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Si Wu

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Published work

29 published item(s)

preprint2026arXiv

DiLA: Disentangled Latent Action World Models

Latent Action Models (LAMs) enable the learning of world models from unlabeled video by inferring abstract actions between consecutive frames. However, LAMs face a fundamental trade-off between action abstraction and generation fidelity. Existing methods typically circumvent this issue by using two-stage training with pre-trained world models or by limiting predictions to optical flow. In this paper, we introduce DiLA, a novel Disentangled Latent Action world model that aims to resolve this trade-off via content-structure disentanglement. Our key insight is that disentanglement and latent action learning are co-evolving: the predictive bottleneck inherent in latent action learning serves as a driving force for disentanglement, compelling the model to distill spatial layouts into the structure pathway while offloading visual details to a separate content pathway for generation. This synergy yields a continuous, semantically structured latent action space without compromising generative quality. DiLA achieves superior results in video generation quality, action transfer, visual planning, and manifold interpretability. These findings establish DiLA as a unified framework that simultaneously achieves high-level action abstraction and high-fidelity generation, advancing the frontier of self-supervised world model learning.

preprint2023arXiv

AI of Brain and Cognitive Sciences: From the Perspective of First Principles

Nowadays, we have witnessed the great success of AI in various applications, including image classification, game playing, protein structure analysis, language translation, and content generation. Despite these powerful applications, there are still many tasks in our daily life that are rather simple to humans but pose great challenges to AI. These include image and language understanding, few-shot learning, abstract concepts, and low-energy cost computing. Thus, learning from the brain is still a promising way that can shed light on the development of next-generation AI. The brain is arguably the only known intelligent machine in the universe, which is the product of evolution for animals surviving in the natural environment. At the behavior level, psychology and cognitive sciences have demonstrated that human and animal brains can execute very intelligent high-level cognitive functions. At the structure level, cognitive and computational neurosciences have unveiled that the brain has extremely complicated but elegant network forms to support its functions. Over years, people are gathering knowledge about the structure and functions of the brain, and this process is accelerating recently along with the initiation of giant brain projects worldwide. Here, we argue that the general principles of brain functions are the most valuable things to inspire the development of AI. These general principles are the standard rules of the brain extracting, representing, manipulating, and retrieving information, and here we call them the first principles of the brain. This paper collects six such first principles. They are attractor network, criticality, random network, sparse coding, relational memory, and perceptual learning. On each topic, we review its biological background, fundamental property, potential application to AI, and future development.

preprint2022arXiv

Crystal growth engineering and origin of the weak ferromagnetism in antiferromagnetic matrix of orthochromates from $t$-$e$ orbital hybridization

We report a combined experimental and theoretical study on intriguing magnetic properties of quasiferroelectric orthochromates. Large single crystals of the family of RECrO$_3$ (RE = Y, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, and Lu) compounds were successfully grown. Neutron Laue study indicates a good quality of the obtained single crystals. Applied magnetic-field and temperature dependent magnetization measurements reveal their intrinsic magnetic properties, especially the antiferromagnetic (AFM) transition temperatures. Density functional theory studies of the electronic structures were carried out using the Perdew-Burke-Ernzerhof functional plus Hubbard $U$ method. Crystallographic information and magnetism were theoretically optimized systematically. When RE$^{3+}$ cations vary from Y$^{3+}$ and Eu$^{3+}$ to Lu$^{3+}$ ions, the calculated $t$-$e$ orbital hybridization degree and Néel temperature behave similarly to the experimentally-determined AFM transition temperature with variation in cationic radius. We found that the $t$-$e$ hybridization is anisotropic, causing a magnetic anisotropy of Cr$^{3+}$ sublattices. This was evaluated with the nearest-neighbour $J_1$-$J_2$ model. Our research provides a picture of the electronic structures during the $t$-$e$ hybridization process while changing RE ions and sheds light on the nature of the weak ferromagnetism coexisting with predominated antiferromagnetism. The available large RECrO$_3$ single crystals build a platform for further studies of orthochromates.

preprint2022arXiv

Possible Dirac quantum spin liquid in a kagome quantum antiferromagnet YCu$_3$(OH)$_6$Br$_2$[Br$_{x}$(OH)$_{1-x}$]

