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Published work

27 published item(s)

preprint2026arXiv

Constructing left-continuous triangular norms on complete lattices

This article focuses on the construction of left-continuous t-norms on complete lattices. The concepts of $\mathfrak{f}$-mappings and weak $\mathfrak{f}$-mappings on complete lattices are first introduced, respectively. They are then applied to establish the following key results: weak $\mathfrak{f}$-mappings are used to induce left-continuous t-subnorms; $\mathfrak{f}$-mappings are used to generate left-continuous t-norms whenever the top element $1$ of the complete lattice is a completely join-irreducible element. Finally, some necessary and sufficient conditions are provided for an operator constructed by the ordinal sum of a series of annihilating binary operators being a left-continuous t-norm on a complete lattice.

preprint2026arXiv

SciEval: A Benchmark for Automatic Evaluation of K-12 Science Instructional Materials

The need to evaluate instructional materials for K-12 science education has become increasingly important, as more educators use generative AI to create instructional materials. However, the review of instructional materials is time-consuming, expertise-intensive, and difficult to scale, motivating interest in automated evaluation approaches. While large language models (LLMs) have shown strong performance on general evaluation tasks, their performance and reliability on instructional materials remain unclear. To address this gap, we formulate Automatic Instructional Materials Evaluation (AIME) as a generative AI task that predicts scores and evidence using the rubric designed by the educator. We create a benchmark dataset and develop baseline models for AIME. First, we curate the first AIME dataset, SciEval, consisting of instructional materials annotated with pedagogy-aligned evaluation scores and evidence-based rationales. Expert annotations achieve high inter-rater reliability, resulting in a dataset of 273 lesson-level instructional materials evaluated across 13 criteria (N=3549) using the EQuIP rubric. Second, we test mainstream LLMs (GPT, Gemini, Llama, and Qwen) on SciEval and find that none achieve strong performance. Then we fine-tune Qwen3 on SciEval. Results on a held-out test set show that domain-aligned fine-tuning can achieve up to 11 percent performance gains, highlighting the importance of domain-specific fine-tuning for AIME and facilitating the use of LLMs in other educational tasks.

preprint2022arXiv

Damping transition in an open generalized Aubry-André-Harper model

We study the damping dynamics of the single-particle correlation for an open system under periodic and aperiodic order, which is dominated by the Lindblad master equation. In the absence of the aperiodic order, the Liouvillian superoperator exhibits the non-Hermitian skin effect, which leads to unidirectional damping dynamics, dubbed as "chiral damping". Due to the non-Hermitian skin effect, the damping dynamics is boundary sensitive: The long-time damping of such open systems is algebraic under periodic boundary conditions but exponential under open boundary conditions. We reveal the phase transition with the inclusion of the hopping amplitude modulation. By using the spectral topology and a finite-size scaling analysis in the commensurate case, we show there exists a phase transition of the skin effect with non-Bloch anti-parity-time symmetry breaking. For the incommensurate case, we find richer phases with the coexistence of the non-Hermitian skin effect and the Anderson localization, which are separated by a generalized mobility edge. We reveal the transition of the damping dynamics as a consequence of the phase transition. Furthermore, we propose a possible scheme with ultracold atoms in a dissipative momentum lattice to realize and detect the damping dynamics.

preprint2022arXiv

Demystifying the Global Convergence Puzzle of Learning Over-parameterized ReLU Nets in Very High Dimensions

