Finite size scaling of the spontaneous symmetry breaking model of X-chromosome inactivation

X-Chromosome inactivation is the process whereby one of the two X-chromosomes in female cells is silenced to prevent the cell producing too much of any X-linked proteins and RNA. The proposed blocking-factor mechanism of X-inactivation is not well understood and hence is the subject of much current research. In this paper we investigated the nature of the phase transition predicted to exist in the spontaneous symmetry breaking model of X-inactivation proposed by Nicodemi and Prisco [Mario Nicodemi, Antonella Prisco, Symmetry breaking model for x-chromosome inactivation, Phs. Rev. Lett. 98 (2007) 108104]. Finite size effects were investigated by using an on lattice Monte Carlo simulation. From the scaling it is concluded that the transition is in general abrupt. The critical temperature of the system was determined to be 1.68±0.01E₀/k_B in the thermodynamic limit when the concentration C=0.025 blocking-factors per lattice site.     

Effects of symmetry breaking in finite quantum systems

The review considers the peculiarities of symmetry breaking and symmetry transformations and the related physical effects in finite quantum systems. Some types of symmetry in finite systems can be broken only asymptotically. However, with a sufficiently large number of particles, crossover transitions become sharp, so that symmetry breaking happens similarly to that in macroscopic systems. This concerns, in particular, global gauge symmetry breaking, related to Bose–Einstein condensation and superconductivity, or isotropy breaking, related to the generation of quantum vortices, and the stratification in multicomponent mixtures. A special type of symmetry transformation, characteristic only for finite systems, is the change of shape symmetry. These phenomena are illustrated by the examples of several typical mesoscopic systems, such as trapped atoms, quantum dots, atomic nuclei, and metallic grains. The specific features of the review are: (i) the emphasis on the peculiarities of the symmetry breaking in finite mesoscopic systems; (ii) the analysis of common properties of physically different finite quantum systems; (iii) the manifestations of symmetry breaking in the spectra of collective excitations in finite quantum systems. The analysis of these features allows for the better understanding of the intimate relation between the type of symmetry and other physical properties of quantum systems. This also makes it possible to predict new effects by employing the analogies between finite quantum systems of different physical nature.     

Dynamical symmetry breaking of lambda- and vee-type three-level systems on quantization of the field modes

We develop a scheme to construct the Hamiltonians of the lambda-, vee- and cascade-type three-level configurations using the generators of SU(3) group. It turns out that this approach provides a well-defined selection rule to give different Hamiltonians for each configuration. The lambda- and vee-type configurations are exactly solved with different initial conditions while taking the two-mode classical and quantized fields. For the classical field, it is shown that the Rabi oscillation of the lambda model is similar to that of the vee model and the dynamics of the vee model can be recovered from lambda model and vice versa simply by inversion. We then proceed to solve the quantized version of both models by introducing a novel Euler matrix formalism. It is shown that this dynamical symmetry exhibited in the Rabi oscillation of two configurations for the semiclassical models is completely destroyed on quantization of the field modes. The symmetry can be restored within the quantized models when both field modes are in the coherent states with large average photon number which is depicted through the collapse and revival of the Rabi oscillations.      

Chiral symmetry breaking: (i) limited enantioselectivity and (ii) mutual inhibition

The stability properties of models of spontaneous mirror symmetry breaking in chemistry are characterized geometrically and analytically. The first model accounts for limited enantioselectivity, while the second is the Frank model in which the mutual inhibition reaction is allowed to be reversible. Both models include the autocatalytic amplification of units of the same chirality as well as chiral inhibition, in unison regarded to be the elementary requirements for achieving symmetry breaking of initially racemic mixtures. When the control parameter for each model falls below its corresponding critical value, the racemic state becomes unstable, and chiral amplification results. These final stable chiral states are not homochiral: mirror symmetry is broken, but the breaking is not absolute. Numerical solutions are obtained in two space dimensions.     