We studied the magnetic properties of YCu$_3$(OH)$_6$Br$_2$[Br$_{1-x}$(OH)$_{x}$] ($x$ = 0.33), where Cu$^{2+}$ ions form two-dimensional kagome layers. There is no magnetic order down to 50 mK while the Curie-Weiss temperature is on the order of -100 K. At zero magnetic field, the low-temperature specific heat shows a $T^2$ dependence. Above 2 T, a linear temperature dependence term in specific heat emerges, and the value of $γ= C/T$ increases linearly with the field. Furthermore, the magnetic susceptibility tends to a constant value at $T = 0$. Our results suggest that the magnetic ground state of YCu$_3$(OH)$_6$Br$_2$[Br$_{1-x}$(OH)$_{x}$] is consistent with a Dirac quantum-spin-liquid state with a linearly dispersing spinon strongly coupled to an emergent gauge field, which has long been theoretically proposed as a candidate ground state in the two-dimensional kagome Heisenberg antiferromagnetic system.

preprint2022arXiv

Temperature-dependent structure of an intermetallic ErPd$_2$Si$_2$ single crystal: A combined synchrotron and in-house X-ray diffraction study

We have grown intermetallic ErPd$_2$Si$_2$ single crystals employing laser-diodes with the floating-zone method. The temperature-dependent crystallography was determined using synchrotron and in-house X-ray powder diffraction measurements from 20 to 500 K. The diffraction patterns fit well with the tetragonal $I$4/$mmm$ space group (No. 139) with two chemical formulas within one unit cell. Our synchrotron X-ray powder diffraction study shows that the refined lattice constants are $a$ = 4.10320(2) Å, $c$ = 9.88393(5) Å at 298 K and $a$ = 4.11737(2) Å, $c$ = 9.88143(5) Å at 500 K, resulting in the unit-cell volume $V$ = 166.408(1) Å$^3$ (298 K) and 167.517(2) Å$^3$ (500 K). In the whole studied temperature range, we did not find any structural phase transition. Upon cooling, the lattice constants a and c are shortened and elongated, respectively.

preprint2020arXiv

Colossal Negative Magnetoresistance Effect in A La$_{1.37}$Sr$_{1.63}$Mn$_2$O$_7$ Single Crystal Grown by Laser-Diode-Heated Floating-Zone Technique

We have grown La$_{1.37}$Sr$_{1.63}$Mn$_2$O$_7$ single crystals with a laser-diode-heated floating-zone furnace and studied the crystallinity, structure, and magnetoresistance (MR) effect by in-house X-ray Laue diffraction, X-ray powder diffraction, and resistance measurements. The La$_{1.37}$Sr$_{1.63}$Mn$_2$O$_7$ single crystal crystallizes into a tetragonal structure with space group \emph{I}4{/}\emph{mmm} at room temperature. At 0 T, the maximum resistance centers around $\sim$166.9 K. Below $\sim$35.8 K, it displays an insulating character with an increase in resistance upon cooling. An applied magnetic field of \emph{B}~=~7~T strongly suppresses the resistance indicative of a negative MR effect. The minimum MR value equals $-$91.23\% at 7 T and 128.7 K. The magnetic-field-dependent resistance shows distinct features at 1.67, 140, and 322 K, from which we calculated the corresponding MR values. At 14 T and 140 K, the colossal negative MR value is down to $-$94.04(5)\%. We schematically fit the MR values with different models for an ideal describing of the interesting features of the MR value versus \emph{B} curves.

preprint2020arXiv

Crystalline and magnetic structures, magnetization, heat capacity and anisotropic magnetostriction effect in a yttrium-chromium oxide