This theoretical paper is devoted to developing a rigorous theory for demystifying the global convergence phenomenon in a challenging scenario: learning over-parameterized Rectified Linear Unit (ReLU) nets for very high dimensional dataset under very mild assumptions. A major ingredient of our analysis is a fine-grained analysis of random activation matrices. The essential virtue of dissecting activation matrices is that it bridges the dynamics of optimization and angular distribution in high-dimensional data space. This angle-based detailed analysis leads to asymptotic characterizations of gradient norm and directional curvature of objective function at each gradient descent iteration, revealing that the empirical loss function enjoys nice geometrical properties in the overparameterized setting. Along the way, we significantly improve existing theoretical bounds on both over-parameterization condition and learning rate with very mild assumptions for learning very high dimensional data. Moreover, we uncover the role of the geometrical and spectral properties of the input data in determining desired over-parameterization size and global convergence rate. All these clues allow us to discover a novel geometric picture of nonconvex optimization in deep learning: angular distribution in high-dimensional data space $\mapsto$ spectrums of overparameterized activation matrices $\mapsto$ favorable geometrical properties of empirical loss landscape $\mapsto$ global convergence phenomenon. Furthremore, our theoretical results imply that gradient-based nonconvex optimization algorithms have much stronger statistical guarantees with much milder over-parameterization condition than exisiting theory states for learning very high dimensional data, which is rarely explored so far.

preprint2022arXiv

Dissecting Service Mesh Overheads

Service meshes play a central role in the modern application ecosystem by providing an easy and flexible way to connect different services that form a distributed application. However, because of the way they interpose on application traffic, they can substantially increase application latency and resource consumption. We develop a decompositional approach and a tool, called MeshInsight, to systematically characterize the overhead of service meshes and to help developers quantify overhead in deployment scenarios of interest. Using MeshInsight, we confirm that service meshes can have high overhead -- up to 185% higher latency and up to 92% more virtual CPU cores for our benchmark applications -- but the severity is intimately tied to how they are configured and the application workload. The primary contributors to overhead vary based on the configuration too. IPC (inter-process communication) and socket writes dominate when the service mesh operates as a TCP proxy, but protocol parsing dominates when it operates as an HTTP proxy. MeshInsight also enables us to study the end-to-end impact of optimizations to service meshes. We show that not all seemingly-promising optimizations lead to a notable overhead reduction in realistic settings.

preprint2022arXiv

Extracting non-Abelian quantum metric tensor and its related Chern numbers

The complete geometry of quantum states in parameter space is characterized by the quantum geometric tensor, which contains the quantum metric and Berry curvature as the real and imaginary parts, respectively. When the quantum states are degenerate, the quantum metric and Berry curvature take non-Abelian forms. The non-Abelian (Abelian) Berry curvature and Abelian quantum metric have been experimentally measured. However, an experimentally feasible scheme to extract all the components of the non-Abelian quantum metric tensor is still lacking. Here we propose a generic protocol to directly extract the non-Abelian quantum metric tensor in arbitrary degenerate quantum states in any dimensional parameter space, based on measuring the transition probabilities after parameter quenches. Furthermore, we show that the non-Abelian quantum metric can be measured to obtain the real Chern number of a generalized Dirac monopole and the second Chern number of a Yang monopole, which can be simulated in three and five-dimensional parameter space of artificial quantum systems, respectively. We also demonstrate the feasibility of our quench scheme for these two applications with numerical simulations.

preprint2022arXiv

Multi-model Ensemble Learning Method for Human Expression Recognition

Analysis of human affect plays a vital role in human-computer interaction (HCI) systems. Due to the difficulty in capturing large amounts of real-life data, most of the current methods have mainly focused on controlled environments, which limit their application scenarios. To tackle this problem, we propose our solution based on the ensemble learning method. Specifically, we formulate the problem as a classification task, and then train several expression classification models with different types of backbones--ResNet, EfficientNet and InceptionNet. After that, the outputs of several models are fused via model ensemble method to predict the final results. Moreover, we introduce the multi-fold ensemble method to train and ensemble several models with the same architecture but different data distributions to enhance the performance of our solution. We conduct many experiments on the AffWild2 dataset of the ABAW2022 Challenge, and the results demonstrate the effectiveness of our solution.

preprint2022arXiv

Neighbor Enhanced Graph Convolutional Networks for Node Classification and Recommendation