Chiral symmetry breaking in FAXY model with roughness exponent method

Chiral symmetry breaking in the frustrated antiferromagnetic XY (FAXY) model on a two-dimensional triangular lattice is investigated. The roughness exponent method is used instead of the standard Metropolis method. Spin configurations are mapped to adatoms on a solid-on-solid (SOS) growth model. Statistical properties of the grown film surface are analyzed. Results show that the chiral transition can be indicated by the sharp increase in the roughness of the film morphologies. The critical temperature at the transition can be identified either by the peak of the noise-reduced interface width (W^∗$W^{\ast }$) or the peak of the noise-reduced roughness exponent (α^∗${\alpha }^{\ast }$). The critical temperature and exponent (ν$\nu$) obtained here are consistent with those obtained from conventional methods.     

A numerical study of SU(3) charge-two monopoles with minimal symmetry breaking

Charge-two SU(3) monopoles with minimal symmetry breaking can be generated via Nahm's equations. This paper investigates the detailed structure of such monopoles, through explicit calculation of the energy density, and the norm and discriminant of the Higgs field. Monopoles may be classified according to the maxima and minima of these quantities.     

Lattice symmetry breaking in cuprate superconductors: stripes,nematics, and superconductivity

This article gives an overview of both theoretical and experimental developments concerning states with lattice symmetry breaking in the cuprate high-temperature superconductors. Recent experiments have provided evidence for states with broken rotation as well as translation symmetry, and will be discussed in terms of nematic and stripe physics. Of particular importance here are results obtained using the techniques of neutron and X-ray scattering and scanning tunnelling spectroscopy. Ideas on the origin of lattice-symmetry-broken states will be reviewed, and effective models accounting for various experimentally observed phenomena will be summarized. These include both weak-coupling and strong-coupling approaches, with a discussion of their distinctions and connections. The collected experimental data indicate that the tendency toward uni-directional stripe-like ordering is common to underdoped cuprates, but becomes weaker with increasing number of adjacent CuO₂ layers.     

Symmetry protected topological phases in spin-1 ladders and their phase transitions

We study two-legged spin-1 ladder systems with D₂×σ$D_2\times \sigma$ symmetry group, where D₂$D_2$ is discrete spin rotational symmetry and σ$\sigma$ means interchain reflection symmetry. The system has one trivial phase and seven nontrivial symmetry protected topological (SPT) phases. We construct Hamiltonians to realize all of these SPT phases and study the phase transitions between them. Our numerical results indicate that there is no direct continuous transition between any two SPT phases we studied. We interpret our results via topological nonlinear sigma model effective field theory, and further conjecture that generally there is no direct continuous transition between two SPT phases in one dimension if the symmetry group is discrete at all length scales.     

Symmetry breaking and finite-size effects in quantum many-body systems

We consider a quantum many-body system on a lattice which exhibits a spontaneous symmetry breaking in its infinite-volume ground states, but in which the corresponding order operator does not commute with the Hamiltonian. Typical examples are the Heisenberg antiferromagnet with a Néel order and the Hubbard model with a (superconducting) off-diagonal long-range order. In the corresponding finite system, the symmetry breaking is usually obscured by quantum fluctuation and one gets a symmetric ground state with a long-range order. In such a situation, Horsch and von der Linden proved that the finite system has a low-lying eigenstate whose excitation energy is not more than of orderN ^–1, whereN denotes the number of sites in the lattice. Here we study the situation where the broken symmetry is a continuous one. For a particular set of states (which are orthogonal to the ground state and with each other), we prove bounds for their energy expectation values. The bounds establish that there exist ever-increasing numbers of low-lying eigenstates whose excitation energies are bounded by a constant timesN ^–1. A crucial feature of the particular low-lying states we consider is that they can be regarded as finite-volume counterparts of the infinite-volume ground states. By forming linear combinations of these low-lying states and the (finite-volume) ground state and by taking infinite-volume limits, we construct infinite-volume ground states with explicit symmetry breaking. We conjecture that these infinite-volume ground states are ergodic, i.e., physically natural. Our general theorems not only shed light on the nature of symmetry breaking in quantum many-body systems, but also provide indispensable information for numerical approaches to these systems. We also discuss applications of our general results to a variety of interesting examples. The present paper is intended to be accessible to readers without background in mathematical approaches to quantum many-body systems.     

