (and closed) states of 5 to ≥50 s. These studies show that a single-molecule approach can provide new insight into metallation-induced changes in DNA structure and dynamics.

Sparse Learning-Based Approximate Dynamic Programming With Barrier Constraints

This letter provides an approximate online adaptive solution to the infinite-horizon optimal control problem for control-affine continuous-time nonlinear systems while formalizing system safety using barrier certificates. The use of a barrier function transform provides safety certificates to formalize system behavior. Specifically, using a barrier function, the system is transformed to aid in developing a controller which maintains the system in a pre-defined constrained region. To aid in online learning of the value function, the state-space is segmented into a number of user-defined segments. Off-policy trajectories are selected in each segment, and sparse Bellman error extrapolation is performed within each respective segment to generate an optimal policy within each segment. A Lyapunov-like stability analysis is included which proves uniformly ultimately bounded regulation in the presence of the barrier function transform and discontinuities. Simulation results are provided for a two-state dynamical system to compare the performance of the developed method to existing methods.

The inverse problem of two-state quantum systems with non-adiabatic static linear coupling

We consider the inverse problem of determining the coupling coefficients in a two-state Schrödinger system. We prove a Lipschitz stability inequality for the zeroth- and first-order coupling terms by finitely many partial lateral measurements of the solution to the coupled Schrödinger equations.

Monte Carlo Simulation Approach to Reliability Analysis of Complex Systems

Abstract The article presents new results concerned with general procedures and algorithms to assess the reliability of complex systems with various reliability structures. The analytical method and based on it the simulation method were used to estimate the reliability characteristics of the port grain transportation system. Finally, the general simulation algorithm was developed to evaluate the reliability characteristics of ageing complex systems. In this case, the systems operating processes were described by any distributions of sojourn times in operation states and the reliability functions of their components were modified in such a way that these components are not characterized by a “lack of memory”. The application of this algorithm has been illustrated by the results for exemplary complex two-state systems.

Particle representation for $NN{\bar K}$ system

In the framework of the Faddeev equations in configuration space we perform an analysis of quasi-bound state of the NN{\bar K}NNK‾ system within a particle model. In our approach, the system NN{\bar K}(s_{NN}=0)NNK‾(sNN=0) (NN{\bar K}(s_{NN}=1))NNK‾(sNN=1)) is described as a superposition of ppK^{-}ppK− and pn{\bar K}^0pnK‾0 (nn{\bar K}^{0}nnK‾0 and pn{ K}^-pnK−) states, which is possible due to a particle transition. The relation of the particle model to the theory of a two-state quantum system is addressed and discussed taking into account the possibilities of deep and shallow NN{\bar K}(s_{NN}=0)NNK‾(sNN=0) quasi-bound states.