The recently proposed Graph Convolutional Networks (GCNs) have achieved significantly superior performance on various graph-related tasks, such as node classification and recommendation. However, currently researches on GCN models usually recursively aggregate the information from all the neighbors or randomly sampled neighbor subsets, without explicitly identifying whether the aggregated neighbors provide useful information during the graph convolution. In this paper, we theoretically analyze the affection of the neighbor quality over GCN models' performance and propose the Neighbor Enhanced Graph Convolutional Network (NEGCN) framework to boost the performance of existing GCN models. Our contribution is three-fold. First, we at the first time propose the concept of neighbor quality for both node classification and recommendation tasks in a general theoretical framework. Specifically, for node classification, we propose three propositions to theoretically analyze how the neighbor quality affects the node classification performance of GCN models. Second, based on the three proposed propositions, we introduce the graph refinement process including specially designed neighbor evaluation methods to increase the neighbor quality so as to boost both the node classification and recommendation tasks. Third, we conduct extensive node classification and recommendation experiments on several benchmark datasets. The experimental results verify that our proposed NEGCN framework can significantly enhance the performance for various typical GCN models on both node classification and recommendation tasks.

preprint2022arXiv

Resolved frustrated tunneling ionization in asymmetrical fast oscillation of above-threshold ionization spectrum

Tunneling ionization is one of the fundamental electron dynamics, which has wide applications in ultrafast physics. When frustrated tunneling ionization (FTI) is considered, the tunneling rate is not equivalent to ionization rate. However, it is hard to resolve the effects of FTI and direct tunneling ionization (DTI) in ionization spectrum experimentally. Here we report the first observation of the asymmetrical fast oscillation in above-threshold ionization (ATI) spectrum of Argon as function of carrier-envelope phase (CEP), to the best of our knowledge. Simulation results identify that in the experimental ATI spectrum, the π/5 oscillation originates from the quantum interference of electrons in FTI, while DTI is responsible for the asymmetry. Our results provide clear evidence to resolve the effects of direct tunneling and FTI in a new physical regime.

preprint2020arXiv

Double exceptional links in a three-dimensional dissipative cold atomic gas

We explore the topological properties of non-Hermitian nodal-link semimetals with dissipative cold atoms in a three-dimensional optical lattice. We construct a two-band continuum model in three dimensions with a spin-dependent gain and loss, where the exceptional points in the energy spectrum can comprise a double Hopf link. The topology of the bulk band is characterized by a winding number defined for a one-dimensional loop in the momentum space and a topological transition of the nodal structures emerges as the change of the non-Hermiticity strength. A non-Bloch theory is built to describe the corresponding lattice model which has anomalous bulk-boundary correspondence. Furthermore, we propose that the model can be realized using ultracold fermionic atoms in an optical lattice and the exceptional nodal links as well as the topological properties can be detected by measuring the atomic spin textures.

preprint2020arXiv

Highly flexible electromagnetic interference shielding films based on ultrathin Ni/Ag composites on paper substrates

Highly flexible electromagnetic interference (EMI) shielding material with excellent shielding performance is of great significance to practical applications in next-generation flexible devices. However, most EMI materials suffer from insufficient flexibility and complicated preparation methods. In this study, we propose a new scheme to fabricate a magnetic Ni particle/Ag matrix composite ultrathin film on a paper surface. For a ~2 micro meter thick film on paper, the EMI shielding effectiveness (SE) was found to be 46.2 dB at 8.1 GHz after bending 200,000 times over a radius of ~2 mm. The sheet resistance (Rsq) remained lower than 2.30 Ohm after bending 200,000 times. Contrary to the change in Rsq, the EMI SE of the film generally increased as the weight ratio of Ag to Ni increased, in accordance with the principle that EMI SE is positively related with an increase in electrical conductivity. Desirable EMI shielding ability, ultrahigh flexibility, and simple processing provide this material with excellent application prospects.