We have studied a nearly stoichiometric insulating Y$_{0.97(2)}$Cr$_{0.98(2)}$O$_{3.00(2)}$ single crystal by performing measurements of magnetization, heat capacity, and neutron diffraction. Albeit that the YCrO$_3$ compound behaviors like a soft ferromagnet with a coersive force of $\sim$ 0.05 T, there exist strong antiferromagnetic (AFM) interactions between Cr$^{3+}$ spins due to a strongly negative paramagnetic Curie-Weiss temperature, i.e., -433.2(6) K. The coexistence of ferromagnetism and antiferromagnetism may indicate a canted AFM structure. The AFM phase transition occurs at $T_\textrm{N} =$ 141.5(1) K, which increases to $T_\textrm{N}$(5T) = 144.5(1) K at 5 T. Within the accuracy of the present neuron-diffraction studies, we determine a G-type AFM structure with a propagation vector \textbf{k} = (1 1 0) and Cr$^{3+}$ spin directions along the crystallographic \emph{c} axis of the orthorhombic structure with space group \emph{Pnma} below $T_\textrm{N}$. At 12 K, the refined moment size is 2.45(6) $μ_\textrm{B}$, $\sim$ 82\% of the theoretical saturation value 3 $μ_\textrm{B}$. The Cr$^{3+}$ spin interactions are probably two-dimensional Ising like within the reciprocal (1 1 0) scattering plane. Below $T_\textrm{N}$, the lattice configuration (\emph{a}, \emph{b}, \emph{c}, and \emph{V}) deviates largely downward from the Gr$\ddot{\textrm{u}}$neisen law, displaying an anisotropic magnetostriction effect and a magnetoelastic effect. Especially, the sample contraction upon cooling is enhanced below the AFM transition temperature. There is evidence to suggest that the actual crystalline symmetry of YCrO$_3$ compound is probably lower than the currently assumed one. Additionally, we compared the $t_{2\textrm{g}}$ YCrO$_3$ and the $e_\textrm{g}$ La$_{7/8}$Sr$_{1/8}$MnO$_3$ single crystals for a further understanding of the reason for the possible symmetry lowering.

preprint2020arXiv

Super-Necking Crystal Growth and Structural and Magnetic Properties of SrTb$_2$O$_4$ Single Crystals

We report on single-crystal growths of the SrTb$_2$O$_4$ compound by a super-necking technique with a laser-floating-zone furnace and study the stoichiometry, growth mode, and structural and magnetic properties by scanning electronic microscopy, neutron Laue, X-ray powder diffraction, and the physical property measurement system. We optimized the growth parameters, mainly the growth speed, atmosphere, and the addition of a Tb$_4$O$_7$ raw material. Neutron Laue diffraction displays the characteristic feature of a single crystal. Our study reveals an atomic ratio of Sr:Tb $ = 0.97(2){:}2.00(1)$ and a possible layer by layer crystal growth mode. Our X-ray powder diffraction study determines the crystal structure, lattice constants and atomic positions. The paramagnetic (PM) Curie--Weiss (CW) temperature $θ_{\texttt{CW}} =$ 5.00(4) K, and the effective PM moment $M^{\texttt{eff}}_{\texttt{mea}} =$ 10.97(1) $μ_\texttt{B}$ per Tb$^{3+}$ ion. The data of magnetization versus temperature can be divided into three regimes, showing a coexistence of antiferromagnetic and ferromagnetic interactions. This probably leads to the magnetic frustration in the SrTb$_2$O$_4$ compound. The magnetization at 2 K and 14 T originates from both the Tb1 and Tb2 sites and is strongly frustrated with an expected saturation field at $\sim$41.5 T, displaying an intricate phase diagram with three ranges.

preprint2020arXiv

Vision at A Glance: Interplay between Fine and Coarse Information Processing Pathways

Object recognition is often viewed as a feedforward, bottom-up process in machine learning, but in real neural systems, object recognition is a complicated process which involves the interplay between two signal pathways. One is the parvocellular pathway (P-pathway), which is slow and extracts fine features of objects; the other is the magnocellular pathway (M-pathway), which is fast and extracts coarse features of objects. It has been suggested that the interplay between the two pathways endows the neural system with the capacity of processing visual information rapidly, adaptively, and robustly. However, the underlying computational mechanisms remain largely unknown. In this study, we build a computational model to elucidate the computational advantages associated with the interactions between two pathways. Our model consists of two convolution neural networks: one mimics the P-pathway, referred to as FineNet, which is deep, has small-size kernels, and receives detailed visual inputs; the other mimics the M-pathway, referred to as CoarseNet, which is shallow, has large-size kernels, and receives low-pass filtered or binarized visual inputs. The two pathways interact with each other via a Restricted Boltzmann Machine. We find that: 1) FineNet can teach CoarseNet through imitation and improve its performance considerably; 2) CoarseNet can improve the noise robustness of FineNet through association; 3) the output of CoarseNet can serve as a cognitive bias to improve the performance of FineNet. We hope that this study will provide insight into understanding visual information processing and inspire the development of new object recognition architectures.

