Dynamics of dissipative Landau-Zener transitions

A non-perturbative treatment, the Dirac-Frenkel time-dependent variation is employed to examine dynamics of the Landau-Zener model with both diagonal and off-diagonal qubit-bath coupling using the multiple Davydov trial states. It is shown that steady-state transition probabilities agree with analytical predictions at long times. Landau-Zener dynamics at intermediate times is little affected by diagonal coupling, and is found to be determined by off-diagonal coupling and tunneling strength between two diabatic states. We investigate effects of bath spectral densities, coupling strengths and interaction angles on Laudau-Zener dynamics. Thanks to the multiple Davydov trial states, detailed boson dynamics can also be analyzed in Landau-Zener transitions. Results presented here may help provide guiding principles to manipulate the Laudau-Zener transitions in circuit QED architectures by tuning off-diagonal coupling and tunneling strength

Algorithms for finding transposons in gene sequences

With the process of evolution, some genes will change their relative positions in gene sequence. These "jumping genes" are called transposons. Through some intuitive rules, we give a criterion to determine transposons among gene sequences of different individuals of the same species. Then we turn this problem into graph theory and give algorithms for different situations with acceptable time complexities. One of these algorithms has been reported briefly as the "iteration algorithm" in Kang et al.'s paper (in this paper, transposon is called "core-gene-defined genome organizational framework", cGOF). This paper provides the omitted details and discussions on general cases.Comment: 5 pages, 2 figure

Effect of off-diagonal exciton-phonon coupling on intramolecular singlet fission

Intramolecular singlet fission (iSF) materials provide remarkable advantages in terms of tunable electronic structures, and quantum chemistry studies have indicated strong electronic coupling modulation by high frequency phonon modes. In this work, we formulate a microscopic model of iSF with simultaneous diagonal and off-diagonal coupling to high-frequency modes. A non-perturbative treatment, the Dirac-Frenkel time-dependent variational approach is adopted using the multiple Davydov trial states. It is shown that both diagonal and off-diagonal coupling can aid efficient singlet fission if excitonic coupling is weak, and fission is only facilitated by diagonal coupling if excitonic coupling is strong. In the presence of off-diagonal coupling, it is found that high frequency modes create additional fission channels for rapid iSF. Results presented here may help provide guiding principles for design of efficient singlet fission materials by directly tuning singlet-triplet interstate coupling

Transient dynamics of a one-dimensional Holstein polaron under the influence of an external electric field

Following the Dirac-Frenkel time-dependent variational principle, transient dynamics of a one-dimensional Holstein polaron with diagonal and off-diagonal exciton-phonon coupling in an external electric field is studied by employing the multi-D$_2$ {\it Ansatz}, also known as a superposition of the usual Davydov D$_2$ trial states. Resultant polaron dynamics has significantly enhanced accuracy, and is in perfect agreement with that derived from the hierarchy equations of motion method. Starting from an initial broad wave packet, the exciton undergoes typical Bloch oscillations. Adding weak exciton-phonon coupling leads to a broadened exciton wave packet and a reduced current amplitude. Using a narrow wave packet as the initial state, the bare exciton oscillates in a symmetric breathing mode, but the symmetry is easily broken by weak coupling to phonons, resulting in a non-zero exciton current. For both scenarios, temporal periodicity is unchanged by exciton-phonon coupling. In particular, at variance with the case of an infinite linear chain, no steady state is found in a finite-sized ring within the anti-adiabatic regime. For strong diagonal coupling, the multi-$\rm D_2$ {\it Anstaz} is found to be highly accurate, and the phonon confinement gives rise to exciton localization and decay of the Bloch oscillations

Dissipative dynamics in a tunable Rabi dimer with periodic harmonic driving

Recent progress on qubit manipulation allows application of periodic driving signals on qubits. In this study, a harmonic driving field is added to a Rabi dimer to engineer photon and qubit dynamics in a circuit quantum electrodynamics device. To model environmental effects, qubits in the Rabi dimer are coupled to a phonon bath with a sub-Ohmic spectral density. A non-perturbative treatment, the Dirac-Frenkel time-dependent variational principle together with the multiple Davydov D$_2$ {\it Ansatz} is employed to explore the dynamical behavior of the tunable Rabi dimer. In the absence of the phonon bath, the amplitude damping of the photon number oscillation is greatly suppressed by the driving field, and photons can be created thanks to resonances between the periodic driving field and the photon frequency. In the presence of the phonon bath, one still can change the photon numbers in two resonators, and indirectly alter the photon imbalance in the Rabi dimer by directly varying the driving signal in one qubit. It is shown that qubit states can be manipulated directly by the harmonic driving. The environment is found to strengthen the interqubit asymmetry induced by the external driving, opening up a new venue to engineer the qubit states

Polaron dynamics with a multitude of Davydov D2_2 trial states

We propose an extension to the Davydov D$_2$ Ansatz in the dynamics study of the Holstein molecular crystal model with diagonal and off-diagonal exciton-phonon coupling using the Dirac-Frenkel time-dependent variational principle. The new trial state by the name of the "multi-D$_2$ Ansatz" is a linear combination of Davydov D$_2$ trial states, and its validity is carefully examined by quantifying how faithfully it follows the Schr\"odinger equation. Considerable improvements in accuracy have been demonstrated in comparison with the usual Davydov trial states, i.e., the single D$_1$ and D$_2$ Ans\"atze. With an increase in the number of the Davydov D$_2$ trial states in the multi-D$_2$ Ansatz, deviation from the exact Schr\"odinger dynamics is gradually diminished, leading to a numerically exact solution to the Schr\"odinger equation.Comment: 14 pages, 15 figure

XCon: Learning with Experts for Fine-grained Category Discovery

We address the problem of generalized category discovery (GCD) in this paper, i.e. clustering the unlabeled images leveraging the information from a set of seen classes, where the unlabeled images could contain both seen classes and unseen classes. The seen classes can be seen as an implicit criterion of classes, which makes this setting different from unsupervised clustering where the cluster criteria may be ambiguous. We mainly concern the problem of discovering categories within a fine-grained dataset since it is one of the most direct applications of category discovery, i.e. helping experts discover novel concepts within an unlabeled dataset using the implicit criterion set forth by the seen classes. State-of-the-art methods for generalized category discovery leverage contrastive learning to learn the representations, but the large inter-class similarity and intra-class variance pose a challenge for the methods because the negative examples may contain irrelevant cues for recognizing a category so the algorithms may converge to a local-minima. We present a novel method called Expert-Contrastive Learning (XCon) to help the model to mine useful information from the images by first partitioning the dataset into sub-datasets using k-means clustering and then performing contrastive learning on each of the sub-datasets to learn fine-grained discriminative features. Experiments on fine-grained datasets show a clear improved performance over the previous best methods, indicating the effectiveness of our method

Polymers of Intrinsic Microporosity (PIMs) in Sensing and in Electroanalysis

Polymers of intrinsic microporosity (PIMs) provide high surface area materials (typically 1000 m2 g-1 apparent BET surface area) that are processable from organic solvents to give glassy films or composite coatings. Multi-functionality for sensing with these materials is achieved (i) based on the polymer backbone itself being fluorescent or chemically active or (ii) based on guest species (chromophores, nano-catalysts, nano-photo-catalysts, etc.) that are readily embedded into PIMs and accessible through micropores in the polymer host. The ease of forming uniform microporous films or composite films is linked to molecular rigidity and highlighted here for sensing/electroanalytical applications