preprint2020arXiv

Label-Aware Graph Convolutional Networks

Recent advances in Graph Convolutional Networks (GCNs) have led to state-of-the-art performance on various graph-related tasks. However, most existing GCN models do not explicitly identify whether all the aggregated neighbors are valuable to the learning tasks, which may harm the learning performance. In this paper, we consider the problem of node classification and propose the Label-Aware Graph Convolutional Network (LAGCN) framework which can directly identify valuable neighbors to enhance the performance of existing GCN models. Our contribution is three-fold. First, we propose a label-aware edge classifier that can filter distracting neighbors and add valuable neighbors for each node to refine the original graph into a label-aware~(LA) graph. Existing GCN models can directly learn from the LA graph to improve the performance without changing their model architectures. Second, we introduce the concept of positive ratio to evaluate the density of valuable neighbors in the LA graph. Theoretical analysis reveals that using the edge classifier to increase the positive ratio can improve the learning performance of existing GCN models. Third, we conduct extensive node classification experiments on benchmark datasets. The results verify that LAGCN can improve the performance of existing GCN models considerably, in terms of node classification.

preprint2020arXiv

Nonlinear Bloch-Zener oscillations for Bose-Einstein condensates in a Lieb optical lattice

We investigate Bloch-Zener oscillations and mean-field Bloch bands of a Bose-Einstein condensate (BEC) in a Lieb optical lattice. We find that the atomic interaction will break the point group symmetry of the system, leading to the destruction of the Dirac cone structure, while the flat band is preserved on the highly symmetric lines. Due to the nonlinear effect, a tubular band structure with a flat band will appear in the system. Furthermore, comparing with that the tight-binding (TB) model fails to describe the interacting bosonic systems in the honeycomb lattice, we show that the TB model is applicable to study the nonlinear energy band structures for the Lieb lattice. In addition, we show that the loop structure can be determined by the observation of the chaos of the state in the Bloch-Zener oscillations.

preprint2020arXiv

Single-Layer Graph Convolutional Networks For Recommendation

Graph Convolutional Networks (GCNs) and their variants have received significant attention and achieved start-of-the-art performances on various recommendation tasks. However, many existing GCN models tend to perform recursive aggregations among all related nodes, which arises severe computational burden. Moreover, they favor multi-layer architectures in conjunction with complicated modeling techniques. Though effective, the excessive amount of model parameters largely hinder their applications in real-world recommender systems. To this end, in this paper, we propose the single-layer GCN model which is able to achieve superior performance along with remarkably less complexity compared with existing models. Our main contribution is three-fold. First, we propose a principled similarity metric named distribution-aware similarity (DA similarity), which can guide the neighbor sampling process and evaluate the quality of the input graph explicitly. We also prove that DA similarity has a positive correlation with the final performance, through both theoretical analysis and empirical simulations. Second, we propose a simplified GCN architecture which employs a single GCN layer to aggregate information from the neighbors filtered by DA similarity and then generates the node representations. Moreover, the aggregation step is a parameter-free operation, such that it can be done in a pre-processing manner to further reduce red the training and inference costs. Third, we conduct extensive experiments on four datasets. The results verify that the proposed model outperforms existing GCN models considerably and yields up to a few orders of magnitude speedup in training, in terms of the recommendation performance.

preprint2020arXiv

SocialTrans: A Deep Sequential Model with Social Information for Web-Scale Recommendation Systems

On social network platforms, a user's behavior is based on his/her personal interests, or influenced by his/her friends. In the literature, it is common to model either users' personal preference or their socially influenced preference. In this paper, we present a novel deep learning model SocialTrans for social recommendations to integrate these two types of preferences. SocialTrans is composed of three modules. The first module is based on a multi-layer Transformer to model users' personal preference. The second module is a multi-layer graph attention neural network (GAT), which is used to model the social influence strengths between friends in social networks. The last module merges users' personal preference and socially influenced preference to produce recommendations. Our model can efficiently fit large-scale data and we deployed SocialTrans to a major article recommendation system in China. Experiments on three data sets verify the effectiveness of our model and show that it outperforms state-of-the-art social recommendation methods.