preprint2015arXiv

A Rich Spectrum of Neural Field Dynamics in the Presence of Short-Term Synaptic Depression

In continuous attractor neural networks (CANNs), spatially continuous information such as orientation, head direction, and spatial location is represented by Gaussian-like tuning curves that can be displaced continuously in the space of the preferred stimuli of the neurons. We investigate how short-term synaptic depression (STD) can reshape the intrinsic dynamics of the CANN model and its responses to a single static input. In particular, CANNs with STD can support various complex firing patterns and chaotic behaviors. These chaotic behaviors have the potential to encode various stimuli in the neuronal system.

preprint2015arXiv

Dynamics of Neural Networks with Continuous Attractors

We investigate the dynamics of continuous attractor neural networks (CANNs). Due to the translational invariance of their neuronal interactions, CANNs can hold a continuous family of stationary states. We systematically explore how their neutral stability facilitates the tracking performance of a CANN, which is believed to have wide applications in brain functions. We develop a perturbative approach that utilizes the dominant movement of the network stationary states in the state space. We quantify the distortions of the bump shape during tracking, and study their effects on the tracking performance. Results are obtained on the maximum speed for a moving stimulus to be trackable, and the reaction time to catch up an abrupt change in stimulus.

preprint2015arXiv

Fluctuation-response Relation Unifies Dynamical Behaviors in Neural Fields

Anticipation is a strategy used by neural fields to compensate for transmission and processing delays during the tracking of dynamical information, and can be achieved by slow, localized, inhibitory feedback mechanisms such as short-term synaptic depression, spike-frequency adaptation, or inhibitory feedback from other layers. Based on the translational symmetry of the mobile network states, we derive generic fluctuation-response relations, providing unified predictions that link their tracking behaviors in the presence of external stimuli to the intrinsic dynamics of the neural fields in their absence.

preprint2014arXiv

Nematic and spin-charge orders driven by hole-doping a charge-transfer insulator

Recent experimental discoveries have brought a diverse set of broken symmetry states to the center stage of research on cuprate superconductors. Here, we focus on a thematic understanding of the diverse phenomenology by exploring a strong-coupling mechanism of symmetry breaking driven by frustration of antiferromagnetic order. We achieve this through a variational study of a three-band model of the CuO$_2$ plane with Kondo-type exchange couplings between doped oxygen holes and classical copper spins. Two main findings from this strong-coupling multi-band perspective are 1) that the symmetry hierarchy of spin stripe, charge stripe, intra-unit-cell nematic order and isotropic phases are all accessible microscopically within the model, 2) many symmetry-breaking patterns compete with energy differences within a few meV per Cu atom to produce a rich phase diagram. These results indicate that the diverse phenomenology of broken-symmetry states in hole-doped antiferromagnetic charge-transfer insulators may indeed arise from hole-doped frustration of antiferromagnetism.

preprint2014arXiv

Solving the inverse problem of noise-driven dynamic networks

Nowadays massive amount of data are available for analysis in natural and social systems. Inferring system structures from the data, i.e., the inverse problem, has become one of the central issues in many disciplines and interdisciplinary studies. In this Letter, we study the inverse problem of stochastic dynamic complex networks. We derive analytically a simple and universal inference formula called double correlation matrix (DCM) method. Numerical simulations confirm that the DCM method can accurately depict both network structures and noise correlations by using available kinetic data only. This inference performance was never regarded possible by theoretical derivation, numerical computation and experimental design.

preprint2013arXiv

Axion response in Weyl semimetals

Weyl semimetal is a new phase of matter that provides the first solid state realization of chiral Weyl fermions. Most of its unique physics is a consequence of chiral anomaly, namely nonconservation of the number of particles of a given chirality. Mathematically, this is expressed in the appearance of the so called $θ$-term in the action of the electromagnetic field, when the Weyl fermions are integrated out. Recently, however, it has been suggested that the analogy between the chiral fermions of quantum field theory with unbounded linear dispersion, and their solid state realization with a dispersion naturally bounded by the bandwidth and crystal momentum defined only within the first Brillouin zone, holds only in a restricted sense, with parts of the $θ$-term absent. Here we demonstrate that this is not the case. We explicitly derive the $θ$-term for a microscopic model of a Weyl semimetal by integrating out fermions coupled to electromagnetic field, and show that the result has exactly the same form as in the case of relativistic chiral fermions.