Confinement and dynamical chiral symmetry breaking in a non-perturbative renormalizable quark model

Inspired by the construction of the Gribov–Zwanziger action in the Landau gauge, we introduce a quark model exhibiting both confinement and chiral symmetry aspects. An important feature is the incorporation of spontaneous chiral symmetry breaking in a renormalizable fashion. The quark propagator in the condensed vacuum turns out to be of a confining type. Besides a real pole, it exhibits complex conjugate poles. The resulting spectral form is explicitly shown to violate positivity, indicative of its unphysical character. Moreover, the ensuing quark mass function fits well to existing lattice data. To further validate the physical nature of the model, we identify a massless pseudoscalar (i.e. a pion) in the chiral limit and present estimates for the ρ$\rho$ meson mass and decay constant.     

Temperature calibration for high-temperature MAS NMR to 913 K: 63Cu MAS NMR of CuBr and CuI, and 23Na MAS NMR of NaNbO3

The solid-state phase transitions of CuBr, CuI and NaNbO₃ can be readily observed using ⁶³Cu and ²³Na high-temperature magic-angle spinning nuclear magnetic resonance spectroscopy. Temperature has large, linear effects on the peak maximum of ⁶³Cu in each solid phase of CuBr and CuI, and there is large jump in shift across each phase transition. The ²³Na MAS NMR peak intensities and the line widths in NaNbO₃ also clearly show its high-temperature transition to the cubic phase. These data can be used to calibrate high-temperature MAS NMR probes up to 913 K, which is two hundred degrees higher than the commonly-used temperature calibration based on the chemical shift of ²⁰⁷Pb in Pb(NO₃)₂.     

Fermionic zero modes for dyons and chiral symmetry breaking in QCD

Dyonic classical solutions of Yang-Mills theory are considered and the complete set of fermionic zero modes of these solutions are studied. Representing the QCD vacuum as a gas of dyons, one obtains chiral symmetry breaking due to zero modes similarly to the case of instantonic vacuum.     

The breaking of O(6) symmetry in 118Xe and 120Xe

The spectra of the isotopes of xenon are analysed from the point of view of O(6) symmetry breaking. It is pointed out that the excitation energies of the states 0 ₃ ⁺ can be used in detecting breaking of the symmetry. The nature of symmetry breaking in ¹¹⁸Xe and ¹²⁰Xe is indicated.     

Lateral predictive coding revisited: internal model,symmetry breaking,and response time

Predictive coding is a promising theoretical framework in neuroscience for understanding information transmission and perception. It posits that the brain perceives the external world through internal models and updates these models under the guidance of prediction errors. Previous studies on predictive coding emphasized top-down feedback interactions in hierarchical multilayered networks but largely ignored lateral recurrent interactions. We perform analytical and numerical investigations in this work on the effects of single-layer lateral interactions. We consider a simple predictive response dynamics and run it on the MNIST dataset of hand-written digits. We find that learning will generally break the interaction symmetry between peer neurons, and that high input correlation between two neurons does not necessarily bring strong direct interactions between them. The optimized network responds to familiar input signals much faster than to novel or random inputs, and it significantly reduces the correlations between the output states of pairs of neurons.     

NMR imaging in human pregnancy: A preliminary study

In an effort to demonstrate the potential of nuclear magnetic resonance imaging (NMR) in the management of pregnancy, 15 patients in the first trimester and one in the third trimester of pregnancy have been investigated in the Aberdeen University NMR imager. Simple measurements of biparietal diameter and crown-rump length were made from both the NMR images and the ultrasound images on the same day, with good correlation between the two. The NMR data was displayed as inversion recovery, calculated T₁, proton density and S₁–S₂ images. The proton density and S₁–S₂ images were found to be the most useful for the demonstration of the fetus and for discriminating between placenta and uterus. The calculated T₁ data provided accurate quantification of the proton-spin lattice relaxation times of the different tissues, indicating that this measurement may be of use in the study of fetal brain development and placental function. The inversion recovery images showed poor tissue discrimination and were found to be of limited value. The unique information available using NMR and the non-invasive nature of the technique indicated that it should provide a useful method for the investigation of both fetal development and placental function in addition to making basic measurements of fetal size.     