preprint2016arXiv

Conditions that the quotient of $L$-fuzzy up-sets forms a complete lattice

This paper deals with conditions under which the quotient of $L$-fuzzy up-sets forms a complete lattice by using terminologies of closure operators. It first gives a condition that a family of some subsets of a nonempty set can be represented by $L$-fuzzy up-sets, which is then used to formulate a necessary and sufficient condition under which the quotient of $L$-fuzzy up-sets forms a complete lattice. This paper finally shows that the quotient of a kind of $L$-fuzzy up-sets is isomorphic to an interval generated by an $L$-fuzzy up-set.

preprint2016arXiv

TDSelector: A Training Data Selection Method for Cross-Project Defect Prediction

In recent years, cross-project defect prediction (CPDP) attracted much attention and has been validated as a feasible way to address the problem of local data sparsity in newly created or inactive software projects. Unfortunately, the performance of CPDP is usually poor, and low quality training data selection has been regarded as a major obstacle to achieving better prediction results. To the best of our knowledge, most of existing approaches related to this topic are only based on instance similarity. Therefore, the objective of this work is to propose an improved training data selection method for CPDP that considers both similarity and the number of defects each training instance has (denoted by defects), which is referred to as TDSelector, and to demonstrate the effectiveness of the proposed method. Our experiments were conducted on 14 projects (including 15 data sets) collected from two public repositories. The results indicate that, in a specific CPDP scenario, the TDSelector-based bug predictor performs, on average, better than those based on the baseline methods, and the AUC (area under ROC curve) values are increased by up to 10.6 and 4.3%, respectively. Besides, an additional experiment shows that selecting those instances with more bugs directly as training data can further improve the performance of the bug predictor trained by our method.

preprint2016arXiv

Universal low energy physics in one-dimensional multicompnent Fermi gases with a strongly repulsive $δ$-function interaction

It was shown [Chin. Phys. Lett. 28, 020503 (2011)] that at zero temperature the ground state of the one-dimensional (1D) $w$-component Fermi gas coincides with that of the spinless Bose gas in the limit $ω\to \infty$. This behaviour was experimentally evidenced through a quasi-1D tightly trapping ultracold ${}^{173}$Yb atoms in the recent paper [Nature Physics 10, 198 (2014)]. However, understanding of low temperature behaviour of the Fermi gases with a repulsive interaction acquires spin-charge separated conformal field theories of an effective Tomonaga-Luttinger liquid and an antiferromagnetic $SU(w)$ Heisenberg spin chain. Here we analytically derive universal thermodynamics of 1D strongly repulsive fermionic gases with $SU(w)$ symmetry via the Yang-Yang thermodynamic Bethe ansatz method. The analytical free energy and magnetic properties of the systems at low temperatures in a weak magnetic field are obtained through the Wiener-Hopf method. In particular, the free energy essentially manifests the spin-charge separated conformal field theories for the high symmetry systems with arbitrary repulsive interaction strength. We also find that the sound velocity of the Fermi gases in the large $w$ limit coincides with that for the spinless Bose gas, whereas the spin velocity vanishes quickly as $w$ becomes large. This indicates a strong suppression of the Fermi exclusion statistics by the commutativity feature among the $w$-component fermions with different spin states in the Tomonaga-Luttinger liquid phase. Moreover, the equations of state and critical behaviour of physical quantities at finite temperatures are analytically derived in terms of the polylogarithm functions in the quantum critical region.