preprint2013arXiv

Non-Abelian toplogical superconductors from topological semimetals and related systems under superconducting proximity effect

Non-Abelian toplogical superconductors are characterized by the existence of {zero-energy} Majorana fermions bound in the quantized vortices. This is a consequence of the nontrivial bulk topology characterized by an {\em odd} Chern number. It is found that in topological semimetals with a single two-bands crossing point all the gapped superconductors are non-Abelian ones. Such a property is generalized to related but more generic systems which will be useful in the search of non-Abelian superconductors and Majorana fermions.

preprint2013arXiv

Resolution enhancement in neural networks with dynamical synapses

Conventionally, information is represented by spike rates in the neural system. Here, we consider the ability of temporally modulated activities in neuronal networks to carry information extra to spike rates. These temporal modulations, commonly known as population spikes, are due to the presence of synaptic depression in a neuronal network model. We discuss its relevance to an experiment on transparent motions in macaque monkeys by Treue et al. in 2000. They found that if the moving directions of objects are too close, the firing rate profile will be very similar to that with one direction. As the difference in the moving directions of objects is large enough, the neuronal system would respond in such a way that the network enhances the resolution in the moving directions of the objects. In this paper, we propose that this behavior can be reproduced by neural networks with dynamical synapses when there are multiple external inputs. We will demonstrate how resolution enhancement can be achieved, and discuss the conditions under which temporally modulated activities are able to enhance information processing performances in general.

preprint2012arXiv

Dynamical Synapses Enhance Neural Information Processing: Gracefulness, Accuracy and Mobility

Experimental data have revealed that neuronal connection efficacy exhibits two forms of short-term plasticity, namely, short-term depression (STD) and short-term facilitation (STF). They have time constants residing between fast neural signaling and rapid learning, and may serve as substrates for neural systems manipulating temporal information on relevant time scales. The present study investigates the impact of STD and STF on the dynamics of continuous attractor neural networks (CANNs) and their potential roles in neural information processing. We find that STD endows the network with slow-decaying plateau behaviors-the network that is initially being stimulated to an active state decays to a silent state very slowly on the time scale of STD rather than on the time scale of neural signaling. This provides a mechanism for neural systems to hold sensory memory easily and shut off persistent activities gracefully. With STF, we find that the network can hold a memory trace of external inputs in the facilitated neuronal interactions, which provides a way to stabilize the network response to noisy inputs, leading to improved accuracy in population decoding. Furthermore, we find that STD increases the mobility of the network states. The increased mobility enhances the tracking performance of the network in response to time-varying stimuli, leading to anticipative neural responses. In general, we find that STD and STP tend to have opposite effects on network dynamics and complementary computational advantages, suggesting that the brain may employ a strategy of weighting them differentially depending on the computational purpose.

preprint2012arXiv

Graphene under spatially varying external potentials: Landau levels, magnetotransport, and topological modes

Superlattices (SLs) in monolayer and bilayer graphene, formed by spatially periodic potential variations, lead to a modified bandstructure with extra finite-energy and zero-energy Dirac fermions with tunable anisotropic velocities. We theoretically show that transport in a weak perpendicular (orbital) magnetic field allows one to not only probe the number of emergent Dirac points but also yields further information about their dispersion. or monolayer graphene, we find that a moderate magnetic field can lead to a strong reversal of the transport anisotropy imposed by the SL potential, an effect which arises due to the SL induced dispersion of the zero energy Landau levels. This effect may find useful applications in switching or other devices. For bilayer graphene, we discuss the structure of Landau level wave functions and local density of states in the presence of a uniform bias, as well as in the presence of a kink in the bias which leads to topologically bound `edge states'. We consider implications of these results for scanning tunneling spectroscopy measurements, valley filtering, and impurity induced breakdown of the quantum Hall effect in bilayer graphene.