低温诱导桑蚕体内腺体相行为的高分辨^13C固体核磁共振研究

为什么蚕在常温常压水溶液条件下即能纺出力学性能优异的蚕丝纤维, 一直是科学家们感兴趣的问题. 在过去的几十年, 人们曾用多种表征手段, 如双折射、扫描电镜、原子力显微镜和电子散射等, 在界观尺度下对蚕在吐丝过程中腺体的相行为进行研究. 发现腺体在靠近吐丝口时呈液晶态, 并认为这是导致蚕丝力学性能的重要因素. 本文则在分子水平尺度下利用核磁共振方法, 对五龄蚕活体在常温和6 ℃下存储数天后解剖的腺体进行研究. 经对化学位移及其线型的各向异性分析发现, 当将体内腺体沿吐丝方向分为3部, 即后部、中部及靠近吐丝口的前部时, 常温下, 腺体后部和中后部分子呈无规线团, 而腺体中中部、中前部和前部分子呈液晶态. 6 ℃时, 中后部分子亦呈液晶态, 前部分子排列则各向异性更大, 说明更为有序. 这种液晶态呈分形结构, 在小于纳米尺度下为无规线团, 大于纳米尺度呈有序排列. 这表明, 降温过程可使呈无规线团的丝素蛋白分子转变为液晶态, 其效果如同蚕在吐丝过程中对其腺体施加的剪切应力. 该结果对于人们探索人工合成高性能类丝素纤维的纺丝工艺和条件将有启发和指导作用.     

Spontaneous breaking of the BRST symmetry in the presence of the Gribov horizon: Renormalizability

An all orders algebraic proof of the multiplicative renormalizability of the novel formulation of the Gribov–Zwanziger action proposed in Dudal (2012) [39], and allowing for an exact but spontaneously broken BRST symmetry, is provided.     

低温诱导桑蚕体内腺体相行为的高分辨13C固体核磁共振研究

为什么蚕在常温常压水溶液条件下即能纺出力学性能优异的蚕丝纤维,一直是科学家们感兴趣的问题. 在过去的几十年,人们曾用多种表征手段,如双折射、扫描电镜、原子力显微镜和电子散射等,在界观尺度下对蚕在吐丝过程中腺体的相行为进行研究. 发现腺体在靠近吐丝口时呈液晶态,并认为这是导致蚕丝力学性能的重要因素. 本文则在分子水平尺度下利用核磁共振方法, 对五龄蚕活体在常温和6 ℃下存储数天后解剖的腺体进行研究. 经对化学位移及其线型的各向异性分析发现,当将体内腺体沿吐丝方向分为3部,即后部、中部及靠近吐丝口的前部时,常温下,腺体后部和中后部分子呈无规线团,而腺体中中部、中前部和前部分子呈液晶态. 6 ℃时, 中后部分子亦呈液晶态,前部分子排列则各向异性更大,说明更为有序. 这种液晶态呈分形结构,在小于纳米尺度下为无规线团,大于纳米尺度呈有序排列. 这表明,降温过程可使呈无规线团的丝素蛋白分子转变为液晶态,其效果如同蚕在吐丝过程中对其腺体施加的剪切应力. 该结果对于人们探索人工合成高性能类丝素纤维的纺丝工艺和条件将有启发和指导作用.      

Solid-state 87Rb NMR study in powdered RbMnCl3

Structural phase transition at 290 K and the implication on the intermediate phase above 290 K in powdered RbMnCl₃ are observed by using a solid-state ⁸⁷Rb NMR spectroscopy. Quadrupole coupling constants (e²qQ/h), the asymmetry parameters (η), and the relative peak intensities for two physically nonequivalent Rb sites, Rb(I) and Rb(II), are determined from nonlinear least-squares fits to the ⁸⁷Rb NMR powder patterns in the temperature range from 260 to 330 K. Quadrupole coupling constants and the asymmetry parameters are examined for the detection of the phase transition resulting in a significant structural change in the Rb(II) site. In addition, changes in the relative peak intensity between the Rb(I) and Rb(II) sites seem to suggest the existence of an anomalous intermediate phase, which is complemented by the differential scanning calorimetry and X-ray diffraction studies.