preprint2015arXiv

A Diffusion-Neuron Hybrid System for Molecular Communication

Diffusion-based and neural communication are two interesting domains in molecular communication. Both of them have distinct advantages and are exploited separately in many works. However, in some cases, neural and diffusion-based ways have to work together for a communication. Therefore, in this paper, we propose a hybrid communication system, in which the diffusion-based and neural communication channels are contained. Multiple connection nano-devices (CND) are used to connect the two channels. We define the practice function of the CNDs and develop the mechanism of exchanging information from diffusion-based to neural channel, based on the biological characteristics of the both channels. In addition, we establish a brief mathematical model to present the complete communication process of the hybrid system. The information exchange process at the CNDs is shown in the simulation. The bit error rate (BER) indicator is used to verify the reliability of communication. The result reveals that based on the biological channels, optimizing some parameters of nano-devices could improve the reliability performance.

preprint2015arXiv

Improving Reliability Performance of Diffusion-based Molecular Communication With Adaptive Threshold Variation Algorithm

In this work, we investigate the communication reliability for diffusion-based molecular communication, using the indicator of bit error rate (BER). A molecular classified model is established to divide molecules into three parts, which are the signal, inter-symbol interference (ISI) and noise. We expand each part separately using molecular absorbing probability, and connect them by a traditional-like formula. Based on the classified model, we do a theoretical analysis to prove the feasibility of improving the BER performance. Accordingly, an adaptive threshold variation (ATV) algorithm is designed in demodulation to implement the goal, which makes the receiver adapt the channel condition properly through learning process. Moreover, the complexity of ATV is calculated and its performance in various noisy channel is discussed. An expression of Signal to Interference plus Noise Ratio (SINR) is defined to verify the system performance. We test some important parameters of the channel model, as well as the ATV algorithm in the simulation section. The results have shown the performance gain of the proposal.

preprint2014arXiv

An Empirical Study on Software Defect Prediction with a Simplified Metric Set

Software defect prediction plays a crucial role in estimating the most defect-prone components of software, and a large number of studies have pursued improving prediction accuracy within a project or across projects. However, the rules for making an appropriate decision between within- and cross-project defect prediction when available historical data are insufficient remain unclear. The objective of this work is to validate the feasibility of the predictor built with a simplified metric set for software defect prediction in different scenarios, and to investigate practical guidelines for the choice of training data, classifier and metric subset of a given project. First, based on six typical classifiers, we constructed three types of predictors using the size of software metric set in three scenarios. Then, we validated the acceptable performance of the predictor based on Top-k metrics in terms of statistical methods. Finally, we attempted to minimize the Top-k metric subset by removing redundant metrics, and we tested the stability of such a minimum metric subset with one-way ANOVA tests. The experimental results indicate that (1) the choice of training data should depend on the specific requirement of prediction accuracy; (2) the predictor built with a simplified metric set works well and is very useful in case limited resources are supplied; (3) simple classifiers (e.g., Naive Bayes) also tend to perform well when using a simplified metric set for defect prediction; and (4) in several cases, the minimum metric subset can be identified to facilitate the procedure of general defect prediction with acceptable loss of prediction precision in practice. The guideline for choosing a suitable simplified metric set in different scenarios is presented in Table 12.

preprint2014arXiv

Quantum Criticality of one-dimensional multicomponent Fermi Gas with Strongly Attractive Interaction

Quantum criticality of strongly attractive Fermi gas with $SU(3)$ symmetry in one dimension is studied via the thermodynamic Bethe ansatz (TBA) equations.The phase transitions driven by the chemical potential $μ$, effective magnetic field $H_1$, $H_2$ (chemical potential biases) are analyzed at the quantum criticality. The phase diagram and critical fields are analytically determined by the thermodynamic Bethe ansatz equations in zero temperature limit. High accurate equations of state, scaling functions are also obtained analytically for the strong interacting gases. The dynamic exponent $z=2$ and correlation length exponent $ν=1/2$ read off the universal scaling form. It turns out that the quantum criticality of the three-component gases involves a sudden change of density of states of one cluster state, two or three cluster states. In general, this method can be adapted to deal with the quantum criticality of multi-component Fermi gases with $SU(N)$ symmetry.