preprint2012arXiv

Graphene: Kinks, Superlattices, Landau levels, and Magnetotransport

We review recent work on superlattices in monolayer and bilayer graphene. We highlight the role of the quasiparticle chirality in generating new Dirac fermion modes with tunable anisotropic velocities in one dimensional (1D) superlattices in both monolayer and bilayer graphene. We discuss the structure of the Landau levels and magnetotransport in such superlattices over a wide range of perpendicular (orbital) magnetic fields. In monolayer graphene, we show that an orbital magnetic field can reverse the anisotropy of the transport imposed by the superlattice potential, suggesting possible switching-type device applications. We also consider topological modes localized at a kink in an electric field applied perpendicular to bilayer graphene, and show how interactions convert these modes into a two-band Luttinger liquid with tunable Luttinger parameters. The band structures of electric field superlattices in bilayer graphene (with or without a magnetic field) are shown to arise naturally from a coupled array of such topological modes. We briefly review some bandstructure results for 2D superlattices. We conclude with a discussion of recent tunneling and transport experiments and point out open issues.

preprint2012arXiv

Weyl semimetal with broken time reversal and inversion symmetries

Weyl semimetal is a new topological state of matter, characterized by the presence of nondegenerate band-touching nodes, separated in momentum space, in its bandstructure. Here we discuss a particular realization of a Weyl semimetal: a superlattice heterostructure, made of alternating layers of topological insulator (TI) and normal insulator (NI) material, introduced by one of us before. The Weyl node splitting is achieved most easily in this system by breaking time-reversal (TR) symmetry, for example by magnetic doping. If, however, spatial inversion (I) symmetry remains, the Weyl nodes will occur at the same energy, making it possible to align the Fermi energy simultaneously with both nodes. The goal of this work is to explore the consequences of breaking the I symmetry in this system. We demonstrate that, while this generally moves the Weyl nodes to different energies, thus eliminating nodal semimetal and producing a state with electron and hole Fermi surfaces, the topological properties of the Weyl semimetal state, i.e. the chiral edge states and the corresponding Hall conductivity, survive for moderate I symmetry breaking. Moreover, we demonstrate that a new topological phenomenon arises in this case, if an external magnetic field along the growth direction of the heterostructure is applied. Namely, this leads to an equilibrium dissipationless current, flowing along the direction of the field, whose magnitude is proportional to the energy difference between the Weyl nodes and to the magnetic field, with a universal coefficient, given by a combination of fundamental constants.

preprint2011arXiv

Band structures of bilayer graphene superlattices

We formulate a low energy effective Hamiltonian to study superlattices in bilayer graphene (BLG) using a minimal model which supports quadratic band touching points. We show that a one dimensional (1D) periodic modulation of the chemical potential or the electric field perpendicular to the layers leads to the generation of zero energy anisotropic massless Dirac fermions and finite energy Dirac points with tunable velocities. The electric field superlattice maps onto a coupled chain model comprised of 'topological' edge modes. 2D superlattice modulations are shown to lead to gaps on the mini-Brillouin zone boundary but do not, for certain symmetries, gap out the quadratic band touching point. Such potential variations, induced by impurities and rippling in biased BLG, could lead to subgap modes which are argued to be relevant to understanding transport measurements.

preprint2011arXiv

Spin Susceptibility and Helical Magnetic Orders at the Edges/Surfaces of Topological Insulators Due to Fermi Surface Nesting

We study spin susceptibility and magnetic order at the edges/surfaces of two-dimensional and three-dimensional topological insulators when the Fermi surface is nested. We find that due to spin-momentum locking as well as time-reversal symmetry, spin susceptibility at the nesting wavevector has a strong {\em helical} feature. It follows then, a {\em helical} spin density wave (SDW) state emerges at low temperature due to Fermi surface nesting. The helical feature of spin susceptibility also has profound impact on the magnetic order in magnetically doped surface of three dimensional topological insulators. In such system, from the mean field Zener theory, we predict a {\em helical} magnetic order.

preprint2010arXiv

Attractor Dynamics with Synaptic Depression

Neuronal connection weights exhibit short-term depression (STD). The present study investigates the impact of STD on the dynamics of a continuous attractor neural network (CANN) and its potential roles in neural information processing. We find that the network with STD can generate both static and traveling bumps, and STD enhances the performance of the network in tracking external inputs. In particular, we find that STD endows the network with slow-decaying plateau behaviors, namely, the network being initially stimulated to an active state will decay to silence very slowly in the time scale of STD rather than that of neural signaling. We argue that this provides a mechanism for neural systems to hold short-term memory easily and shut off persistent activities naturally.

preprint2010arXiv

Larkin-Ovchinnikov-Fulde-Ferrell phase in the superconductor (TMTSF)2ClO4: Theory versus experiment

We consider a formation of the Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) phase in a quasi-one-dimensional (Q1D) conductor in a magnetic field, parallel to its conducting chains, where we take into account both the paramagnetic spin-splitting and orbital destructive effects against superconductivity. We show that, due to a relative weakness of the orbital effects in a Q1D case, the LOFF phase appears in (TMTSF)$_2$ClO$_4$ superconductor for real values of its Q1D band parameters. We compare our theoretical calculations with the recent experimental data by Y. Maeno's group [S. Yonezawa et al., Phys. Rev. Lett. \textbf{100}, 117002 (2008)] and show that there is a good qualitative and quantitative agreement between the theory and experimental data.

preprint2010arXiv

Unification Theory of Angular Magnetoresistance Oscillations in Quasi-One-Dimensional Conductors

We present a unification theory of angular magnetoresistance oscillations, experimentally observed in quasi-one-dimensional organic conductors, by solving the Boltzmann kinetic equation in the extended Brillouin zone. We find that, at commensurate directions of a magnetic field, resistivity exhibits strong minima. In two limiting cases, our general solution reduces to the results, previously obtained for the Lebed Magic Angles and Lee-Naughton-Lebed oscillations. We demonstrate that our theoretical results are in good qualitative and quantitative agreement with the existing measurements of resistivity in (TMTSF)$_2$ClO$_4$ conductor.

preprint2009arXiv

A Moving Bump in a Continuous Manifold: A Comprehensive Study of the Tracking Dynamics of Continuous Attractor Neural Networks

Understanding how the dynamics of a neural network is shaped by the network structure, and consequently how the network structure facilitates the functions implemented by the neural system, is at the core of using mathematical models to elucidate brain functions. This study investigates the tracking dynamics of continuous attractor neural networks (CANNs). Due to the translational invariance of neuronal recurrent interactions, CANNs can hold a continuous family of stationary states. They form a continuous manifold in which the neural system is neutrally stable. We systematically explore how this property facilitates the tracking performance of a CANN, which is believed to have clear correspondence with brain functions. By using the wave functions of the quantum harmonic oscillator as the basis, we demonstrate how the dynamics of a CANN is decomposed into different motion modes, corresponding to distortions in the amplitude, position, width or skewness of the network state. We then develop a perturbative approach that utilizes the dominating movement of the network's stationary states in the state space. This method allows us to approximate the network dynamics up to an arbitrary accuracy depending on the order of perturbation used. We quantify the distortions of a Gaussian bump during tracking, and study their effects on the tracking performance. Results are obtained on the maximum speed for a moving stimulus to be trackable and the reaction time for the network to catch up with an abrupt change in the stimulus.

preprint2009arXiv

Soliton Wall Superlattice Charge-Density-Wave Phase in Quasi-One-Dimensional Conductor (Per)$_2$Pt(mnt)$_2$

We demonstrate that the Pauli spin-splitting effects in a magnetic field improve nesting properties of a realistic quasi-one-dimensional electron spectrum. As a result, a high resistance Peierls charge-density-wave (CDW) phase is stabilized in high enough magnetic fields in (Per)$_2$Pt(mnt)$_2$ conductor. We show that, in low and very high magnetic fields, the Pauli spin-splitting effects lead to a stabilization of a soliton wall superlattice (SWS) CDW phase, which is characterized by periodically arranged soliton and anti-soliton walls. We suggest experimental studies of the predicted first order phase transitions between the Peierls and SWS phases to discover a unique SWS phase. It is important that, in the absence of a magnetic field and in a limit of very high magnetic fields, the suggested model is equivalent to the exactly solvable model of Brazovskii, Dzyaloshinskii, and Kirova.

preprint2009arXiv

Tracking Dynamics of Two-Dimensional Continuous Attractor Neural Networks

We introduce an analytically solvable model of two-dimensional continuous attractor neural networks (CANNs). The synaptic input and the neuronal response form Gaussian bumps in the absence of external stimuli, and enable the network to track external stimuli by its translational displacement in the two-dimensional space. Basis functions of the two-dimensional quantum harmonic oscillator in polar coordinates are introduced to describe the distortion modes of the Gaussian bump. The perturbative method is applied to analyze its dynamics. Testing the method by considering the network behavior when the external stimulus abruptly changes its position, we obtain results of the reaction time and the amplitudes of various distortion modes, with excellent agreement with simulation results.