preprint2014arXiv

Simplification of Training Data for Cross-Project Defect Prediction

Cross-project defect prediction (CPDP) plays an important role in estimating the most likely defect-prone software components, especially for new or inactive projects. To the best of our knowledge, few prior studies provide explicit guidelines on how to select suitable training data of quality from a large number of public software repositories. In this paper, we have proposed a training data simplification method for practical CPDP in consideration of multiple levels of granularity and filtering strategies for data sets. In addition, we have also provided quantitative evidence on the selection of a suitable filter in terms of defect-proneness ratio. Based on an empirical study on 34 releases of 10 open-source projects, we have elaborately compared the prediction performance of different defect predictors built with five well-known classifiers using training data simplified at different levels of granularity and with two popular filters. The results indicate that when using the multi-granularity simplification method with an appropriate filter, the prediction models based on Naive Bayes can achieve fairly good performance and outperform the benchmark method.

preprint2014arXiv

Towards Cross-Project Defect Prediction with Imbalanced Feature Sets

Cross-project defect prediction (CPDP) has been deemed as an emerging technology of software quality assurance, especially in new or inactive projects, and a few improved methods have been proposed to support better defect prediction. However, the regular CPDP always assumes that the features of training and test data are all identical. Hence, very little is known about whether the method for CPDP with imbalanced feature sets (CPDP-IFS) works well. Considering the diversity of defect data sets available on the Internet as well as the high cost of labeling data, to address the issue, in this paper we proposed a simple approach according to a distribution characteristic-based instance (object class) mapping, and demonstrated the validity of our method based on three public defect data sets (i.e., PROMISE, ReLink and AEEEM). Besides, the empirical results indicate that the hybrid model composed of CPDP and CPDP-IFS does improve the prediction performance of the regular CPDP to some extent.

preprint2011arXiv

Thermodynamics and spin-charge separation of one-dimensional strongly repulsive three-component fermions

The low temperature thermodynamics of one-dimensional strongly repulsive SU(3) fermions in the presence of a magnetic field is investigated via the Yang-Yang thermodynamic Bethe ansatz method. The analytical free energy and magnetic properties of the model at low temperatures in a weak magnetic field are derived via the Wiener-Hopf method. It is shown that the low energy physics can be described by spin-charge separated conformal field theories of an effective Tomonaga-Luttinger liquid and an antiferromagnetic SU(3) Heisenberg spin chain. Beyond the Tomonaga-Luttinger liquid regime, the equation of state is given in terms of the polylog function for a weak external field. The results obtained are essential for further study of quantum criticality in strongly repulsive three-component fermions.

preprint2010arXiv

Analytical thermodynamics of a strongly attractive three-component Fermi gas in one dimension

Ultracold three-component atomic Fermi gases in one dimension are expected to exhibit rich physics due to the presence of trions and different pairing states. Quantum phase transitions from the trion state into a paired phase and a normal Fermi liquid occur at zero temperature. We derive the analytical thermodynamics of strongly attractive three-component one-dimensional fermions with SU(3) symmetry via the thermodynamic Bethe ansatz method in unequal Zeeman splitting fields $H_1$ and $H_2$. We find explicitly that for low temperature the system acts like either a two-component or a three-component Tomonaga-Luttinger liquid dependent on the system parameters. The phase diagrams for the chemical potential and specific heat are presented for illustrative values of the Zeeman splitting. We also demonstrate that crossover between different Tomonaga-Luttinger liquid phases evolve singular behaviour in specific heat and entropy as the temperature tends to zero. Beyond Tomonaga-Luttinger liquid physics, we obtain the equation of state which provides a precise description of universal thermodynamics and quantum criticality in three-component strongly attractive Fermi gases.